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# Called in the OrdinaryDiffEQ.__init; All `OrdinaryDiffEqAlgorithm`s have one function OrdinaryDiffEq.initialize!(integ, cache::GaussianODEFilterCache) if integ.opts.dense && !integ.alg.smooth error("To use `dense=true` you need to set `smooth=true`!") elseif !integ.opts.dense && integ.alg.smooth @warn "If you set dense=false for efficiency, you might also want to set smooth=false." end if !integ.opts.save_everystep && integ.alg.smooth error("If you do not save all values, you do not need to smooth!") end @assert integ.saveiter == 1 integ.kshortsize = 1 resize!(integ.k, integ.kshortsize) integ.k[1] = integ.u # Update the initial state to the known (given or computed with AD) initial values initial_update!(integ, cache, integ.alg.initialization) # These are necessary since the solution object is not 100% initialized by default OrdinaryDiffEq.copyat_or_push!(integ.sol.x_filt, integ.saveiter, cache.x) OrdinaryDiffEq.copyat_or_push!( integ.sol.pu, integ.saveiter, mul!(cache.pu_tmp, cache.SolProj, cache.x), ) return nothing end """Perform a step Not necessarily successful! For that, see `step!(integ)`. Basically consists of the following steps - Coordinate change / Predonditioning - Prediction step - Measurement: Evaluate f and Jf; Build z, S, H - Calibration; Adjust prediction / measurement covs if the diffusion model "dynamic" - Update step - Error estimation - Undo the coordinate change / Predonditioning """ function OrdinaryDiffEq.perform_step!( integ, cache::GaussianODEFilterCache, repeat_step=false, ) @unpack t, dt = integ @unpack d, SolProj = integ.cache @unpack x, x_pred, u_pred, x_filt, u_filt, err_tmp = integ.cache @unpack x_tmp, x_tmp2 = integ.cache @unpack A, Q, Ah, Qh = integ.cache make_preconditioners!(cache, dt) @unpack P, PI = integ.cache tnew = t + dt # Build the correct matrices @. Ah = PI.diag .* A .* P.diag' X_A_Xt!(Qh, Q, PI) if isdynamic(cache.diffusionmodel) # Calibrate, then predict cov # Predict predict_mean!(x_pred, x, Ah) mul!(view(u_pred, :), SolProj, x_pred.μ) # Measure evaluate_ode!(integ, x_pred, tnew) # Estimate diffusion cache.local_diffusion, cache.global_diffusion = estimate_diffusion(cache.diffusionmodel, integ) # Adjust prediction and measurement predict_cov!(x_pred, x, Ah, Qh, cache.C1, cache.global_diffusion) # Compute measurement covariance only now compute_measurement_covariance!(cache) else predict_mean!(x_pred, x, Ah) predict_cov!(x_pred, x, Ah, Qh, cache.C1) mul!(view(u_pred, :), SolProj, x_pred.μ) evaluate_ode!(integ, x_pred, tnew) compute_measurement_covariance!(cache) cache.local_diffusion, cache.global_diffusion = estimate_diffusion(cache.diffusionmodel, integ) end # Likelihood # cache.log_likelihood = logpdf(cache.measurement, zeros(d)) # Update x_filt = update!(integ, x_pred) # Estimate error for adaptive steps - can already be done before filtering if integ.opts.adaptive err_est_unscaled = estimate_errors(cache) if integ.f isa DynamicalODEFunction # second-order ODE DiffEqBase.calculate_residuals!( err_tmp, dt * err_est_unscaled, integ.u[1, :], u_pred[1, :], integ.opts.abstol, integ.opts.reltol, integ.opts.internalnorm, t, ) else # regular first-order ODE DiffEqBase.calculate_residuals!( err_tmp, dt * err_est_unscaled, integ.u, u_pred, integ.opts.abstol, integ.opts.reltol, integ.opts.internalnorm, t, ) end integ.EEst = integ.opts.internalnorm(err_tmp, t) # scalar end # If the step gets rejected, we don't even need to perform an update! reject = integ.opts.adaptive && integ.EEst >= one(integ.EEst) if !reject # Save into u_filt and integ.u mul!(view(u_filt, :), SolProj, x_filt.μ) integ.u .= u_filt # Advance the state here copy!(integ.cache.x, integ.cache.x_filt) integ.sol.log_likelihood += integ.cache.log_likelihood end end function evaluate_ode!( integ::OrdinaryDiffEq.ODEIntegrator{<:AbstractEK}, x_pred, t, second_order::Val{false}, ) @unpack f, p, dt, alg = integ @unpack u_pred, du, ddu, measurement, R, H = integ.cache @assert iszero(R) @unpack E0, E1, E2 = integ.cache z, S = measurement.μ, measurement.Σ # Mean _eval_f!(du, u_pred, p, t, f) integ.destats.nf += 1 # z .= MM*E1*x_pred.μ .- du if f.mass_matrix == I H .= E1 elseif f.mass_matrix isa UniformScaling H .= f.mass_matrix.λ .* E1 else _matmul!(H, f.mass_matrix, E1) end _matmul!(z, H, x_pred.μ) z .-= du[:] # If EK1, evaluate the Jacobian and adjust H if alg isa EK1 || alg isa IEKS u_lin = (alg isa IEKS && !isnothing(alg.linearize_at)) ? alg.linearize_at(t).μ : u_pred # Jacobian is computed either with the given jac, or ForwardDiff if !isnothing(f.jac) _eval_f_jac!(ddu, u_lin, p, t, f) elseif isinplace(f) ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_lin) integ.destats.nf += 1 else ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_lin) integ.destats.nf += 1 end integ.destats.njacs += 1 # _matmul!(H, f.mass_matrix, E1) # This is already the case (see above) _matmul!(H, ddu, E0, -1.0, 1.0) end return nothing end function evaluate_ode!( integ::OrdinaryDiffEq.ODEIntegrator{<:EK1FDB}, x_pred, t, second_order::Val{false}, ) @unpack f, p, dt, alg = integ @unpack d, u_pred, du, ddu, measurement, R, H = integ.cache @assert iszero(R) @unpack E0, E1, E2 = integ.cache z, S = measurement.μ, measurement.Σ (f.mass_matrix != I) && error("EK1FDB does not support mass-matrices right now") # Mean _eval_f!(du, u_pred, p, t, f) integ.destats.nf += 1 # z .= MM*E1*x_pred.μ .- du H1, H2 = view(H, 1:d, :), view(H, d+1:2d, :) z1, z2 = view(z, 1:d), view(z, d+1:2d) H1 .= E1 _matmul!(z1, H1, x_pred.μ) z1 .-= @view du[:] # If EK1, evaluate the Jacobian and adjust H u_lin = u_pred if !isnothing(f.jac) _eval_f_jac!(ddu, u_lin, p, t, f) elseif isinplace(f) ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_lin) integ.destats.nf += 1 else ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_lin) integ.destats.nf += 1 end integ.destats.njacs += 1 _matmul!(H1, ddu, E0, -1.0, 1.0) z2 .= (E2 * x_pred.μ .- ddu * du) if integ.alg.jac_quality == 1 # EK0-type approach H2 .= E2 elseif integ.alg.jac_quality == 2 H2 .= E2 - ddu * ddu * E0 elseif integ.alg.jac_quality == 3 _z2(m) = begin u_pred = E0 * m du = zeros(eltype(m), d) ddu = zeros(eltype(m), d, d) _eval_f!(du, u_pred, p, t, f) if !isnothing(f.jac) _eval_f_jac!(ddu, u_pred, p, t, f) elseif isinplace(f) ForwardDiff.jacobian!(ddu, (du, u) -> f(du, u, p, t), du, u_pred) # integ.destats.nf += 1 else ddu .= ForwardDiff.jacobian(u -> f(u, p, t), u_pred) # integ.destats.nf += 1 end # integ.destats.njacs += 1 return (E2 * m .- ddu * du) end H2 .= ForwardDiff.jacobian(_z2, x_pred.μ) else error("EK1FDB's `jac_quality` has to be in [1,2,3]") end return nothing end function evaluate_ode!( integ::OrdinaryDiffEq.ODEIntegrator{<:AbstractEK}, x_pred, t, second_order::Val{true}, ) @unpack f, p, dt, alg = integ @unpack d, u_pred, du, ddu, measurement, R, H = integ.cache @assert iszero(R) du2 = du @unpack E0, E1, E2 = integ.cache z, S = measurement.μ, measurement.Σ # Mean # _u_pred = E0 * x_pred.μ # _du_pred = E1 * x_pred.μ if isinplace(f) f.f1(du2, view(u_pred, 1:d), view(u_pred, d+1:2d), p, t) else du2 .= f.f1(view(u_pred, 1:d), view(u_pred, d+1:2d), p, t) end integ.destats.nf += 1 _matmul!(z, E2, x_pred.μ) z .-= @view du2[:] # Cov if alg isa EK1 (alg isa IEKS) && error("IEKS is currently not supported for SecondOrderODEProbems") if isinplace(f) H .= E2 J = ddu ForwardDiff.jacobian!( J, (du2, du_u) -> f.f1(du2, view(du_u, 1:d), view(du_u, d+1:2d), p, t), du2, u_pred, ) integ.destats.nf += 1 integ.destats.njacs += 1 _matmul!(H, J, integ.cache.SolProj, -1.0, 1.0) else J = ForwardDiff.jacobian( (du_u) -> f.f1(view(du_u, 1:d), view(du_u, d+1:2d), p, t), u_pred, ) integ.destats.nf += 1 integ.destats.njacs += 1 H .= E2 .- J * integ.cache.SolProj end end return measurement end evaluate_ode!(integ, x_pred, t) = evaluate_ode!(integ, x_pred, t, Val(integ.f isa DynamicalODEFunction)) # The following functions are just there to handle both IIP and OOP easily _eval_f!(du, u, p, t, f::AbstractODEFunction{true}) = f(du, u, p, t) _eval_f!(du, u, p, t, f::AbstractODEFunction{false}) = (du .= f(u, p, t)) _eval_f_jac!(ddu, u, p, t, f::AbstractODEFunction{true}) = f.jac(ddu, u, p, t) _eval_f_jac!(ddu, u, p, t, f::AbstractODEFunction{false}) = (ddu .= f.jac(u, p, t)) compute_measurement_covariance!(cache) = X_A_Xt!(cache.measurement.Σ, cache.x_pred.Σ, cache.H) function update!(integ, prediction) @unpack measurement, H, R, x_filt = integ.cache @unpack K1, K2, x_tmp2, m_tmp = integ.cache update!(x_filt, prediction, measurement, H, K1, x_tmp2.Σ.mat, m_tmp) return x_filt end function smooth_all!(integ) integ.sol.x_smooth = copy(integ.sol.x_filt) @unpack A, Q = integ.cache @unpack x_smooth, t, diffusions = integ.sol @unpack x_tmp, x_tmp2 = integ.cache x = x_smooth for i in length(x)-1:-1:1 dt = t[i+1] - t[i] if iszero(dt) copy!(x[i], x[i+1]) continue end make_preconditioners!(integ.cache, dt) P, PI = integ.cache.P, integ.cache.PI mul!(x_tmp, P, x[i]) mul!(x_tmp2, P, x[i+1]) smooth!(x_tmp, x_tmp2, A, Q, integ, diffusions[i]) mul!(x[i], PI, x_tmp) end end function estimate_errors(cache::GaussianODEFilterCache) @unpack local_diffusion, Qh, H, d = cache if local_diffusion isa Real && isinf(local_diffusion) return Inf end L = cache.m_tmp.Σ.squareroot if local_diffusion isa Diagonal _matmul!(L, H, sqrt.(local_diffusion) * Qh.squareroot) error_estimate = sqrt.(diag(L * L')) return view(error_estimate, 1:d) elseif local_diffusion isa Number _matmul!(L, H, Qh.squareroot) # error_estimate = local_diffusion .* diag(L*L') @tullio error_estimate[i] := L[i, j] * L[i, j] error_estimate .*= local_diffusion # @info "it's small anyways I guess?" error_estimate cache.measurement.μ .^ 2 # error_estimate .+= cache.measurement.μ .^ 2 error_estimate .= sqrt.(error_estimate) return view(error_estimate, 1:d) end end
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module Day07 using Statistics import ..data_dir # from parent module input = read(joinpath(data_dir, "day07"), String) export part1, part2 """ The total fuel required to align all crab submarines to `target` This function accepts an optional `fuel_cost_function` which calculates the fuel required to move a crab submarine from one location to another. This function should act on non-negative integer values (ie. absolute difference). The default is the `identity` function, in which the distance between the two locations is also the fuel cost. """ function fuel_to_align( positions::Vector{Int64}, target::Integer, fuel_cost_function::Function = identity ) absolute_movements = abs.(positions .- target) fuel_costs = fuel_cost_function.(absolute_movements) sum(fuel_costs) end """ I'm calling this `brute_force` since it inelegantly searches the entire solution space for a minimum cost. If this function isn't good enough for part 2 I can look for leaner search strategies (starting from median position maybe?). Starting with the assumption that the optimal position must be somewhere between the minimum and maximum positions, we can check each possible position between the two to determine the minimum fuel consumption. """ function brute_force(positions::Vector{Int64}, fuel_cost_function::Function = identity) minimum_fuel = Inf for position = minimum(positions):maximum(positions) required_fuel = fuel_to_align(positions, position, fuel_cost_function) minimum_fuel = min(required_fuel, minimum_fuel) end Integer(minimum_fuel) end function part1(input = input) positions = [parse(Int64, position) for position in split(input, ",")] brute_force(positions) end """ I think this is an appropriate name? We're summing an arithmetic sequence. """ arithmetic_fuel_cost(movement::Int64) = movement * (movement + 1) / 2 function part2(input = input) positions = [parse(Int64, position) for position in split(input, ",")] brute_force(positions, arithmetic_fuel_cost) end end # module
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module juliaAllotter using CSV using LinearAlgebra using Statistics using JLD include("core.jl") import Random Random.seed!(2^13 - 1) courseFile = "data/courseFile.csv" studentsFile = "data/studentsFile.csv" choiceIndices = [0, 1, 2, 3, 4, 5] choiceWeights = [10, 1, 2, 3, 4, 5] costWeights = [-1.0, 1.0, 1.0] iterations = 4900 coursesDF = CSV.read(courseFile) studentsDF = CSV.read(studentsFile) courseCount = length(coursesDF[:, 1]) studentCount = length(studentsDF[:, 1]) cpiArray = Array(studentsDF.CPI) times = Array(coursesDF.CourseNeeds) choiceIdx = makeArray(studentCount, studentsDF, courseCount, coursesDF, choiceIndices) choiceWeights = makeArray(studentCount, studentsDF, courseCount, coursesDF, choiceWeights) initialAllotment = allotment(studentCount, courseCount, times, Matrix{Float64}(I, studentCount, studentCount)) initialAllotment = squeezeAllotment(initialAllotment) choiceGoodnessOld, cpiGoodnessOld = calcGoodness(initialAllotment, choiceWeights, cpiArray) finalAllottment, utility = runMCMC(initialAllotment, iterations, studentCount, courseCount, costWeights, choiceIdx, choiceWeights, studentsDF, cpiArray, times) choiceGoodnessNew, cpiGoodnessNew = calcGoodness(finalAllottment, choiceWeights, cpiArray) writePerformance(finalAllottment, choiceGoodnessOld, cpiGoodnessOld, choiceGoodnessNew, cpiGoodnessNew, utility) end # module
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struct PolicyValueRewardTest <: TrainingTest idx::Integer state::AbstractEnvState image::AbstractImage actions::Vector{<:Integer} value::Float32 action::Integer reward::Float32 end mutable struct PolicyValueRewardTests <: TrainingTests tests::Vector{PolicyValueRewardTest} images::AbstractArray{Float32, 4} actual_value::AbstractArray{Float32, 2} actual_reward::AbstractArray{Float32, 2} period::Int warmup::Int function PolicyValueRewardTests(tests; period=1, warmup=0) new( tests, tensorize(get_image.(tests)), Flux.unsqueeze(get_value.(tests), 1), Flux.unsqueeze(get_reward.(tests), 1), period, warmup, ) end end function gettestfn(tests::PolicyValueRewardTests) function fn(n::Network) initial_output = initialinferencefn(tests)(n) acc, fails = getpolicyacc(tests, initial_output) value_mse = getvaluemse(tests, initial_output) recurrent_output = recurrentinferencefn(tests, initial_output)(n) reward_mse = getrewardmse(tests, recurrent_output) acc, fails, value_mse, reward_mse end end struct PolicyValueRewardTestsSVG tests::PolicyValueRewardTests end svg(x::PolicyValueRewardTests) = PolicyValueRewardTestsSVG(x) function Base.show(io::IO, m::MIME"image/svg+xml", x::PolicyValueRewardTestsSVG) num_tests = length(x.tests) range = 1:(min(10, num_tests)) subset = 1:num_tests subset_indices = subset[range] svgbatch = [gridsvg(x.tests[i]) for i in subset_indices] Base.show(io, m, GridSVG(svgbatch, main_title="RVP Tests")) end
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2.401439
695
include("ToricVarieties.jl") ###################### # 1: The Julia type for ToricDivisors ###################### struct toric_divisor GapToricDivisor::GapObj end export toric_divisor ###################### # 2: Generic constructors ###################### function create_divisor( coeffs::Vector{Int}, v::toric_variety ) # create the divisor gap_coeffs = GapObj( coeffs ) gap_divisor = GAP.Globals.CreateDivisor( gap_coeffs, v.GapToricVariety ) # wrap and return return toric_divisor( gap_divisor ) end export create_divisor function divisor_of_character( character::Vector{Int}, v::toric_variety ) # create the divisor gap_character = GapObj( character ) gap_divisor = GAP.Globals.DivisorOfCharacter( gap_character, v.GapToricVariety ) # wrap and return return toric_divisor( gap_divisor ) end export divisor_of_character function divisor_of_class( v::toric_variety, class::Vector{Int} ) # create the divisor gap_class = GapObj( class ) gap_divisor = GAP.Globals.DivisorOfGivenClass( v.GapToricVariety, gap_class ) # wrap and return return toric_divisor( gap_divisor ) end export divisor_of_class ###################### # 3: Properties ###################### function is_cartier( d::toric_divisor ) return GAP.Globals.IsCartier( d.GapToricDivisor )::Bool end export is_cartier function is_principal( d::toric_divisor ) return GAP.Globals.IsPrincipal( d.GapToricDivisor )::Bool end export is_principal function is_primedivisor( d::toric_divisor ) return GAP.Globals.IsPrimedivisor( d.GapToricDivisor )::Bool end export is_primedivisor function is_basepoint_free( d::toric_divisor ) return GAP.Globals.IsBasepointFree( d.GapToricDivisor )::Bool end export is_basepoint_free function is_ample( d::toric_divisor ) return GAP.Globals.IsAmple( d.GapToricDivisor )::Bool end export is_ample function is_very_ample( d::toric_divisor ) if ! is_ample( d ) @warn "Can (current) only tell for ample toric divisors if they are very ample." return "fail" end return GAP.Globals.IsVeryAmple( d.GapToricDivisor )::Bool end export is_very_ample function is_numerically_effective( d::toric_divisor ) return GAP.Globals.IsNumericallyEffective( d.GapToricDivisor )::Bool end export is_numerically_effective
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2.462827
955
@testset "Spaces" begin Qx, x = PolynomialRing(FlintQQ, "x") K, a = NumberField(x^2 - 2, "a1") Kt, t = K["t"] E, b = NumberField(t^2 + 3) F = GF(3) Hecke.change_base_ring(::Hecke.NfRel, ::Hecke.gfp_mat) = error("asd") @test_throws ErrorException hermitian_space(E, F[1 2; 2 1]) Hecke.change_base_ring(::Hecke.NfRel, x::Hecke.gfp_mat) = x @test_throws ErrorException hermitian_space(E, F[1 2; 2 1]) V = @inferred hermitian_space(E, FlintQQ[1 2; 2 1]) @test V isa Hecke.HermSpace end
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2.09465
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using JuMP, EAGO m = Model() EAGO.register_eago_operators!(m) @variable(m, -1 <= x[i=1:3] <= 1) @variable(m, -3.428579430434188 <= q <= 8.991868736935128) add_NL_constraint(m, :(gelu(0.758903986598098 + 0.8106379052679875*gelu(0.47487042435595583 + 0.4488775132618512*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.015398554931854491*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3])))) + -0.6668215058198093*gelu(0.8216722410540171 + 0.5667551555087149*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.5912184082121308*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))))) + gelu(-0.09143860592972564 + 0.3407854070498746*gelu(0.47487042435595583 + 0.4488775132618512*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.015398554931854491*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3])))) + 0.24612879529032217*gelu(0.8216722410540171 + 0.5667551555087149*gelu(0.1716391672055586 + 0.7301849089692007*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + 0.6276077641275091*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))) + 0.5912184082121308*gelu(0.8366427516313624 + 0.8654420505988725*gelu(0.33202390613731003 + -0.8931954910636541*$(x[1]) + 0.7142724585602056*$(x[2]) + -0.28852147983722487*$(x[3])) + -0.07448940361379819*gelu(-0.8935890604396688 + -0.29936605585485676*$(x[1]) + -0.5391102865466948*$(x[2]) + 0.8633503800224367*$(x[3]))))) - $q <= 0.0)) @objective(m, Min, q) return m
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1.764286
1,820
""" Nghttp2 Julia bindings. """ """ Items: [x] add basic unit test, server, client [x] unit test to submit_response with payload > 16 KB [ ] verify trailers are sent at the end with request is send with multiple packages [ ] add unit test with invalid response [x] return an error if failure occurs in Http2Stream [ ] nghttp2_on_stream_close_callback, close stream on error [ ] ensure sessions are destroyed [x] submit request should return correct stream [x] create a new request stream - nghttp2_xxx functions returns error code, except _new functions. session reading loop read and dispatch single Http2Session read() multiple entries from read stream until it is available Multiple Http2Streams are reading from a single Http2Session. ┌─────────────────┐ │Http2Stream::read│─ ─ ─ └─────────────────┘ │ session.read_lock ┌─────────────────┐ ─ ─ ▶ ╔════╗ ┌─────────────┐ │Http2Stream::read│───────────────╣Lock╠─────▶│Session::read│ └─────────────────┘ ─ ─ ▶ ╚════╝ └─────────────┘ ┌─────────────────┐ │ │Http2Stream::read│─ ─ ─ └─────────────────┘ """ module Nghttp2 export Http2ClientSession, Http2ServerSession, Http2Stream, Http2ProtocolError export send, recv, try_recv, submit_request, submit_response, read, eof, bytesavailable, close, isopen export nghttp2_version using nghttp2_jll using BitFlags using Sockets const Option{T} = Union{Nothing,T} where {T} """ Error codes used by Nghttp2 library. """ @enum(Nghttp2Error::Int32, # Invalid argument passed. NGHTTP2_ERR_INVALID_ARGUMENT = -501, # Out of buffer space. NGHTTP2_ERR_BUFFER_ERROR = -502, # The specified protocol version is not supported. NGHTTP2_ERR_UNSUPPORTED_VERSION = -503, # Used as a return value from nghttp2_send_callback, nghttp2_recv_callback and nghttp2_send_data_callback to indicate that the operation would block. NGHTTP2_ERR_WOULDBLOCK = -504, # General protocol error. NGHTTP2_ERR_PROTO = -505, # The frame is invalid. NGHTTP2_ERR_INVALID_FRAME = -506, # The peer performed a shutdown on the connection. NGHTTP2_ERR_EOF = -507, # Used as a return value from nghttp2_data_source_read_callback() to indicate that data transfer is postponed. See nghttp2_data_source_read_callback() for details. NGHTTP2_ERR_DEFERRED = -508, # Stream ID has reached the maximum value. Therefore no stream ID is available. NGHTTP2_ERR_STREAM_ID_NOT_AVAILABLE = -509, # The stream is already closed; or the stream ID is invalid. NGHTTP2_ERR_STREAM_CLOSED = -510, # RST_STREAM has been added to the outbound queue. The stream is in closing state. NGHTTP2_ERR_STREAM_CLOSING = -511, # The transmission is not allowed for this stream (e.g., a frame with END_STREAM flag set has already sent). NGHTTP2_ERR_STREAM_SHUT_WR = -512, # The stream ID is invalid. NGHTTP2_ERR_INVALID_STREAM_ID = -513, # The state of the stream is not valid (e.g., DATA cannot be sent to the stream if response HEADERS has not been sent). NGHTTP2_ERR_INVALID_STREAM_STATE = -514, # Another DATA frame has already been deferred. NGHTTP2_ERR_DEFERRED_DATA_EXIST = -515, # Starting new stream is not allowed (e.g., GOAWAY has been sent and/or received). NGHTTP2_ERR_START_STREAM_NOT_ALLOWED = -516, # GOAWAY has already been sent. NGHTTP2_ERR_GOAWAY_ALREADY_SENT = -517, # The received frame contains the invalid header block. NGHTTP2_ERR_INVALID_HEADER_BLOCK = -518, # Indicates that the context is not suitable to perform the requested operation. NGHTTP2_ERR_INVALID_STATE = -519, # The user callback function failed due to the temporal error. NGHTTP2_ERR_TEMPORAL_CALLBACK_FAILURE = -521, # The length of the frame is invalid, either too large or too small. NGHTTP2_ERR_FRAME_SIZE_ERROR = -522, # Header block inflate/deflate error. NGHTTP2_ERR_HEADER_COMP = -523, # Flow control error. NGHTTP2_ERR_FLOW_CONTROL = -524, # Insufficient buffer size given to function. NGHTTP2_ERR_INSUFF_BUFSIZE = -525, # Callback was paused by the application. NGHTTP2_ERR_PAUSE = -526, # There are too many in-flight SETTING frame and no more transmission of SETTINGS is allowed. NGHTTP2_ERR_TOO_MANY_INFLIGHT_SETTINGS = -527, # The server push is disabled. NGHTTP2_ERR_PUSH_DISABLED = -528, # DATA or HEADERS frame for a given stream has been already submitted and has not been fully processed yet. NGHTTP2_ERR_DATA_EXIST = -529, # The current session is closing due to a connection error or nghttp2_session_terminate_session() is called. NGHTTP2_ERR_SESSION_CLOSING = -530, # Invalid HTTP header field was received and stream is going to be closed. NGHTTP2_ERR_HTTP_HEADER = -531, # Violation in HTTP messaging rule. NGHTTP2_ERR_HTTP_MESSAGING = -532, # Stream was refused. NGHTTP2_ERR_REFUSED_STREAM = -533, # Unexpected internal error, but recovered. NGHTTP2_ERR_INTERNAL = -534, # Indicates that a processing was canceled. NGHTTP2_ERR_CANCEL = -535, # When a local endpoint expects to receive SETTINGS frame, it receives an other type of frame. NGHTTP2_ERR_SETTINGS_EXPECTED = -536, # When a local endpoint receives too many settings entries in a single SETTINGS frame. NGHTTP2_ERR_TOO_MANY_SETTINGS = -537, # The errors < nghttp2_error.NGHTTP2_ERR_FATAL mean that the library is under unexpected condition and processing was terminated. NGHTTP2_ERR_FATAL = -900, # Out of memory. This is a fatal error. NGHTTP2_ERR_NOMEM = -901, # The user callback function failed. This is a fatal error. NGHTTP2_ERR_CALLBACK_FAILURE = -902, # Invalid client magic (see NGHTTP2_CLIENT_MAGIC) was received and further processing is not possible. NGHTTP2_ERR_BAD_CLIENT_MAGIC = -903, # Possible flooding by peer was detected in this HTTP/2 session. NGHTTP2_ERR_FLOODED = -904) """ The frame types in HTTP/2 specification. """ @enum(Nghttp2FrameType::UInt8, # The DATA frame. NGHTTP2_DATA = 0, # The HEADERS frame. NGHTTP2_HEADERS = 0x01, # The PRIORITY frame. NGHTTP2_PRIORITY = 0x02, # The RST_STREAM frame. NGHTTP2_RST_STREAM = 0x03, # The SETTINGS frame. NGHTTP2_SETTINGS = 0x04, # The PUSH_PROMISE frame. NGHTTP2_PUSH_PROMISE = 0x05, # The PING frame. NGHTTP2_PING = 0x06, # The GOAWAY frame. NGHTTP2_GOAWAY = 0x07, # The WINDOW_UPDATE frame. NGHTTP2_WINDOW_UPDATE = 0x08, # The CONTINUATION frame. This frame type won't be passed to any # callbacks because the library processes this frame type and its # preceding HEADERS/PUSH_PROMISE as a single frame. NGHTTP2_CONTINUATION = 0x09, # The ALTSVC frame, which is defined in `RFC 7383 # <https://tools.ietf.org/html/rfc7838#section-4>`_. NGHTTP2_ALTSVC = 0x0a, # The ORIGIN frame, which is defined by `RFC 8336 # <https://tools.ietf.org/html/rfc8336>`_. NGHTTP2_ORIGIN = 0x0c) """ The category of HEADERS, which indicates the role of the frame. In HTTP/2 spec, request, response, push response and other arbitrary headers (e.g., trailer fields) are all called just HEADERS. To give the application the role of incoming HEADERS frame, we define several categories. """ @enum(Nghttp2FrameHeadersCategory::UInt32, # The HEADERS frame is opening new stream, which is analogous to SYN_STREAM in SPDY. NGHTTP2_HCAT_REQUEST = 0, # The HEADERS frame is the first response headers, which is # analogous to SYN_REPLY in SPDY. NGHTTP2_HCAT_RESPONSE = 1, # The HEADERS frame is the first headers sent against reserved stream. NGHTTP2_HCAT_PUSH_RESPONSE = 2, # The HEADERS frame which does not apply for the above categories, # which is analogous to HEADERS in SPDY. If non-final response # (e.g., status 1xx) is used, final response HEADERS frame will be # categorized here. NGHTTP2_HCAT_HEADERS = 3) """ The flags for HTTP/2 frames. This enum defines all flags for all frames. """ @enum(Nghttp2FrameFlags::UInt8, # No flag set. NGHTTP2_FLAG_NONE = 0, # The END_STREAM flag. # The ACK flag. NGHTTP2_FLAG_END_STREAM = 0x01, # The END_HEADERS flag. NGHTTP2_FLAG_END_HEADERS = 0x04, # The PADDED flag. NGHTTP2_FLAG_PADDED = 0x08, # The PRIORITY flag. NGHTTP2_FLAG_PRIORITY = 0x20) const NGHTTP2_FLAG_ACK = NGHTTP2_FLAG_END_STREAM """ The status codes for the RST_STREAM and GOAWAY frames. """ @enum(Nghttp2ErrorCode::UInt32, # No errors. NGHTTP2_NO_ERROR = 0x0, # PROTOCOL_ERROR. NGHTTP2_PROTOCOL_ERROR = 0x1, # INTERNAL_ERROR. NGHTTP2_INTERNAL_ERROR = 0x2, # FLOW_CONTROL_ERROR. NGHTTP2_FLOW_CONTROL_ERROR = 0x3, # SETTINGS_TIMEOUT. NGHTTP2_SETTINGS_TIMEOUT = 0x4, # STREAM_CLOSED. NGHTTP2_STREAM_CLOSED = 0x5, # FRAME_SIZE_ERROR. NGHTTP2_FRAME_SIZE_ERROR = 0x6, # REFUSED_STREAM. NGHTTP2_REFUSED_STREAM = 0x7, # CANCEL. NGHTTP2_CANCEL = 0x8, # COMPRESSION_ERROR. NGHTTP2_COMPRESSION_ERROR = 0x9, #CONNECT_ERROR. NGHTTP2_CONNECT_ERROR = 0xa, # ENHANCE_YOUR_CALM. NGHTTP2_ENHANCE_YOUR_CALM = 0xb, # INADEQUATE_SECURITY. NGHTTP2_INADEQUATE_SECURITY = 0xc, # HTTP_1_1_REQUIRED. NGHTTP2_HTTP_1_1_REQUIRED = 0xd) """ The flags for header field name/value pair. """ @enum(Nghttp2NvFlags::UInt8, # No flag set. NGHTTP2_NV_FLAG_NONE = 0, # Indicates that this name/value pair must not be indexed ("Literal # Header Field never Indexed" representation must be used in HPACK # encoding). Other implementation calls this bit as "sensitive". NGHTTP2_NV_FLAG_NO_INDEX = 0x01, # This flag is set solely by application. If this flag is set, the # library does not make a copy of header field name. This could # improve performance. NGHTTP2_NV_FLAG_NO_COPY_NAME = 0x02, # This flag is set solely by application. If this flag is set, the # library does not make a copy of header field value. This could # improve performance. NGHTTP2_NV_FLAG_NO_COPY_VALUE = 0x04) """ The SETTINGS ID. """ @enum(Nghttp2SettingsId::UInt32, # SETTINGS_HEADER_TABLE_SIZE NGHTTP2_SETTINGS_HEADER_TABLE_SIZE = 0x01, # SETTINGS_ENABLE_PUSH, client only option. NGHTTP2_SETTINGS_ENABLE_PUSH = 0x02, # SETTINGS_MAX_CONCURRENT_STREAMS NGHTTP2_SETTINGS_MAX_CONCURRENT_STREAMS = 0x03, # SETTINGS_INITIAL_WINDOW_SIZE NGHTTP2_SETTINGS_INITIAL_WINDOW_SIZE = 0x04, # SETTINGS_MAX_FRAME_SIZE NGHTTP2_SETTINGS_MAX_FRAME_SIZE = 0x05, # SETTINGS_MAX_HEADER_LIST_SIZE NGHTTP2_SETTINGS_MAX_HEADER_LIST_SIZE = 0x06) """ The flags used to set in |data_flags| output parameter in :type:`nghttp2_data_source_read_callback`. """ @bitflag Nghttp2DataFlags::UInt32 begin # No flag set. NGHTTP2_DATA_FLAG_NONE = 0 # Indicates EOF was sensed. NGHTTP2_DATA_FLAG_EOF = 0x01 # Indicates that END_STREAM flag must not be set even if # NGHTTP2_DATA_FLAG_EOF is set. Usually this flag is used to send # trailer fields with `nghttp2_submit_request()` or # `nghttp2_submit_response()`. NGHTTP2_DATA_FLAG_NO_END_STREAM = 0x02 # Indicates that application will send complete DATA frame in # :type:`nghttp2_send_data_callback`. NGHTTP2_DATA_FLAG_NO_COPY = 0x04 end """ The SETTINGS ID/Value pair. """ struct SettingsEntry settings_id::Nghttp2SettingsId value::UInt32 end const DEFAULT_SERVER_SETTINGS = Vector{SettingsEntry}( [ SettingsEntry(NGHTTP2_SETTINGS_MAX_CONCURRENT_STREAMS, 100) ]) const DEFAULT_CLIENT_SETTINGS = Vector{SettingsEntry}( [ SettingsEntry(NGHTTP2_SETTINGS_MAX_CONCURRENT_STREAMS, 100), SettingsEntry(NGHTTP2_SETTINGS_ENABLE_PUSH, 1), ]) """ The name/value pair, which mainly used to represent header fields. It creates a copy of the strings using malloc. String pointers can be safely passed to C function. """ struct NVPair name::Ptr{Cchar} value::Ptr{Cchar} namelen::Csize_t valuelen::Csize_t flags::UInt8 NVPair(nothing) = new(C_NULL, C_NULL, 0, 0, UInt8(0)) NVPair(nv_pair::Pair{String,String}) = NVPair(nv_pair.first, nv_pair.second, UInt8(0)) function NVPair(name::String, value::String, flags::UInt8) name_len = length(name) value_len = length(value) # Reserve 2 bytes for the string terminator name_ptr = Ptr{UInt8}(Libc.calloc(name_len + value_len + 2, 1)) value_ptr = name_ptr + name_len + 1 GC.@preserve name unsafe_copyto!(name_ptr, pointer(name), name_len) GC.@preserve value unsafe_copyto!(value_ptr, pointer(value), value_len) return nv_pair = new(name_ptr, value_ptr, name_len, value_len, flags) end end free(nv_pair::NVPair) = Libc.free(nv_pair.name) """ Helper functions to convert vector of string pairs to vector of NVPair. """ const NVPairs = Vector{NVPair} const StringPairs = Vector{Pair{String,String}} function convert_to_nvpairs(input::StringPairs) nv_pairs = NVPairs() foreach(pair -> push!(nv_pairs, NVPair(pair)), input) finalizer(free, nv_pairs) return nv_pairs end free(nv_pairs::NVPairs) = for i in 1:length(nv_pairs) free(nv_pairs[i]) nv_pairs[i] = NVPair(nothing) end """ Nghttp2 library options. """ mutable struct Nghttp2Option ptr::Ptr{Cvoid} """ Creates an instance of Nghttp2Options. """ function Nghttp2Option()::Nghttp2Option nghttp2_option = new(C_NULL) result = ccall( (:nghttp2_option_new, libnghttp2), Cint, (Ref{Nghttp2Option},), nghttp2_option) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end finalizer(free, nghttp2_option) return nghttp2_option end end function free(nghttp2_option::Nghttp2Option) ccall( (:nghttp2_option_del, libnghttp2), Cvoid, (Nghttp2Option,), nghttp2_option) nghttp2_option.ptr = C_NULL return nothing end mutable struct Nghttp2Session ptr::Ptr{Cvoid} end mutable struct Nghttp2Frame ptr::Ptr{Cvoid} end """ The frame header. """ struct Nghttp2FrameHeader # The length field of this frame, excluding frame header. length::Csize_t # The stream identifier (aka, stream ID) stream_id::Int32 # The type of this frame. See `nghttp2_frame_type`. type::Nghttp2FrameType # The flags. flags::UInt8 # Reserved bit in frame header. Currently, this is always set to 0 # and application should not expect something useful in here. reserved::UInt8 end """ The structure to specify stream dependency. """ struct Nghttp2PrioritySpec # The stream ID of the stream to depend on. Specifying 0 makes stream not depend any other stream. stream_id::Int32 # The weight of this dependency. weight::Int32 # Nonzero means exclusive dependency. exclusive::UInt8 end """ The HEADERS frame. """ struct Nghttp2HeadersFrame # The frame header. frame_header::Nghttp2FrameHeader # The length of the padding in this frame. This includes PAD_HIGH and PAD_LOW. pad_len::Csize_t # The priority specification pri_spec::Nghttp2PrioritySpec # The name/value pairs. nva::Ptr{Cvoid} # The number of name/value pairs in |nva|. nvlen::Csize_t # The category of this HEADERS frame. cat::Nghttp2FrameHeadersCategory end """ Nghttp2 library information. """ struct Nghttp2Info age::Cint version_num::Cint version_str::Cstring proto_str::Cstring end mutable struct DataSource send_stream::IO trailer::NVPairs end mutable struct DataProvider data_source::Ptr{DataSource} read_callback::Ptr{Cvoid} end """ Http2ProtocolError. """ mutable struct Http2ProtocolError <: Exception lib_error_code::Nghttp2Error msg::String Http2ProtocolError(lib_error_code::Nghttp2Error, msg::String) = new(lib_error_code, msg) function Http2ProtocolError(lib_error_code::Nghttp2Error) str_error = ccall( (:nghttp2_strerror, libnghttp2), Cstring, (Nghttp2Error,), lib_error_code) return new(lib_error_code, unsafe_string(str_error)) end end abstract type AbstractSession end """ Library definition. """ mutable struct Http2Stream <: IO session::AbstractSession stream_id::Int32 buffer::IOBuffer headers::Dict{String,String} lock::ReentrantLock eof::Bool Http2Stream(session::AbstractSession, stream_id::Int32) = return new( session, stream_id, PipeBuffer(), Dict{String,String}(), ReentrantLock(), false) end """ Tests whether an HTTP2 stream is at end-of-file. """ function Base.eof(http2_stream::Http2Stream)::Bool lock(http2_stream.lock) do return http2_stream.eof && eof(http2_stream.buffer) end end """ Returns number of bytes available for reading before a read from this stream will block. """ function Base.bytesavailable(http2_stream::Http2Stream) lock(http2_stream.lock) do return bytesavailable(http2_stream.buffer) end end """ Determines whether the underlying session IO is not yet closed. Even if the stream is closed, it may still have data to read in its buffer; use eof to check for the ability to read data. """ function Base.isopen(http2_stream::Http2Stream) return isopen(http2_stream.session.io) end """ Ensures there are requested number of bytes in the Http2Stream. """ function ensure_in_buffer(http2_stream::Http2Stream, nb::Integer) should_read = true # Process HTTP2 stack until there is no more available data in HTTP2 stream. while should_read lock(http2_stream.lock) do if bytesavailable(http2_stream.buffer) >= nb || http2_stream.eof should_read = false end end if should_read && internal_read!(http2_stream.session) continue end # Read failed break end # Throw exception if session is in error state. if has_error(http2_stream.session) throw(http2_stream.session.exception) end end """ Reads available data from the HTTP2 stream. """ function Base.read(http2_stream::Http2Stream)::Vector{UInt8} ensure_in_buffer(http2_stream, 1) lock(http2_stream.lock) do result_buffer = read(http2_stream.buffer) return result_buffer end end """ Reads at most nb bytes from from the HTTP2 stream. """ function Base.read(http2_stream::Http2Stream, nb::Integer)::Vector{UInt8} ensure_in_buffer(http2_stream, nb) lock(http2_stream.lock) do if bytesavailable(http2_stream.buffer) < nb throw(EOFError()) end result_buffer = read(http2_stream.buffer, nb) return result_buffer end end function Base.read(http2_stream::Http2Stream, ::Type{UInt8})::UInt8 return read(http2_stream, Core.sizeof(UInt8))[begin + 0] end function Base.unsafe_read(http2_stream::Http2Stream, p::Ptr{UInt8}, nb::UInt) ensure_in_buffer(http2_stream, nb) lock(http2_stream.lock) do if bytesavailable(http2_stream.buffer) < nb throw(EOFError()) end result_buffer = read(http2_stream.buffer, nb) GC.@preserve result_buffer unsafe_copyto!(p, pointer(result_buffer), nb) end end """ Writes the data to the Http2 stream. """ function Base.write(http2_stream::Http2Stream, out_buffer::Vector{UInt8}) lock(http2_stream.lock) do # Write the data to the steam. return write(http2_stream.buffer, out_buffer) end end """ Internal HTTP2 session. """ mutable struct Session <: AbstractSession io::IO nghttp2_session::Nghttp2Session recv_streams::Dict{Int32,Http2Stream} recv_streams_id::Set{Int32} exception::Option{Exception} lock::ReentrantLock read_lock::ReentrantLock function Session(io::IO, nghttp2_session::Nghttp2Session) return new( io, nghttp2_session, Dict{Int32,Http2Stream}(), Set{Int32}(), nothing, ReentrantLock(), ReentrantLock()) end end """ Retrieves the Session object from the nghttp2_session data. The Session object must be pinned. """ function session_from_data(user_data::Ptr{Cvoid})::Session session::Session = unsafe_pointer_to_objref(user_data) return session end """ Sets the session object in Nghttp2Session structure. The Session object must be pinned. """ function session_set_data(session::Session) return ccall( (:nghttp2_session_set_user_data, libnghttp2), Cvoid, (Nghttp2Session, Ptr{Cvoid}), session.nghttp2_session, pointer_from_objref(session)) end function nghttp2_option_set_no_auto_window_update(nghttp2_option::Nghttp2Option, value::Cint) return ccall( (:nghttp2_option_set_no_auto_window_update, libnghttp2), Cvoid, (Nghttp2Option, Cint), nghttp2_option, value) end """ Session callbacks. """ mutable struct Nghttp2SessionCallbacks ptr::Ptr{Cvoid} function Nghttp2SessionCallbacks()::Nghttp2SessionCallbacks callbacks = new(C_NULL) result = ccall( (:nghttp2_session_callbacks_new, libnghttp2), Cint, (Ref{Nghttp2SessionCallbacks},), callbacks) if (result != 0) throw(Http2ProtocolError(Nghttp2Error(result))) end finalizer(free, callbacks) ccall( (:nghttp2_session_callbacks_set_on_frame_recv_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_frame_recv_callback_ptr) ccall( (:nghttp2_session_callbacks_set_recv_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_recv_callback_ptr) ccall( (:nghttp2_session_callbacks_set_on_begin_headers_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_begin_headers_callback_ptr) ccall( (:nghttp2_session_callbacks_set_on_header_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_header_recv_callback_ptr) ccall( (:nghttp2_session_callbacks_set_on_data_chunk_recv_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_data_chunk_recv_callback_ptr) ccall( (:nghttp2_session_callbacks_set_send_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_send_callback_ptr) ccall( (:nghttp2_session_callbacks_set_error_callback2, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_error_callback_ptr) ccall( (:nghttp2_session_callbacks_set_on_stream_close_callback, libnghttp2), Cvoid, (Nghttp2SessionCallbacks, Ptr{Cvoid}), callbacks, NGHTTP2_CALLBACKS.x.on_stream_close_callback_ptr) return callbacks end end function free(nghttp2_callbacks::Nghttp2SessionCallbacks) ccall( (:nghttp2_session_callbacks_del, libnghttp2), Cvoid, (Nghttp2SessionCallbacks,), nghttp2_callbacks) nghttp2_callbacks.ptr = C_NULL return nothing end """ Server session. Creates a new server session and stores the session object in the lookup dictionary. """ function server_session_new(io::IO)::Session nghttp2_session::Nghttp2Session = Nghttp2Session(C_NULL) nghttp2_session_callbacks = Nghttp2SessionCallbacks() result = ccall( (:nghttp2_session_server_new, libnghttp2), Cint, (Ref{Nghttp2Session}, Nghttp2SessionCallbacks, Ptr{Cvoid}), nghttp2_session, nghttp2_session_callbacks, C_NULL) if (result != 0) throw(Http2ProtocolError(Nghttp2Error(result))) end finalizer(free, nghttp2_session) session = Session(io, nghttp2_session) finalize(nghttp2_session_callbacks) return session end """ Client session. Creates a new client session. """ function client_session_new(io::IO)::Session nghttp2_session::Nghttp2Session = Nghttp2Session(C_NULL) nghttp2_session_callbacks = Nghttp2SessionCallbacks() result = ccall( (:nghttp2_session_client_new, libnghttp2), Cint, (Ref{Nghttp2Session}, Nghttp2SessionCallbacks, Ptr{Cvoid}), nghttp2_session, nghttp2_session_callbacks, C_NULL) if (result != 0) throw(Http2ProtocolError(Nghttp2Error(result))) end finalizer(free, nghttp2_session) session = Session(io, nghttp2_session) finalize(nghttp2_session_callbacks) return session end """ Nghttp2Session. """ function is_nghttp2_server_session(nghttp2_session::Nghttp2Session)::Bool result = ccall( (:nghttp2_session_check_server_session, libnghttp2), Cint, (Nghttp2Session,), nghttp2_session) return result != 0 end function free(nghttp2_session::Nghttp2Session) ccall( (:nghttp2_session_del, libnghttp2), Cvoid, (Nghttp2Session,), nghttp2_session) nghttp2_session.ptr = C_NULL return nothing end function nghttp2_session_terminate_session(nghttp2_session::Nghttp2Session, error_code::UInt32) return ccall( (:nghttp2_session_terminate_session, libnghttp2), Cint, (Nghttp2Session, UInt32), nghttp2_session, error_code) end function nghttp2_submit_shutdown_notice(nghttp2_session::Nghttp2Session) return ccall( (:nghttp2_submit_shutdown_notice, libnghttp2), Cint, (Nghttp2Session,), nghttp2_session) end function nghttp2_session_send(nghttp2_session::Nghttp2Session) return ccall( (:nghttp2_session_send, libnghttp2), Cint, (Nghttp2Session,), nghttp2_session) end function nghttp2_session_submit_settings(nghttp2_session::Nghttp2Session, settings::Vector{SettingsEntry}) return ccall( (:nghttp2_submit_settings, libnghttp2), Cint, (Nghttp2Session, UInt8, Ptr{Cvoid}, Csize_t), nghttp2_session, NGHTTP2_FLAG_NONE, pointer(settings), length(settings)) end function nghttp2_submit_goaway(nghttp2_session::Nghttp2Session) return ccall( (:nghttp2_submit_goaway, libnghttp2), Cint, (Nghttp2Session, UInt8, Cint, UInt32, Ptr{Cvoid}, Csize_t), nghttp2_session, NGHTTP2_FLAG_NONE, 0, NGHTTP2_NO_ERROR, C_NULL, 0) end function nghttp2_session_mem_recv(nghttp2_session::Nghttp2Session, input_data::Vector{UInt8}) return ccall( (:nghttp2_session_mem_recv, libnghttp2), Cssize_t, (Nghttp2Session, Ptr{UInt8}, Csize_t), nghttp2_session, input_data, length(input_data)) end function nghttp2_session_recv(nghttp2_session::Nghttp2Session) return ccall( (:nghttp2_session_recv, libnghttp2), Cint, (Nghttp2Session,), nghttp2_session) end function nghttp2_submit_window_update(nghttp2_session::Nghttp2Session, stream_id::Int32, window_size_increment::Int32) return ccall( (:nghttp2_submit_window_update, libnghttp2), Cint, (Nghttp2Session, UInt8, Cint, Cint), nghttp2_session, NGHTTP2_FLAG_NONE, stream_id, window_size_increment) end """ Errors. """ nghttp2_error_to_string(error::Nghttp2Error) = unsafe_string( ccall( (:nghttp2_strerror, libnghttp2), Cstring, (Cint,), error)) nghttp2_version() = unsafe_load( ccall( (:nghttp2_version, libnghttp2), Ptr{Nghttp2Info}, (Cint,), 0)) function Base.show(io::IO, nghttp2_info::Nghttp2Info) return println( io, """NGHttp2 lib: $(nghttp2_info.version_num) path: $(libnghttp2) version: $(unsafe_string(nghttp2_info.version_str)) protocol: $(unsafe_string(nghttp2_info.proto_str))""") end function Base.show(io::IO, nghttp2_frame_header::Nghttp2FrameHeader) return println( io, """Frame: length: $(nghttp2_frame_header.length) stream_id: $(nghttp2_frame_header.stream_id) type: $(Nghttp2FrameType(nghttp2_frame_header.type)) flags: $(nghttp2_frame_header.flags)""") end function Base.show(io::IO, nv_pair::NVPair) local nv_pair_str::String if (nv_pair.name == C_NULL) nv_pair_str = "nothing" else nv_pair_str = "NVPair: { name: '$(unsafe_string(nv_pair.name)) $(nv_pair.name)', value: '$(unsafe_string(nv_pair.value)) $(nv_pair.value)' }" end return println(io, "NVPair: { $nv_pair_str }") end """ Callback implementation. """ function on_recv_callback( nghttp2_session::Nghttp2Session, buf::Ptr{UInt8}, len::Csize_t, flags::Cint, user_data::Ptr{Cvoid})::Cssize_t # Get the server session object. session = session_from_data(user_data) result::Cssize_t = 0 return result end function on_frame_recv_callback(nghttp2_session::Nghttp2Session, frame::Nghttp2Frame, user_data::Ptr{Cvoid})::Cint # Get the server session object. session = session_from_data(user_data) frame_header = unsafe_load(Ptr{Nghttp2FrameHeader}(frame.ptr)) stream_id = frame_header.stream_id last_frame = stream_id != 0 && frame_header.flags & UInt8(NGHTTP2_FLAG_END_STREAM) != 0 if last_frame # Last frame in the stream detected, mark the stream as EOF. local http2_stream::Http2Stream lock(session.lock) do return http2_stream = session.recv_streams[frame_header.stream_id] end lock(http2_stream.lock) do return http2_stream.eof = true end end result::Cint = 0 return result end function on_begin_headers_callback(nghttp2_session::Nghttp2Session, frame::Nghttp2Frame, user_data::Ptr{Cvoid})::Cint # Get the server session object. session = session_from_data(user_data) frame_header = unsafe_load(Ptr{Nghttp2FrameHeader}(frame.ptr)) # Create a new stream. lock(session.lock) do if !haskey(session.recv_streams, frame_header.stream_id) session.recv_streams[frame_header.stream_id] = Http2Stream(session, frame_header.stream_id) push!(session.recv_streams_id, frame_header.stream_id) end end result::Cint = 0 return result end function on_header_recv_callback( nghttp2_session::Nghttp2Session, frame::Nghttp2Frame, name::Ptr{UInt8}, namelen::Csize_t, value::Ptr{UInt8}, valuelen::Csize_t, flags::UInt8, user_data::Ptr{Cvoid})::Cint # Get the server session object. session = session_from_data(user_data) frame_header = unsafe_load(Ptr{Nghttp2FrameHeader}(frame.ptr)) # Copy from received buffer to the local data. header_name = Vector{UInt8}(undef, namelen) GC.@preserve header_name unsafe_copyto!(pointer(header_name), name, namelen) header_value = Vector{UInt8}(undef, valuelen) GC.@preserve header_value unsafe_copyto!(pointer(header_value), value, valuelen) # Store the header in the session stream. local recv_stream::Http2Stream lock(session.lock) do return recv_stream = session.recv_streams[frame_header.stream_id] end lock(recv_stream.lock) do return recv_stream.headers[String(header_name)] = String(header_value) end result::Cint = 0 return result end function on_data_chunk_recv_callback( nghttp2_session::Nghttp2Session, flags::UInt8, stream_id::Cint, buf::Ptr{UInt8}, len::Csize_t, user_data::Ptr{Cvoid})::Cint # Get the server session object. session = session_from_data(user_data) # Copy from received buffer to the local data. data = Vector{UInt8}(undef, len) GC.@preserve data unsafe_copyto!(pointer(data), buf, len) # Write received data to the received stream buffer. local http2_stream::Http2Stream lock(session.lock) do return http2_stream = session.recv_streams[stream_id] end write(http2_stream, data) result::Cint = 0 return result end function on_send_callback( nghttp2_session::Nghttp2Session, data::Ptr{UInt8}, length::Csize_t, flags::Cint, user_data::Ptr{Cvoid})::Csize_t # Get the server session object. session = session_from_data(user_data) # Copy send data to the buffer. out_buffer = Vector{UInt8}(undef, length) GC.@preserve out_buffer unsafe_copyto!(pointer(out_buffer), data, length) try write(session.io, out_buffer) catch ex lock(session.lock) do return session.exception = ex end return Int(NGHTTP2_ERR_CALLBACK_FAILURE) % Csize_t end return length end function on_error_callback( nghttp2_session::Nghttp2Session, lib_error_code::Cint, msg::Ptr{UInt8}, len::Csize_t, user_data::Ptr{Cvoid})::Cint # Get the server session object. session = session_from_data(user_data) println("on_error_callback session:$(session.nghttp2_session) nghtt2_error_code: $(lib_error_code)") # Create HTTP2 error object, include Nghttp2 error. http2_protocol_error = Http2ProtocolError(Nghttp2Error(lib_error_code), unsafe_string(msg)) lock(session.lock) do return session.exception = http2_protocol_error end @show session.exception result::Cint = 0 return result end function on_data_source_read_callback( nghttp2_session::Nghttp2Session, stream_id::Cint, buf::Ptr{UInt8}, buf_length::Csize_t, data_flags::Ptr{UInt32}, data_source::Ptr{Ptr{IOBuffer}}, user_data::Ptr{Cvoid})::Cssize_t # Get DataSource object. data_source = unsafe_load(data_source) data_source = unsafe_pointer_to_objref(data_source) # TODO on_data_source_read_callback here in_buffer = read(data_source.send_stream, buf_length) in_length = length(in_buffer) GC.@preserve in_buffer unsafe_copyto!(buf, pointer(in_buffer), in_length) source_stream_eof = eof(data_source.send_stream) source_has_trailer = source_stream_eof && length(data_source.trailer) != 0 send_data_flags::Nghttp2DataFlags = NGHTTP2_DATA_FLAG_NONE if source_stream_eof send_data_flags |= NGHTTP2_DATA_FLAG_EOF end if source_has_trailer send_data_flags |= NGHTTP2_DATA_FLAG_NO_END_STREAM # Submit the trailer. result = ccall( (:nghttp2_submit_trailer, libnghttp2), Cint, (Nghttp2Session, Int32, Ptr{Cvoid}, Csize_t), nghttp2_session, stream_id, pointer(data_source.trailer), length(data_source.trailer)) end unsafe_store!(data_flags, UInt32(send_data_flags)) result::Cssize_t = in_length return result end function on_stream_close_callback( nghttp2_session::Nghttp2Session, stream_id::Cint, error_code::UInt32, user_data::Ptr{Cvoid})::Cint # Get the server session object. session = session_from_data(user_data) result::Cint = 0 return result end """ Nghttp2 callbacks. """ struct Nghttp2Callbacks on_recv_callback_ptr::Ptr{Nothing} on_frame_recv_callback_ptr::Ptr{Nothing} on_begin_headers_callback_ptr::Ptr{Nothing} on_header_recv_callback_ptr::Ptr{Nothing} on_data_chunk_recv_callback_ptr::Ptr{Nothing} on_send_callback_ptr::Ptr{Nothing} on_error_callback_ptr::Ptr{Nothing} on_data_source_read_callback_ptr::Ptr{Nothing} on_stream_close_callback_ptr::Ptr{Nothing} function Nghttp2Callbacks() on_recv_callback_ptr = @cfunction on_recv_callback Cssize_t ( Nghttp2Session, Ptr{UInt8}, Csize_t, Cint, Ptr{Cvoid}) on_frame_recv_callback_ptr = @cfunction on_frame_recv_callback Cint ( Nghttp2Session, Nghttp2Frame, Ptr{Cvoid}) on_begin_headers_callback_ptr = @cfunction on_begin_headers_callback Cint ( Nghttp2Session, Nghttp2Frame, Ptr{Cvoid}) on_header_recv_callback_ptr = @cfunction on_header_recv_callback Cint ( Nghttp2Session, Nghttp2Frame, Ptr{UInt8}, Csize_t, Ptr{UInt8}, Csize_t, UInt8, Ptr{Cvoid}) on_data_chunk_recv_callback_ptr = @cfunction on_data_chunk_recv_callback Cint ( Nghttp2Session, UInt8, Cint, Ptr{UInt8}, Csize_t, Ptr{Cvoid}) on_send_callback_ptr = @cfunction on_send_callback Csize_t ( Nghttp2Session, Ptr{UInt8}, Csize_t, Cint, Ptr{Cvoid}) on_error_callback_ptr = @cfunction on_error_callback Cint ( Nghttp2Session, Cint, Ptr{UInt8}, Csize_t, Ptr{Cvoid}) on_data_source_read_callback_ptr = @cfunction on_data_source_read_callback Cssize_t ( Nghttp2Session, Cint, Ptr{UInt8}, Csize_t, Ptr{UInt32}, Ptr{Ptr{IOBuffer}}, Ptr{Cvoid}) on_stream_close_callback_ptr = @cfunction on_stream_close_callback Cint ( Nghttp2Session, Cint, UInt32, Ptr{Cvoid}) return new( on_recv_callback_ptr, on_frame_recv_callback_ptr, on_begin_headers_callback_ptr, on_header_recv_callback_ptr, on_data_chunk_recv_callback_ptr, on_send_callback_ptr, on_error_callback_ptr, on_data_source_read_callback_ptr, on_stream_close_callback_ptr) end end """ HTTP2 session. """ function submit_settings(session::Session, settings::Vector{SettingsEntry}) GC.@preserve session begin session_set_data(session) result = nghttp2_session_submit_settings(session.nghttp2_session, settings) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end result = nghttp2_session_send(session.nghttp2_session) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end end end """ Returns true, if session is in error state. """ function has_error(session::Session)::Bool lock(session.lock) do return !isnothing(session.exception) end end function set_error(session::Session, http2_protocol_error::Http2ProtocolError) lock(session.lock) do if !isnothing(session.exception) session.exception = http2_protocol_error end end end """ Reads from the session input IO and sends it to HTTP2 stack. Returns true if there is more data available. Ensure only one task is reading from the session. """ function internal_read!(session::Session)::Bool # Return if there are errors. if has_error(session) return false end lock(session.read_lock) do if bytesavailable(session.io) != 0 || (isreadable(session.io) && !eof(session.io)) available_bytes = bytesavailable(session.io) input_data = read(session.io, available_bytes) GC.@preserve session begin session_set_data(session) result = nghttp2_session_mem_recv(session.nghttp2_session, input_data) if result < 0 set_error(session, Http2ProtocolError(Nghttp2Error(result))) end result = nghttp2_session_send(session.nghttp2_session) if result < 0 set_error(session, Http2ProtocolError(Nghttp2Error(result))) end end return true end end return false end """ Receives next Http2Stream from the session. """ function Sockets.recv(session::Session)::Option{Http2Stream} should_read = true while should_read lock(session.lock) do # Throw exception if errors occurred. if !isnothing(session.exception) throw(session.exception) end # Break, if there is no data available in the session's IO and # there are no more HTTP2 streams to return. if !isempty(session.recv_streams_id) || eof(session.io) should_read = false end end if should_read # Process received data through the HTTP2 stack. internal_read!(session) continue end break end lock(session.lock) do # If available, return a new HTTP2 stream. if !isempty(session.recv_streams_id) recv_stream_id = pop!(session.recv_streams_id) recv_stream = session.recv_streams[recv_stream_id] return recv_stream end eof(session.io) return nothing end end """ Receives expected Http2Stream from the session. """ function Sockets.recv(session::Session, stream_id::Int32)::Option{Http2Stream} should_read = true while should_read lock(session.lock) do # Throw exception if errors occurred. if !isnothing(session.exception) throw(session.exception) end # Break, if there is no data available in the session's IO and there are no more HTTP2 streams to return. if stream_id in session.recv_streams_id || !isreadable(session.io) || eof(session.io) should_read = false end end if should_read # Process received data through the HTTP2 stack. internal_read!(session) continue end break end lock(session.lock) do # If available, return a new HTTP2 stream. if stream_id in session.recv_streams_id delete!(session.recv_streams_id, stream_id) recv_stream = session.recv_streams[stream_id] return recv_stream end if isempty(session.recv_streams_id) eof(session.io) end return nothing end end """ Returns available Http2Streams. If there are no active Http2Streams, returns nothing. """ function try_recv(session::Session)::Option{Http2Stream} lock(session.lock) do # Throw exception if errors occurred. if !isnothing(session.exception) throw(session.exception) end # If available, return Http2Stream. if !isempty(session.recv_streams_id) recv_stream_id = pop!(session.recv_streams_id) recv_stream = session.recv_streams[recv_stream_id] return recv_stream end return nothing end end """ Sends the data in IO stream via HTTP2 session. """ function send( session::Session, stream_id::Int32, send_buffer::IO, header::StringPairs=StringPairs(), trailer::StringPairs=StringPairs()) headers::NVPairs = convert_to_nvpairs(header) trailers::NVPairs = convert_to_nvpairs(trailer) GC.@preserve session send_buffer headers trailers begin session_set_data(session) data_source = DataSource(send_buffer, trailers) GC.@preserve data_source begin data_provider = DataProvider( pointer_from_objref(data_source), NGHTTP2_CALLBACKS.x.on_data_source_read_callback_ptr) GC.@preserve data_provider begin # send headers, data, and trailers result = ccall( (:nghttp2_submit_response, libnghttp2), Cint, (Nghttp2Session, Int32, Ptr{Cvoid}, Csize_t, Ptr{Cvoid}), session.nghttp2_session, stream_id, pointer(headers), length(headers), pointer_from_objref(data_provider)) if result < 0 set_error(session, Http2ProtocolError(Nghttp2Error(result))) end result = nghttp2_session_send(session.nghttp2_session) if result < 0 set_error(session, Http2ProtocolError(Nghttp2Error(result))) end while !eof(send_buffer) && !has_error(session) internal_read!(session) end end end end # Release headers and trailers after sending the frame. finalize(headers) finalize(trailers) # Throw if error occurred. if has_error(session) throw(session.exception) end end function send(session::Session, send_buffer::IO, header::StringPairs=StringPairs(), trailer::StringPairs=StringPairs()) headers::NVPairs = convert_to_nvpairs(header) trailers::NVPairs = convert_to_nvpairs(trailer) GC.@preserve session send_buffer headers trailers begin session_set_data(session) data_source = DataSource(send_buffer, trailers) GC.@preserve data_source begin data_provider = DataProvider( pointer_from_objref(data_source), NGHTTP2_CALLBACKS.x.on_data_source_read_callback_ptr) GC.@preserve data_provider begin # send headers, data, and trailers stream_id = ccall( (:nghttp2_submit_request, libnghttp2), Cint, (Nghttp2Session, Ptr{Cvoid}, Ptr{Cvoid}, Csize_t, Ptr{Cvoid}), session.nghttp2_session, C_NULL, pointer(headers), length(headers), pointer_from_objref(data_provider)) if stream_id < 0 throw(Http2ProtocolError(Nghttp2Error(stream_id))) end result = nghttp2_session_send(session.nghttp2_session) if result < 0 set_error(session, Http2ProtocolError(Nghttp2Error(result))) end while !eof(send_buffer) && !has_error(session) internal_read!(session) end end end end # Release headers and trailers after sending the frame. finalize(headers) finalize(trailers) # Throw if error occurred. if has_error(session) throw(session.exception) end return stream_id end function is_server_session(session::Session)::Bool return is_nghttp2_server_session(session.nghttp2_session) end """ Public API. Wrapper classes around Http2Session. """ """ Http2 client session. """ struct Http2ClientSession session::Session end function open(io::IO)::Http2ClientSession session = client_session_new(io) result = submit_settings(session, DEFAULT_CLIENT_SETTINGS) return Http2ClientSession(session) end """ Submit a request. """ function submit_request(http2_client_session::Http2ClientSession, io::IO) return submit_request(http2_client_session, io, StringPairs(), StringPairs()) end function submit_request(http2_client_session::Http2ClientSession, io::IO, header::StringPairs) return submit_request(http2_client_session, io, header, StringPairs()) end function submit_request( http2_client_session::Http2ClientSession, io::IO, header::StringPairs, trailer::StringPairs)::Option{Http2Stream} # Send the request. response_stream_id = send(http2_client_session.session, io, header, trailer) response_stream = recv(http2_client_session.session, response_stream_id) return response_stream end """ Http2 server session. """ struct Http2ServerSession session::Session end function from_accepted(io::IO)::Http2ServerSession session = server_session_new(io) result = submit_settings(session, DEFAULT_SERVER_SETTINGS) return Http2ServerSession(session) end function Sockets.recv(http2_server_session::Http2ServerSession) return recv(http2_server_session.session) end function Base.close(http2_server_session::Http2ServerSession) result = nghttp2_submit_shutdown_notice(http2_server_session.session.nghttp2_session) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end result = nghttp2_session_send(http2_server_session.session.nghttp2_session) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end result = nghttp2_submit_goaway(http2_server_session.session.nghttp2_session) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end result = nghttp2_session_send(http2_server_session.session.nghttp2_session) if result != 0 throw(Http2ProtocolError(Nghttp2Error(result))) end return close(http2_server_session.session.io) end """ Http2 stream. """ function submit_response( http2_stream::Http2Stream, io::IO, header::StringPairs=StringPairs(), trailer::StringPairs=StringPairs()) return send( http2_stream.session, http2_stream.stream_id, io, header, trailer) end """ Runme. """ const NGHTTP2_CALLBACKS = Ref{Nghttp2Callbacks}() """ Initialize the module. """ function __init__() println("$(@__MODULE__)::__init") NGHTTP2_CALLBACKS.x = Nghttp2Callbacks() return nothing end end # module Nghttp2
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312, 796, 1461, 0, 7, 29891, 13, 8344, 85, 62, 5532, 82, 62, 312, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 664, 85, 62, 5532, 796, 6246, 13, 8344, 85, 62, 5532, 82, 58, 8344, 85, 62, 5532, 62, 312, 60, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1441, 664, 85, 62, 5532, 198, 220, 220, 220, 220, 220, 220, 220, 886, 628, 220, 220, 220, 220, 220, 220, 220, 1441, 2147, 198, 220, 220, 220, 886, 198, 437, 198, 198, 37811, 198, 220, 220, 220, 311, 2412, 262, 1366, 287, 24418, 4269, 2884, 14626, 17, 6246, 13, 198, 37811, 198, 8818, 3758, 7, 198, 220, 220, 220, 6246, 3712, 36044, 11, 198, 220, 220, 220, 4269, 62, 312, 3712, 5317, 2624, 11, 198, 220, 220, 220, 3758, 62, 22252, 3712, 9399, 11, 198, 220, 220, 220, 13639, 3712, 10100, 47, 3468, 28, 10100, 47, 3468, 22784, 198, 220, 220, 220, 12268, 3712, 10100, 47, 3468, 28, 10100, 47, 3468, 28955, 198, 220, 220, 220, 24697, 3712, 45, 8859, 3468, 796, 10385, 62, 1462, 62, 77, 36133, 3468, 7, 25677, 8, 198, 220, 220, 220, 33122, 3712, 45, 8859, 3468, 796, 10385, 62, 1462, 62, 77, 36133, 3468, 7, 9535, 5329, 8, 628, 220, 220, 220, 20145, 13, 31, 18302, 3760, 6246, 3758, 62, 22252, 24697, 33122, 2221, 198, 220, 220, 220, 220, 220, 220, 220, 6246, 62, 2617, 62, 7890, 7, 29891, 8, 628, 220, 220, 220, 220, 220, 220, 220, 1366, 62, 10459, 796, 6060, 7416, 7, 21280, 62, 22252, 11, 33122, 8, 628, 220, 220, 220, 220, 220, 220, 220, 20145, 13, 31, 18302, 3760, 1366, 62, 10459, 2221, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1366, 62, 15234, 1304, 796, 6060, 29495, 7, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 17562, 62, 6738, 62, 26801, 5420, 7, 7890, 62, 10459, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 39058, 40717, 17, 62, 34, 7036, 31098, 50, 13, 87, 13, 261, 62, 7890, 62, 10459, 62, 961, 62, 47423, 62, 20692, 8, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 20145, 13, 31, 18302, 3760, 1366, 62, 15234, 1304, 2221, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1303, 3758, 24697, 11, 1366, 11, 290, 33122, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1255, 796, 269, 13345, 7, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 357, 25, 77, 456, 29281, 17, 62, 46002, 62, 26209, 11, 9195, 77, 456, 29281, 17, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 327, 600, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 357, 45, 456, 29281, 17, 36044, 11, 2558, 2624, 11, 350, 2213, 90, 34, 19382, 5512, 327, 7857, 62, 83, 11, 350, 2213, 90, 34, 19382, 92, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 6246, 13, 77, 456, 29281, 17, 62, 29891, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 4269, 62, 312, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 17562, 7, 50145, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 4129, 7, 50145, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 17562, 62, 6738, 62, 26801, 5420, 7, 7890, 62, 15234, 1304, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 611, 1255, 1279, 657, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 900, 62, 18224, 7, 29891, 11, 367, 29281, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1255, 796, 299, 456, 29281, 17, 62, 29891, 62, 21280, 7, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 611, 1255, 1279, 657, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 900, 62, 18224, 7, 29891, 11, 367, 29281, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 981, 5145, 68, 1659, 7, 21280, 62, 22252, 8, 11405, 5145, 10134, 62, 18224, 7, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 5387, 62, 961, 0, 7, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1303, 13868, 24697, 290, 33122, 706, 7216, 262, 5739, 13, 198, 220, 220, 220, 2457, 1096, 7, 50145, 8, 198, 220, 220, 220, 2457, 1096, 7, 9535, 34393, 8, 628, 220, 220, 220, 1303, 22481, 611, 4049, 5091, 13, 198, 220, 220, 220, 611, 468, 62, 18224, 7, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 29891, 13, 1069, 4516, 8, 198, 220, 220, 220, 886, 198, 437, 198, 198, 8818, 3758, 7, 29891, 3712, 36044, 11, 3758, 62, 22252, 3712, 9399, 11, 13639, 3712, 10100, 47, 3468, 28, 10100, 47, 3468, 22784, 12268, 3712, 10100, 47, 3468, 28, 10100, 47, 3468, 28955, 198, 220, 220, 220, 24697, 3712, 45, 8859, 3468, 796, 10385, 62, 1462, 62, 77, 36133, 3468, 7, 25677, 8, 198, 220, 220, 220, 33122, 3712, 45, 8859, 3468, 796, 10385, 62, 1462, 62, 77, 36133, 3468, 7, 9535, 5329, 8, 628, 220, 220, 220, 20145, 13, 31, 18302, 3760, 6246, 3758, 62, 22252, 24697, 33122, 2221, 198, 220, 220, 220, 220, 220, 220, 220, 6246, 62, 2617, 62, 7890, 7, 29891, 8, 628, 220, 220, 220, 220, 220, 220, 220, 1366, 62, 10459, 796, 6060, 7416, 7, 21280, 62, 22252, 11, 33122, 8, 628, 220, 220, 220, 220, 220, 220, 220, 20145, 13, 31, 18302, 3760, 1366, 62, 10459, 2221, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1366, 62, 15234, 1304, 796, 6060, 29495, 7, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 17562, 62, 6738, 62, 26801, 5420, 7, 7890, 62, 10459, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 39058, 40717, 17, 62, 34, 7036, 31098, 50, 13, 87, 13, 261, 62, 7890, 62, 10459, 62, 961, 62, 47423, 62, 20692, 8, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 20145, 13, 31, 18302, 3760, 1366, 62, 15234, 1304, 2221, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1303, 3758, 24697, 11, 1366, 11, 290, 33122, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 4269, 62, 312, 796, 269, 13345, 7, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 357, 25, 77, 456, 29281, 17, 62, 46002, 62, 25927, 11, 9195, 77, 456, 29281, 17, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 327, 600, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 357, 45, 456, 29281, 17, 36044, 11, 350, 2213, 90, 34, 19382, 5512, 350, 2213, 90, 34, 19382, 5512, 327, 7857, 62, 83, 11, 350, 2213, 90, 34, 19382, 92, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 6246, 13, 77, 456, 29281, 17, 62, 29891, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 327, 62, 33991, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 17562, 7, 50145, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 4129, 7, 50145, 828, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 17562, 62, 6738, 62, 26801, 5420, 7, 7890, 62, 15234, 1304, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 611, 4269, 62, 312, 1279, 657, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 43481, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 5532, 62, 312, 22305, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1255, 796, 299, 456, 29281, 17, 62, 29891, 62, 21280, 7, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 611, 1255, 1279, 657, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 900, 62, 18224, 7, 29891, 11, 367, 29281, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 981, 5145, 68, 1659, 7, 21280, 62, 22252, 8, 11405, 5145, 10134, 62, 18224, 7, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 5387, 62, 961, 0, 7, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1303, 13868, 24697, 290, 33122, 706, 7216, 262, 5739, 13, 198, 220, 220, 220, 2457, 1096, 7, 50145, 8, 198, 220, 220, 220, 2457, 1096, 7, 9535, 34393, 8, 628, 220, 220, 220, 1303, 22481, 611, 4049, 5091, 13, 198, 220, 220, 220, 611, 468, 62, 18224, 7, 29891, 8, 198, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 29891, 13, 1069, 4516, 8, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1441, 4269, 62, 312, 198, 437, 198, 198, 8818, 318, 62, 15388, 62, 29891, 7, 29891, 3712, 36044, 2599, 25, 33, 970, 198, 220, 220, 220, 1441, 318, 62, 77, 456, 29281, 17, 62, 15388, 62, 29891, 7, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 437, 198, 198, 37811, 198, 220, 220, 220, 5094, 7824, 13, 628, 220, 220, 220, 27323, 2848, 6097, 1088, 367, 29281, 17, 36044, 13, 198, 37811, 198, 198, 37811, 198, 220, 220, 220, 367, 29281, 17, 5456, 6246, 13, 198, 37811, 198, 7249, 367, 29281, 17, 11792, 36044, 198, 220, 220, 220, 6246, 3712, 36044, 198, 437, 198, 198, 8818, 1280, 7, 952, 3712, 9399, 2599, 25, 43481, 17, 11792, 36044, 198, 220, 220, 220, 6246, 796, 5456, 62, 29891, 62, 3605, 7, 952, 8, 198, 220, 220, 220, 1255, 796, 9199, 62, 33692, 7, 29891, 11, 5550, 38865, 62, 5097, 28495, 62, 28480, 51, 20754, 8, 628, 220, 220, 220, 1441, 367, 29281, 17, 11792, 36044, 7, 29891, 8, 198, 437, 198, 198, 37811, 198, 220, 220, 220, 39900, 257, 2581, 13, 198, 37811, 198, 8818, 9199, 62, 25927, 7, 4023, 17, 62, 16366, 62, 29891, 3712, 43481, 17, 11792, 36044, 11, 33245, 3712, 9399, 8, 198, 220, 220, 220, 1441, 9199, 62, 25927, 7, 4023, 17, 62, 16366, 62, 29891, 11, 33245, 11, 10903, 47, 3468, 22784, 10903, 47, 3468, 28955, 198, 437, 198, 198, 8818, 9199, 62, 25927, 7, 4023, 17, 62, 16366, 62, 29891, 3712, 43481, 17, 11792, 36044, 11, 33245, 3712, 9399, 11, 13639, 3712, 10100, 47, 3468, 8, 198, 220, 220, 220, 1441, 9199, 62, 25927, 7, 4023, 17, 62, 16366, 62, 29891, 11, 33245, 11, 13639, 11, 10903, 47, 3468, 28955, 198, 437, 198, 198, 8818, 9199, 62, 25927, 7, 198, 220, 220, 220, 2638, 17, 62, 16366, 62, 29891, 3712, 43481, 17, 11792, 36044, 11, 198, 220, 220, 220, 33245, 3712, 9399, 11, 198, 220, 220, 220, 13639, 3712, 10100, 47, 3468, 11, 198, 220, 220, 220, 12268, 3712, 10100, 47, 3468, 2599, 25, 19722, 90, 43481, 17, 12124, 92, 198, 220, 220, 220, 1303, 16290, 262, 2581, 13, 198, 220, 220, 220, 2882, 62, 5532, 62, 312, 796, 3758, 7, 4023, 17, 62, 16366, 62, 29891, 13, 29891, 11, 33245, 11, 13639, 11, 12268, 8, 628, 220, 220, 220, 2882, 62, 5532, 796, 664, 85, 7, 4023, 17, 62, 16366, 62, 29891, 13, 29891, 11, 2882, 62, 5532, 62, 312, 8, 628, 220, 220, 220, 1441, 2882, 62, 5532, 198, 437, 198, 198, 37811, 198, 220, 220, 220, 367, 29281, 17, 4382, 6246, 13, 198, 37811, 198, 7249, 367, 29281, 17, 10697, 36044, 198, 220, 220, 220, 6246, 3712, 36044, 198, 437, 198, 198, 8818, 422, 62, 13635, 276, 7, 952, 3712, 9399, 2599, 25, 43481, 17, 10697, 36044, 198, 220, 220, 220, 6246, 796, 4382, 62, 29891, 62, 3605, 7, 952, 8, 198, 220, 220, 220, 1255, 796, 9199, 62, 33692, 7, 29891, 11, 5550, 38865, 62, 35009, 5959, 62, 28480, 51, 20754, 8, 628, 220, 220, 220, 1441, 367, 29281, 17, 10697, 36044, 7, 29891, 8, 198, 437, 198, 198, 8818, 311, 11603, 13, 8344, 85, 7, 4023, 17, 62, 15388, 62, 29891, 3712, 43481, 17, 10697, 36044, 8, 198, 220, 220, 220, 1441, 664, 85, 7, 4023, 17, 62, 15388, 62, 29891, 13, 29891, 8, 198, 437, 198, 198, 8818, 7308, 13, 19836, 7, 4023, 17, 62, 15388, 62, 29891, 3712, 43481, 17, 10697, 36044, 8, 198, 220, 220, 220, 1255, 796, 299, 456, 29281, 17, 62, 46002, 62, 49625, 2902, 62, 42138, 7, 4023, 17, 62, 15388, 62, 29891, 13, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 220, 220, 220, 611, 1255, 14512, 657, 198, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 43481, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1255, 796, 299, 456, 29281, 17, 62, 29891, 62, 21280, 7, 4023, 17, 62, 15388, 62, 29891, 13, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 220, 220, 220, 611, 1255, 14512, 657, 198, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 43481, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1255, 796, 299, 456, 29281, 17, 62, 46002, 62, 2188, 8272, 7, 4023, 17, 62, 15388, 62, 29891, 13, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 220, 220, 220, 611, 1255, 14512, 657, 198, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 43481, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1255, 796, 299, 456, 29281, 17, 62, 29891, 62, 21280, 7, 4023, 17, 62, 15388, 62, 29891, 13, 29891, 13, 77, 456, 29281, 17, 62, 29891, 8, 198, 220, 220, 220, 611, 1255, 14512, 657, 198, 220, 220, 220, 220, 220, 220, 220, 3714, 7, 43481, 17, 19703, 4668, 12331, 7, 45, 456, 29281, 17, 12331, 7, 20274, 22305, 198, 220, 220, 220, 886, 628, 220, 220, 220, 1441, 1969, 7, 4023, 17, 62, 15388, 62, 29891, 13, 29891, 13, 952, 8, 198, 437, 198, 198, 37811, 198, 220, 220, 220, 367, 29281, 17, 4269, 13, 198, 37811, 198, 8818, 9199, 62, 26209, 7, 198, 220, 220, 220, 2638, 17, 62, 5532, 3712, 43481, 17, 12124, 11, 198, 220, 220, 220, 33245, 3712, 9399, 11, 198, 220, 220, 220, 13639, 3712, 10100, 47, 3468, 28, 10100, 47, 3468, 22784, 198, 220, 220, 220, 12268, 3712, 10100, 47, 3468, 28, 10100, 47, 3468, 28955, 198, 220, 220, 220, 1441, 3758, 7, 198, 220, 220, 220, 220, 220, 220, 220, 2638, 17, 62, 5532, 13, 29891, 11, 198, 220, 220, 220, 220, 220, 220, 220, 2638, 17, 62, 5532, 13, 5532, 62, 312, 11, 198, 220, 220, 220, 220, 220, 220, 220, 33245, 11, 198, 220, 220, 220, 220, 220, 220, 220, 13639, 11, 198, 220, 220, 220, 220, 220, 220, 220, 12268, 8, 198, 437, 198, 198, 37811, 198, 220, 220, 220, 5660, 1326, 13, 198, 37811, 198, 198, 9979, 39058, 40717, 17, 62, 34, 7036, 31098, 50, 796, 6524, 90, 45, 456, 29281, 17, 14134, 10146, 92, 3419, 198, 198, 37811, 198, 220, 220, 220, 20768, 1096, 262, 8265, 13, 198, 37811, 198, 8818, 11593, 15003, 834, 3419, 198, 220, 220, 220, 44872, 7203, 3, 7, 31, 834, 33365, 24212, 834, 2599, 25, 834, 15003, 4943, 198, 220, 220, 220, 39058, 40717, 17, 62, 34, 7036, 31098, 50, 13, 87, 796, 399, 456, 29281, 17, 14134, 10146, 3419, 198, 220, 220, 220, 1441, 2147, 198, 437, 198, 198, 437, 1303, 8265, 399, 456, 29281, 17, 198 ]
2.240696
22,543
module TestProj using Example export hello end
[ 21412, 6208, 2964, 73, 198, 198, 3500, 17934, 198, 39344, 23748, 198, 198, 437, 198 ]
3.266667
15
module TiledViews using IndexFunArrays # needed for the default window function. using NDTools # for linear_index # using NDTools export TiledView, get_num_tiles, TiledWindowView, tile_centers, get_window, tiled_processing export get_num_tiles, eachtile, eachtilenumber, eachtilerelpos tuple_len(::NTuple{N, Any}) where {N} = Val{N}() # T refers to the result type. N to the dimensions of the final array, and M to the dimensions of the raw array struct TiledView{T, N, M, AA<:AbstractArray{T, M}} <: AbstractArray{T, N} # stores the data. parent::AA # output size of the array tile_size::NTuple{M, Int} tile_period::NTuple{M, Int} tile_offset::NTuple{M, Int} # the distance from the wrapping arrray to the start of stored data pad_value::T # Constructor function function TiledView{T, N, M}(data::AA; tile_size::NTuple{M,Int}, tile_period::NTuple{M,Int}, tile_offset::NTuple{M,Int}, pad_value=nothing) where {T,M,N,AA} if isnothing(pad_value) if T <: NTuple pad_value = T(Base.Iterators.repeated(0)) # elseif T <: AbstractArray else pad_value = convert(T,0) # this may crash, but then the user should specify a valid pad_value end end return new{T, N, M, AA}(data, tile_size, tile_period, tile_offset, pad_value) end end function center(data) return size(data) .÷2 .+1 end """ TiledView(data::F, tile_size::NTuple{N,Int}, tile_overlap::NTuple{N,Int}, tile_center::NTuple{M,Int} = (mod.(tile_size,2) .+1); pad_value::T, keep_center=true) Creates an 2N dimensional view of the data by tiling the N-dimensional data as specified by tile_size, tile_overlap and optionally tile_center. `data`. the inputdata to decompose into a TiledView. No copies are made for the TiledView and the raw data can be accessed via myview.parent. `tile_size`. A Tuple describing the size of each tile. This size will form the first N dimensions of the result of size(myview). The second N dimensions refer to N-dimensional tile numbering. `tile_overlap`. Tuple specifying the overlap between successive tiles in voxels. This implicitely defines the pitch between tiles as (tile_size .- tile_overlap). `pad_value`. Specifies the answer that is returned when get_index is applied to a position outside the source array. `keep_center`. This boolean specifies whether the center of the parant `data` will be aligned with the center of the central tile. If `false`, the first tile starts at offset zero. `tile_center`. Only used if `keep_center` is true. It defines the center position in the central tile. The default is `tile_size .÷ 2 .+1`. # Examples ```jldoctest julia> a = TiledView(reshape(1:49,(7,7)), (4, 4),(1, 1)); julia> a.parent 7×7 reshape(::UnitRange{Int64}, 7, 7) with eltype Int64: 1 8 15 22 29 36 43 2 9 16 23 30 37 44 3 10 17 24 31 38 45 4 11 18 25 32 39 46 5 12 19 26 33 40 47 6 13 20 27 34 41 48 7 14 21 28 35 42 49 julia> size(a) (4, 4, 3, 3) ``` """ function TiledView(data::AbstractArray{T,M}, tile_size::NTuple{M,Int}, tile_overlap::NTuple{M,Int}=tile_size .* 0, tile_center::NTuple{M,Int} = (tile_size .÷ 2 .+1); pad_value=nothing, keep_center=true) where {T, M} # Note that N refers to the original number of dimensions tile_period = tile_size .- tile_overlap if keep_center data_center = center(data) tile_offset = mod.((data_center .- tile_center), tile_period) else tile_offset = tile_period .* 0 end N = 2*M return TiledView{T,N,M}(data; tile_size=tile_size, tile_period=tile_period, tile_offset=tile_offset, pad_value=pad_value) end function get_num_tiles(data::TiledView) num_tiles = ((size(data.parent) .+ data.tile_offset .- 1) .÷ data.tile_period) .+ 1 return num_tiles end # define AbstractArray function to allow to treat the generator as an array # See https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-array function Base.size(A::TiledView) return (A.tile_size...,(get_num_tiles(A))...) end function zeros_like(A::TiledView, ::Type{T}=eltype(A.parent)) where {T} TiledView{T,ndims(A),length(A.tile_size)}(zeros(T, size(A.parent)); tile_size=A.tile_size, tile_period=A.tile_period, tile_offset=A.tile_offset, pad_value=A.pad_value) end function ones_like(A::TiledView, ::Type{T}=eltype(A.parent)) where {T} TiledView{T,ndims(A),length(A.tile_size)}(ones(T, size(A.parent)); tile_size=A.tile_size, tile_period=A.tile_period, tile_offset=A.tile_offset, pad_value=A.pad_value) end # Note that the similar function below will most of the times expand the overall required datasize function Base.similar(A::TiledView, ::Type{T}=eltype(A.parent), dims::Dims=size(A)) where {T} # The first N coordinates are position within a tile, the second N coordinates are tile number #= N = length(A.tile_size) new_tile_sz = dims[1:N] new_num_tiles = dims[N + 1:end] new_tile_period = A.tile_period .+ new_tile_sz .- A.tile_size new_core_sz = new_num_tiles .* new_tile_period .- A.tile_offset # keep the overlap the same as before TiledView{T,ndims(A),length(A.tile_size)}(similar(A.parent, T, new_core_sz); tile_size=new_tile_sz, tile_period=new_tile_period, tile_offset=A.tile_offset, pad_value=A.pad_value) =# similar(A.parent, T, dims) # this returns an ordinary array, but this seems the only way to handle cases like: my_tiled_array[:,:,2,3] which expect a 2D array end # Array{eltype(A)}(undef, size...) # %24 = Base.getproperty(A, :parent)::AbstractMatrix{Float64} # calculate the entry according to the index # Base.getindex(A::IndexFunArray{T,N}, I::Vararg{B, N}) where {T,N, B} = return A.generator(I) function pos_from_tile(A::TiledView{T,N}, TilePos::NTuple{M,Int}, TileNum::NTuple{M,Int}) where {T,N,M} Tuple(TilePos[n] - A.tile_offset[n] + (TileNum[n]-1) * A.tile_period[n] for n in 1:M) end # calculate the entry according to the index Base.@propagate_inbounds function Base.getindex(A::TiledView{T,N,M,AA}, I::Vararg{Int, N})::T where {T,N,M,AA} @boundscheck checkbounds(A, I...) @inbounds pos = (I[n] - A.tile_offset[n] + (I[n+M].-1) * A.tile_period[n] for n in 1:M) if Base.checkbounds(Bool, A.parent, pos...) return Base.getindex(A.parent, pos...)::T else return A.pad_value :: T; end end Base.setindex!(A::TiledView{T,N,M,AA}, v, I::Vararg{Int,N}) where {T,N,M,AA} = begin @boundscheck checkbounds(A, I...) @inbounds pos = (I[n] - A.tile_offset[n] + (I[n+M].-1) * A.tile_period[n] for n in 1:M) # pos = TilePos .- A.tile_offset .+ (TileNum.-1) .* A.tile_period if Base.checkbounds(Bool, A.parent, pos...) return setindex!(A.parent, v, pos... ) else return convert(T,0) end end ## Some functions for generating useful tilings """ get_window(A::TiledView; window_function=window_hanning, get_norm=false, verbose=false, offset = CtrFT); Calculates a window matching to the `TiledView`. `window_function`. The window function as defined in IndexFunArrays to apply to the TiledView. The result is currently not any longer a view as it is unclear how to wrap the multiplication into a view. For this reason the TiledView without the window applied is also returned and can be used for assignments. By default a von Hann window (window_hanning) is used. For even sizes the window is centered at the integer coordinate right of the middle position (`CtrFT`). `get_norm`. An optional Boolean argument allowing to also obtain the normalization map for the boarder pixels, which not necessarily undergo all required window operations. In a future version it may be possible to automatically lay out the windowing such that this effect can be avoided. `verbose`. If true, diagnostic information on the window layout is printed. `offset`. defines where the center of the window is placed. See `IndexFunArrays.jl` for details. # Returns `matching_window`. a window that can be applied to the view via multiplication myview.*matching_window This is intentionally not provided as a product to separate the features conceptually when it comes to write access. `normalized`. only returned for get_norm=true. Contains an array with the normalization information by mapping the window back to the original data. This is useful for incomplete coverage of the tiles as well as using windows which do not sum up to one in the tiling process. # Examples ```jldoctest julia> data = ones(10,10).+0.0; julia> myview = TiledView(data, (5, 5), (2,2)); julia> win = get_window(myview, verbose=true); Tiles with pitch (3, 3) overlap by (2, 2) pixels. Window starts at (0.5, 0.5) and ends at (2.5, 2.5). julia> win 5×5 IndexFunArrays.IndexFunArray{Float64, 2, IndexFunArrays.var"#329#331"{Float64, Tuple{Float64, Float64}, Tuple{Int64, Int64}, Tuple{Float64, Float64}, Tuple{Float64, Float64}}}: 0.0214466 0.125 0.146447 0.125 0.0214466 0.125 0.728553 0.853553 0.728553 0.125 0.146447 0.853553 1.0 0.853553 0.146447 0.125 0.728553 0.853553 0.728553 0.125 0.0214466 0.125 0.146447 0.125 0.0214466 see TiledWindowView() for more examples. """ function get_window(A::TiledView; window_function=window_hanning, get_norm=false, verbose=false, offset=CtrFT) tile_size = A.tile_size tile_pitch = A.tile_period tile_overlap = tile_size .- tile_pitch winend = (tile_size ./ 2.0) winstart = (winend .- tile_overlap) if verbose print("Tiles with pitch $tile_pitch overlap by $tile_overlap pixels.\n") print("Window starts at $winstart and ends at $winend.\n") end if get_norm == false return window_function(tile_size; scale=ScaUnit, offset=offset, border_in=winstart, border_out= winend) else my_view = ones_like(A) normalization = A.parent normalization .= 0 my_view .+= A .*window_function(tile_size;scale=ScaUnit, offset=offset, border_in=winstart, border_out= winend) return (window_function(tile_size; scale=ScaUnit, offset=offset, border_in=winstart, border_out= winend), normalization) end end """ function TiledWindowView(data::AbstractArray{T,M}, tile_size::NTuple{M,Int}; rel_overlap::NTuple{M,Float64}=tile_size .*0 .+ 1.0, window_function=window_hanning, get_norm=false, verbose=false, offset=CtrFT) where {T, M} Creates an 2N dimensional view of the data by tiling the N-dimensional data as specified by tile_size, tile_overlap and optionally tile_center. Additionally a window is applied to this view. If the window_type as defined in IndexFunArrays sums up to one, which is the case for window_linear and window_hanning, a linear decomposition of the data is obtained apart from possible border effects. `data`. the inputdata to decompose into a TiledView. No copies are made for the TiledView and the raw data can be accessed via myview.parent. `tile_size`. A Tuple describing the size of each tile. This size will form the first N dimensions of the result of size(myview). The second N dimensions refer to N-dimensional tile numbering. `rel_overlap`. Tuple specifying the relative overlap between successive tiles. The absolute overlap is then calculated as `round.(Int,tile_size./2.0 .* rel_overlap)`. `window_function`. The window function as defined in IndexFunArrays to apply to the TiledView. The result is currently not any longer a view as it is unclear how to wrap the multiplication into a view. For this reason the TiledView without the window applied is also returned and can be used for assignments. By default a von Hann window (window_hanning) is used. `get_norm`. An optional Boolean argument allowing to also obtain the normalization map for the boarder pixels, which not necessarily undergo all required window operations. In a future version it may be possible to automatically lay out the windowing such that this effect can be avoided. `verbose`. If true, diagnostic information on the window layout is printed. `offset`. defines where the center of the window is placed. See `IndexFunArrays.jl` for details. # Returns myview, matching_window = TiledWindowView ... a Tuple of two or three (get_norm=true) with `myview`. the TiledView of the data without the window which can also be written to. `matching_window`. a window that can be applied to the view via multiplication myview.*matching_window This is intentionally not provided as a product to separate the features conceptually when it comes to write access. `normalized`. only returned for get_norm=true. Contains an array with the normalization information by mapping the window back to the original data. This is useful for incomplete coverage of the tiles as well as using windows which do not sum up to one in the tiling process. Note that it may be dangerous to directly access the view via a simple .+= operation as it is not entirely clear, whether it is always garanteed that there could not be any running conditions with read-write operations, since some points in the referenced array are accessed multiple times. To avoid such an effect, you can, for example, only acess every second tile along each dimension in one call. # Examples ```jldoctest julia> data = ones(10,10).+0.0; julia> myview, matching_window = TiledWindowView(data, (5, 5);verbose=true); Tiles with pitch (3, 3) overlap by (2, 2) pixels. Window starts at (0.5, 0.5) and ends at (2.5, 2.5). julia> size(myview) (5, 5, 4, 4) julia> matching_window 5×5 IndexFunArray{Float64, 2, IndexFunArrays.var"#199#200"{Float64, Tuple{Float64, Float64}, Tuple{Int64, Int64}, Tuple{Float64, Float64}, Tuple{Float64, Float64}}}: 0.0214466 0.125 0.146447 0.125 0.0214466 0.125 0.728553 0.853553 0.728553 0.125 0.146447 0.853553 1.0 0.853553 0.146447 0.125 0.728553 0.853553 0.728553 0.125 0.0214466 0.125 0.146447 0.125 0.0214466 julia> windowed = collect(myview .* matching_window); julia> myview[:,:,:,:].=0 # cleares the original array julia> myview.parent 10×10 Matrix{Float64}: 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 julia> myview .+= windowed # writes the windowed data back into the array julia> data # lets see if the weigths correctly sum to one? 10×10 Matrix{Float64}: 0.728553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.853553 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 ``` # This result may also be used for subsequent normalization but can also be directly obtained by julia> myview, matching_window, normalized = TiledWindowView(rand(10,10).+0, (5, 5);get_norm=true); """ function TiledWindowView(data::AbstractArray{T,M}, tile_size::NTuple{M,Int}; rel_overlap::NTuple{M,Float64}=tile_size .*0 .+ 1.0, window_function=window_hanning, get_norm=false, verbose=false, keep_center=true, offset=CtrFT) where {T, M} tile_overlap = round.(Int,tile_size./2.0 .* rel_overlap) changeable = TiledView(data,tile_size, tile_overlap, keep_center=keep_center); win = get_window(changeable, window_function= window_function, get_norm=get_norm, verbose=verbose, offset=offset) if get_norm return (changeable, win...) else return (changeable, win) end end """ tile_centers(A, scale=nothing) returns the relative center coordinates of integer tile centers with respect to the integer center `1 .+ size(A) .÷ 2 ` The tuple `scale` is used to multiply the relative position with a physical pixelsize. See also: `eachtilerelpos` for a corresponding iterator """ function tile_centers(A, scale=nothing) return collect(eachtilerelpos(A, scale)) end """ eachtilerelpos(A, scale=nothing) returns a generator that iterates through the relative distance of each tile center `1 .+ size(A).÷2` to the center of the the untiled parent array `1 .+ size(parent).÷2` The tuple `scale` is used to multiply the relative position with a physical pixelsize. """ function eachtilerelpos(A, scale=nothing) nd = ndims(A)/2 ctr_array = (size(A.parent) .÷ 2) .+ 1 # center of the parent array num_tiles = size(A)[end-nd+1:end] # ctr_tile = (num_tiles.÷2 .+1) tile_ctr = (size(A)[1:nd] .÷ 2) .+ 1 if isnothing(scale) (pos_from_tile(A, tile_ctr, Tuple(idx)) .- ctr_array for idx in CartesianIndices(num_tiles)) # Only the "[" generate a 2D array # [(Tuple(idx).-1).* A.tile_period .+ ctr for idx in CartesianIndices(num_tiles)] else (scale .* (pos_from_tile(A, tile_ctr, Tuple(idx)) .- ctr_array) for idx in CartesianIndices(num_tiles)) end end """ eachtile(tiled_view::TiledView) returns an iterator which iterates through all tiles. Depending on your application you may also want to use `tiled_processing` for a convenient way to apply a function to each tile and join all tiles back together. If you need simultaneous access to the tiles and tile numbers, you can also use `eachtilenumber`. """ function eachtile(tiled_view::TiledView) nd = ndims(tiled_view)÷2 nz = ((size(tiled_view)[1:nd])..., prod(size(tiled_view)[nd+1:end])) reshaped = reshape(tiled_view, nz) return eachslice(reshaped, dims=nd+1) end """ eachtilenumber(tiled_view::TiledView) returns an iterator iterating though all the tile numbers. If you need access to the tiles themselves, use `eachtile` """ function eachtilenumber(tiled_view::TiledView) return (Tuple(tn) for tn in CartesianIndices(get_num_tiles(tiled_view))) end """ tiled_processing(tiled_view::TiledView, fct; verbose=true, dtype=eltype(tiled_view.parent), window_function=window_hanning) processes a raw dataset using tiled views by submitting each tile to the function `fct` and merging the results via the `window_function`. """ function tiled_processing(tiled_view::TiledView, fct; verbose=true, dtype=eltype(tiled_view.parent), window_function=window_hanning) @time res = zeros_like(tiled_view, dtype) res.parent .= zero(dtype) @time win = get_window(tiled_view, window_function=window_function) ttn = get_num_tiles(tiled_view) for (src, dest, tn) in zip(eachtile(tiled_view), eachtile(res), eachtilenumber(res)) if verbose perc = round(100 * (linear_index(tn, ttn)-1) ./ prod(ttn)) print("processing tile $(tn) out of $(ttn), $(perc)%\n") end size(src) res_tile = fct(collect(src)) dest .+= win .* res_tile end return res end """ tiled_processing(data, fct; verbose=true, dtype=eltype(data), window_function=window_hanning) processes a raw dataset using tiled views by submitting each tile to the function `fct` and merging the results via the `window_function`. """ function tiled_processing(data, fct, tile_size, tile_overlap; verbose=true, dtype=eltype(data), keep_center=false, window_function=window_hanning) tiles = TiledView(data, tile_size, tile_overlap, keep_center=keep_center); return tiled_processing(tiles,fct; verbose=verbose, dtype=dtype, window_function=window_function) end end # module
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2.520674
8,126
@everywhere function extForm(td, ωd, inheritData, baseProb, τ, Δt, T, fData, bData, dData, pDistr,coneBool = false) # extensive formulation could not have variable/constraint names # inheritData: [1]: sp, [2]: w, [3]: u (only contains the information for the linking time period) println("========= Disruption time $(td), scenario $(ωd) modeling ========="); # precalculate data Rdict = Dict(); Xdict = Dict(); for k in fData.brList Rdict[k] = fData.g[k]/(fData.g[k]^2 + fData.b[k]^2); Xdict[k] = -fData.b[k]/(fData.g[k]^2 + fData.b[k]^2); end Ω = [ω for ω in keys(pDistr.ωDistrn)]; Bparams = Dict(); for t in td:T # create B parameters for k in fData.brList # if the line is disrupted and it is within disruption time if (((k[1],k[2]) == ωd)|((k[2],k[1]) == ωd))&(t <= td + τ) Bparams[k,t] = 0; else Bparams[k,t] = 1; end end for i in fData.genIDList if (i == ωd)&(t <= td + τ) Bparams[i,t] = 0; else Bparams[i,t] = 1; end end end # set up the variables spDict = Dict(); sqDict = Dict(); for i in fData.genIDList for t in (td - 1):T spDict[i,t] = @variable(mExt, lowerbound = fData.Pmin[i], upperbound = fData.Pmax[i], basename="sp_$(td)_$(i)_$(t)"); sqDict[i,t] = @variable(mExt, lowerbound = fData.Qmin[i], upperbound = fData.Qmax[i], basename="sq_$(td)_$(i)_$(t)"); end end sphatsum = Dict(); for t in td:T for i in fData.IDList sphatsum[i,t] = @expression(mExt,0.0); if i in keys(fData.LocRev) for j in fData.LocRev[i] sphatsum[i,t] += spDict[j,t]; end end end end sqhatsum = Dict(); for t in td:T for i in fData.IDList sqhatsum[i,t] = @expression(mExt,0.0); if i in keys(fData.LocRev) for j in fData.LocRev[i] sqhatsum[i,t] += sqDict[j,t]; end end end end pDict = Dict(); qDict = Dict(); vDict = Dict(); wDict = Dict(); yDict = Dict(); zpDict = Dict(); zqDict = Dict(); lppDict = Dict(); lqpDict = Dict(); lpmDict = Dict(); lqmDict = Dict(); uDict = Dict(); fsDict = Dict(); for k in fData.brList for t in td:T pDict[k,t] = @variable(mExt, basename="p_$(td)_$(k)_$(t)"); qDict[k,t] = @variable(mExt, basename="q_$(td)_$(k)_$(t)"); end end for i in fData.IDList for t in td:T vDict[i,t] = @variable(mExt, lowerbound = fData.Vmin[i]^2, upperbound = fData.Vmax[i]^2, basename="v_$td"); lppDict[i,t] = @variable(mExt, lowerbound = 0, basename="lpp_$(td)_$(i)_$(t)"); lqpDict[i,t] = @variable(mExt, lowerbound = 0, basename="lqp_$(td)_$(i)_$(t)"); lpmDict[i,t] = @variable(mExt, lowerbound = 0, basename="lpm_$(td)_$(i)_$(t)"); lqmDict[i,t] = @variable(mExt, lowerbound = 0, basename="lqm_$(td)_$(i)_$(t)"); end end for i in bData.IDList wDict[i,td - 1] = @variable(mExt, lowerbound = 0, upperbound = bData.cap[i], basename="w_$(td)_$(i)_$(td - 1)"); uDict[i] = @variable(mExt, lowerbound = 0, upperbound = bData.uCap[i], basename="u_$(td)_$(i)"); for t in td:T wDict[i,t] = @variable(mExt, lowerbound = 0, upperbound = bData.cap[i], basename="w_$(td)_$(i)_$(t)"); yDict[i,t] = @variable(mExt, basename="y_$(td)_$(i)_$(t)"); zpDict[i,t] = @variable(mExt, basename="zp_$(td)_$(i)_$(t)"); zqDict[i,t] = @variable(mExt, basename="zq_$(td)_$(i)_$(t)"); end end # set up the constraints for i in fData.IDList for t in td:T @constraint(mExt, sum(zpDict[b,t] for b in bData.IDList if bData.Loc[b] == i) + lppDict[i,t] - lpmDict[i,t] + sphatsum[i,t] - dData.pd[i][t] == sum(pDict[k,t] for k in fData.branchDict1[i])); @constraint(mExt, sum(zqDict[b,t] for b in bData.IDList if bData.Loc[b] == i) + lqpDict[i,t] - lqmDict[i,t] + sqhatsum[i,t] - dData.qd[i][t] == sum(qDict[k,t] for k in fData.branchDict1[i])); end end for i in fData.genIDList if td != 1 @constraint(mExt, spDict[i,td - 1] == inheritData[1][i]); end for t in td:T if (t != 1)&(Bparams[i,t] == 1) @constraint(mExt, spDict[i,t] - spDict[i,t - 1] <= fData.RU[i]); @constraint(mExt, spDict[i,t] - spDict[i,t - 1] >= fData.RD[i]); end if Bparams[i,t] == 0 @constraint(mExt, spDict[i,t] == 0); @constraint(mExt, sqDict[i,t] == 0); end end end for k in fData.brList for t in td:T @constraint(mExt, pDict[k,t] == -pDict[(k[2],k[1],k[3]),t]); @constraint(mExt, qDict[k,t] == -qDict[(k[2],k[1],k[3]),t]); if Bparams[k,t] == 1 if coneBool @constraint(mExt, norm([pDict[k,t],qDict[k,t]]) <= fData.rateA[k]); else @constraint(mExt, pDict[k,t]^2 + qDict[k,t]^2 <= fData.rateA[k]^2); end @constraint(mExt, vDict[k[2],t] == vDict[k[1],t] - 2*(Rdict[k]*pDict[k,t] + Xdict[k]*qDict[k,t])); else @constraint(mExt, pDict[k,t] == 0); @constraint(mExt, qDict[k,t] == 0); end end end for i in bData.IDList if td != 1 @constraint(mExt, uDict[i] == inheritData[3][i]); end @constraint(mExt, wDict[i,td - 1] == inheritData[2][i]); for t in td:T @constraint(mExt, wDict[i,t] == wDict[i,t - 1] - yDict[i,t]*Δt); if coneBool @constraint(mExt, norm([zpDict[i,t],zqDict[i,t]]) <= uDict[i]); else @constraint(mExt, zpDict[i,t]^2 + zqDict[i,t]^2 <= uDict[i]^2); end for l in 1:length(bData.ηα[i]) @constraint(mExt, zpDict[i,t] <= bData.ηα[i][l]*yDict[i,t] + bData.ηβ[i][l]); end @constraint(mExt, wDict[i,t] <= bData.cap[i]); end end # recursion through the possible scenario tList = sort([t for t in keys(pDistr.tDistrn)]); objExpr = getobjective(mExt); if td == 1 objExpr += sum(bData.cost[i]*uDict[i] for i in bData.IDList); # only the first pass will execute this end for tp in tList if td == 1 if td + tp > T # if the next disruption is over the time horizon dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:T); for t in td:T for i in fData.genIDList # add generator cost if fData.cp[i].n == 3 if coneBool fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)"); dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t]; @constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4); else dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t]; end elseif fData.cp[i].n == 2 dExpr += fData.cp[i].params[1]*spDict[i,t]; end end end objExpr += baseProb*pDistr.tDistrn[tp]*dExpr; @objective(mExt, Min, objExpr); else # if not dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:(td + tp - 1)); for t in td:(td + tp - 1) for i in fData.genIDList # add generator cost if fData.cp[i].n == 3 if coneBool fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)"); dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t]; @constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4); else dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t]; end elseif fData.cp[i].n == 2 dExpr += fData.cp[i].params[1]*spDict[i,t]; end end end for ω in Ω objExpr += baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω]*dExpr; spInherit = Dict(); wInherit = Dict(); uInherit = Dict(); for i in fData.genIDList spInherit[i] = spDict[i,td + tp - 1]; end for i in bData.IDList wInherit[i] = wDict[i,td + tp - 1]; uInherit[i] = uDict[i]; end inheritData = [spInherit,wInherit,uInherit]; @objective(mExt, Min, objExpr); # println("=========================",1," ",td," ",tp,"========================="); # println(mExt.obj); global mExt = extForm(td + tp, ω, inheritData, baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω], τ, Δt, T, fData, bData, dData, pDistr, coneBool); # println("=========================",11," ",td," ",tp,"========================="); # println(mExt.obj); objExpr = getobjective(mExt); end end else if td + τ + tp > T # if the next disruption is over the time horizon # add to the objective function dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:T); for t in td:T for i in fData.genIDList # add generator cost if fData.cp[i].n == 3 if coneBool fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)"); dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t]; @constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4); else dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t]; end elseif fData.cp[i].n == 2 dExpr += fData.cp[i].params[1]*spDict[i,t]; end end end objExpr += baseProb*pDistr.tDistrn[tp]*dExpr; @objective(mExt, Min, objExpr); else # if not # add the current part to the objective function # recursion to the next disruption dExpr = fData.cz*sum(sum(lppDict[i,t] + lqpDict[i,t] + lpmDict[i,t] + lqmDict[i,t] for i in fData.IDList) for t in td:(td + tp + τ - 1)); for t in td:(td + tp + τ - 1) for i in fData.genIDList # add generator cost if fData.cp[i].n == 3 if coneBool fsDict[i,t] = @variable(mExt, lowerbound = 0, basename = "fs_$(td)_$(i)_$(t)"); dExpr += fData.cp[i].params[1]*fsDict[i,t] + fData.cp[i].params[2]*spDict[i,t]; @constraint(mExt, norm([spDict[i,t],fsDict[i,t] - 1/4]) <= fsDict[i,t] + 1/4); else dExpr += fData.cp[i].params[1]*(spDict[i,t]^2) + fData.cp[i].params[2]*spDict[i,t]; end elseif fData.cp[i].n == 2 dExpr += fData.cp[i].params[1]*spDict[i,t]; end end end for ω in Ω objExpr += baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω]*dExpr; spInherit = Dict(); wInherit = Dict(); uInherit = Dict(); for i in fData.genIDList spInherit[i] = spDict[i,td + tp + τ - 1]; end for i in bData.IDList wInherit[i] = wDict[i,td + tp + τ - 1]; uInherit[i] = uDict[i]; end inheritData = [spInherit,wInherit,uInherit]; @objective(mExt, Min, objExpr); # println("=========================",2," ",td," ",tp,"========================="); # println(mExt.obj); global mExt = extForm(td + tp + τ, ω, inheritData, baseProb*pDistr.tDistrn[tp]*pDistr.ωDistrn[ω], τ, Δt, T, fData, bData, dData, pDistr, coneBool); # println("=========================",22," ",td," ",tp,"========================="); # println(mExt.obj); objExpr = getobjective(mExt); end end end end return mExt; end
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1.588136
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# \file # \brief Callbacks, Attributes and Attribute Values definitions. # Avoid using these definitions. Use the strings instead. # # See Copyright Notice in iup.h # # Deprecated definitions # # Avoid using these definitions. Use the strings instead. # # Define __IUPDEF_H to avoid the inclusion of this header # constant RUN = "RUN" constant ENGLISH = "ENGLISH" constant PORTUGUESE = "PORTUGUESE" constant SBH = "SBH" constant SBV = "SBV" ########################################################################## # Callbacks # ########################################################################## constant DEFAULT_ACTION = "DEFAULT_ACTION" constant IDLE_ACTION = "IDLE_ACTION" constant ACTION = "ACTION" constant GETFOCUS_CB = "GETFOCUS_CB" constant KILLFOCUS_CB = "KILLFOCUS_CB" constant K_ANY = "K_ANY" constant KEYPRESS_CB = "KEYPRESS_CB" constant HELP_CB = "HELP_CB" constant SCROLL_CB = "SCROLL_CB" constant RESIZE_CB = "RESIZE_CB" constant MOTION_CB = "MOTION_CB" constant BUTTON_CB = "BUTTON_CB" constant ENTERWINDOW_CB = "ENTERWINDOW_CB" constant LEAVEWINDOW_CB = "LEAVEWINDOW_CB" constant WHEEL_CB = "WHEEL_CB" constant MASK_CB = "MASK_CB" constant OPEN_CB = "OPEN_CB" constant HIGHLIGHT_CB = "HIGHLIGHT_CB" constant MENUCLOSE_CB = "MENUCLOSE_CB" constant MAP_CB = "MAP_CB" constant CLOSE_CB = "CLOSE_CB" constant SHOW_CB = "SHOW_CB" constant DROPFILES_CB = "DROPFILES_CB" constant WOM_CB = "WOM_CB" ########################################################################## # Attributes # ########################################################################## constant DIRECTION = "DIRECTION" constant ACTIVE = "ACTIVE" constant BGCOLOR = "BGCOLOR" constant FRAMECOLOR = "FRAMECOLOR" constant FGCOLOR = "FGCOLOR" constant COLOR = "COLOR" constant WID = "WID" constant SIZE = "SIZE" constant RASTERSIZE = "RASTERSIZE" constant TITLE = "TITLE" constant VALUE = "VALUE" constant VISIBLE = "VISIBLE" constant FONT = "FONT" constant TIP = "TIP" constant EXPAND = "EXPAND" constant SEPARATOR = "SEPARATOR" constant HOTSPOT = "HOTSPOT" constant HEIGHT = "HEIGHT" constant WIDTH = "WIDTH" constant KEY = "KEY" constant MULTIPLE = "MULTIPLE" constant DROPDOWN = "DROPDOWN" constant VISIBLE_ITEMS = "VISIBLE_ITEMS" constant MARGIN = "MARGIN" constant GAP = "GAP" constant ALIGNMENT = "ALIGNMENT" constant IMAGE = "IMAGE" constant IMINACTIVE = "IMINACTIVE" constant IMPRESS = "IMPRESS" constant WIN_SAVEBITS = "WIN_SAVEBITS" constant NC = "NC" constant MASK = "MASK" constant APPEND = "APPEND" constant BORDER = "BORDER" constant CARET = "CARET" constant SELECTION = "SELECTION" constant SELECTEDTEXT = "SELECTEDTEXT" constant INSERT = "INSERT" constant CONID = "CONID" constant CURSOR = "CURSOR" constant ICON = "ICON" constant MENUBOX = "MENUBOX" constant MINBOX = "MINBOX" constant MAXBOX = "MAXBOX" constant RESIZE = "RESIZE" constant MENU = "MENU" constant STARTFOCUS = "STARTFOCUS" constant PARENTDIALOG = "PARENTDIALOG" constant SHRINK = "SHRINK" constant DEFAULTENTER = "DEFAULTENTER" constant DEFAULTESC = "DEFAULTESC" constant X = "X" constant Y = "Y" constant TOOLBOX = "TOOLBOX" constant CONTROL = "CONTROL" constant READONLY = "READONLY" constant SCROLLBAR = "SCROLLBAR" constant POSY = "POSY" constant POSX = "POSX" constant DX = "DX" constant DY = "DY" constant XMAX = "XMAX" constant XMIN = "XMIN" constant YMAX = "YMAX" constant YMIN = "YMIN" constant RED = "255 0 0" constant GREEN = "0 255 0" constant BLUE = "0 0 255" constant MIN = "MIN" constant MAX = "MAX" constant TIME = "TIME" constant DRAG = "DRAG" constant DROP = "DROP" constant REPAINT = "REPAINT" constant TOPMOST = "TOPMOST" constant CLIPCHILDREN = "CLIPCHILDREN" constant DIALOGTYPE = "DIALOGTYPE" constant FILE = "FILE" constant MULTIPLEFILES = "MULTIPLEFILES" constant FILTER = "FILTER" constant FILTERUSED = "FILTERUSED" constant FILTERINFO = "FILTERINFO" constant EXTFILTER = "EXTFILTER" constant DIRECTORY = "DIRECTORY" constant ALLOWNEW = "ALLOWNEW" constant NOOVERWRITEPROMPT = "NOOVERWRITEPROMPT" constant NOCHANGEDIR = "NOCHANGEDIR" constant FILEEXIST = "FILEEXIST" constant STATUS = "STATUS" constant LOCKLOOP = "LOCKLOOP" constant SYSTEM = "SYSTEM" constant DRIVER = "DRIVER" constant SCREENSIZE = "SCREENSIZE" constant SYSTEMLANGUAGE = "SYSTEMLANGUAGE" constant COMPUTERNAME = "COMPUTERNAME" constant USERNAME = "USERNAME" constant OPEN = "OPEN" constant SAVE = "SAVE" constant DIR = "DIR" constant HORIZONTAL = "HORIZONTAL" constant VERTICAL = "VERTICAL" ########################################################################## # Attribute Values # ########################################################################## constant YES = "YES" constant NO = "NO" constant ON = "ON" constant OFF = "OFF" constant ACENTER = "ACENTER" constant ALEFT = "ALEFT" constant ARIGHT = "ARIGHT" constant ATOP = "ATOP" constant ABOTTOM = "ABOTTOM" constant NORTH = "NORTH" constant SOUTH = "SOUTH" constant WEST = "WEST" constant EAST = "EAST" constant NE = "NE" constant SE = "SE" constant NW = "NW" constant SW = "SW" constant FULLSCREEN = "FULLSCREEN" constant FULL = "FULL" constant HALF = "HALF" constant THIRD = "THIRD" constant QUARTER = "QUARTER" constant EIGHTH = "EIGHTH" constant ARROW = "ARROW" constant BUSY = "BUSY" constant RESIZE_N = "RESIZE_N" constant RESIZE_S = "RESIZE_S" constant RESIZE_E = "RESIZE_E" constant RESIZE_W = "RESIZE_W" constant RESIZE_NE = "RESIZE_NE" constant RESIZE_NW = "RESIZE_NW" constant RESIZE_SE = "RESIZE_SE" constant RESIZE_SW = "RESIZE_SW" constant MOVE = "MOVE" constant HAND = "HAND" constant NONE = "NONE" constant IUP = "IUP" constant CROSS = "CROSS" constant PEN = "PEN" constant TEXT = "TEXT" constant RESIZE_C = "RESIZE_C" constant OPENHAND = "OPENHAND" ################### # Fonts # ################### constant HELVETICA_NORMAL_8 = "HELVETICA_NORMAL_8" constant HELVETICA_ITALIC_8 = "HELVETICA_ITALIC_8" constant HELVETICA_BOLD_8 = "HELVETICA_BOLD_8" constant HELVETICA_NORMAL_10 = "HELVETICA_NORMAL_10" constant HELVETICA_ITALIC_10 = "HELVETICA_ITALIC_10" constant HELVETICA_BOLD_10 = "HELVETICA_BOLD_10" constant HELVETICA_NORMAL_12 = "HELVETICA_NORMAL_12" constant HELVETICA_ITALIC_12 = "HELVETICA_ITALIC_12" constant HELVETICA_BOLD_12 = "HELVETICA_BOLD_12" constant HELVETICA_NORMAL_14 = "HELVETICA_NORMAL_14" constant HELVETICA_ITALIC_14 = "HELVETICA_ITALIC_14" constant HELVETICA_BOLD_14 = "HELVETICA_BOLD_14" constant COURIER_NORMAL_8 = "COURIER_NORMAL_8" constant COURIER_ITALIC_8 = "COURIER_ITALIC_8" constant COURIER_BOLD_8 = "COURIER_BOLD_8" constant COURIER_NORMAL_10 = "COURIER_NORMAL_10" constant COURIER_ITALIC_10 = "COURIER_ITALIC_10" constant COURIER_BOLD_10 = "COURIER_BOLD_10" constant COURIER_NORMAL_12 = "COURIER_NORMAL_12" constant COURIER_ITALIC_12 = "COURIER_ITALIC_12" constant COURIER_BOLD_12 = "COURIER_BOLD_12" constant COURIER_NORMAL_14 = "COURIER_NORMAL_14" constant COURIER_ITALIC_14 = "COURIER_ITALIC_14" constant COURIER_BOLD_14 = "COURIER_BOLD_14" constant TIMES_NORMAL_8 = "TIMES_NORMAL_8" constant TIMES_ITALIC_8 = "TIMES_ITALIC_8" constant TIMES_BOLD_8 = "TIMES_BOLD_8" constant TIMES_NORMAL_10 = "TIMES_NORMAL_10" constant TIMES_ITALIC_10 = "TIMES_ITALIC_10" constant TIMES_BOLD_10 = "TIMES_BOLD_10" constant TIMES_NORMAL_12 = "TIMES_NORMAL_12" constant TIMES_ITALIC_12 = "TIMES_ITALIC_12" constant TIMES_BOLD_12 = "TIMES_BOLD_12" constant TIMES_NORMAL_14 = "TIMES_NORMAL_14" constant TIMES_ITALIC_14 = "TIMES_ITALIC_14" constant TIMES_BOLD_14 = "TIMES_BOLD_14" ########################################################################## # Keys # ########################################################################## constant K_exclam = "K_exclam" constant K_quotedbl = "K_quotedbl" constant K_numbersign = "K_numbersign" constant K_dollar = "K_dollar" constant K_percent = "K_percent" constant K_ampersand = "K_ampersand" constant K_quoteright = "K_quoteright" constant K_parentleft = "K_parentleft" constant K_parentright = "K_parentright" constant K_asterisk = "K_asterisk" constant K_plus = "K_plus" constant K_comma = "K_comma" constant K_minus = "K_minus" constant K_period = "K_period" constant K_slash = "K_slash" constant K_0 = "K_0" constant K_1 = "K_1" constant K_2 = "K_2" constant K_3 = "K_3" constant K_4 = "K_4" constant K_5 = "K_5" constant K_6 = "K_6" constant K_7 = "K_7" constant K_8 = "K_8" constant K_9 = "K_9" constant K_colon = "K_colon" constant K_semicolon = "K_semicolon " constant K_less = "K_less" constant K_equal = "K_equal" constant K_greater = "K_greater" constant K_question = "K_question" constant K_at = "K_at" constant K_A = "K_A" constant K_B = "K_B" constant K_C = "K_C" constant K_D = "K_D" constant K_E = "K_E" constant K_F = "K_F" constant K_G = "K_G" constant K_H = "K_H" constant K_I = "K_I" constant K_J = "K_J" constant K_K = "K_K" constant K_L = "K_L" constant K_M = "K_M" constant K_N = "K_N" constant K_O = "K_O" constant K_P = "K_P" constant K_Q = "K_Q" constant K_R = "K_R" constant K_S = "K_S" constant K_T = "K_T" constant K_U = "K_U" constant K_V = "K_V" constant K_W = "K_W" constant K_X = "K_X" constant K_Y = "K_Y" constant K_Z = "K_Z" constant K_bracketleft = "K_bracketleft" constant K_backslash = "K_backslash" constant K_bracketright = "K_bracketright" constant K_circum = "K_circum" constant K_underscore = "K_underscore" constant K_quoteleft = "K_quoteleft" constant K_a = "K_a" constant K_b = "K_b" constant K_c = "K_c" constant K_d = "K_d" constant K_e = "K_e" constant K_f = "K_f" constant K_g = "K_g" constant K_h = "K_h" constant K_i = "K_i" constant K_j = "K_j" constant K_k = "K_k" constant K_l = "K_l" constant K_m = "K_m" constant K_n = "K_n" constant K_o = "K_o" constant K_p = "K_p" constant K_q = "K_q" constant K_r = "K_r" constant K_s = "K_s" constant K_t = "K_t" constant K_u = "K_u" constant K_v = "K_v" constant K_w = "K_w" constant K_x = "K_x" constant K_y = "K_y" constant K_z = "K_z" constant K_braceleft = "K_braceleft" constant K_bar = "K_bar" constant K_braceright = "K_braceright" constant K_tilde = "K_tilde" constant K_cA = "K_cA" constant K_cB = "K_cB" constant K_cC = "K_cC" constant K_cD = "K_cD" constant K_cE = "K_cE" constant K_cF = "K_cF" constant K_cG = "K_cG" constant K_cJ = "K_cJ" constant K_cK = "K_cK" constant K_cL = "K_cL" constant K_cN = "K_cN" constant K_cO = "K_cO" constant K_cP = "K_cP" constant K_cQ = "K_cQ" constant K_cR = "K_cR" constant K_cS = "K_cS" constant K_cT = "K_cT" constant K_cU = "K_cU" constant K_cV = "K_cV" constant K_cW = "K_cW" constant K_cX = "K_cX" constant K_cY = "K_cY" constant K_cZ = "K_cZ" constant K_mA = "K_mA" constant K_mB = "K_mB" constant K_mC = "K_mC" constant K_mD = "K_mD" constant K_mE = "K_mE" constant K_mF = "K_mF" constant K_mG = "K_mG" constant K_mH = "K_mH" constant K_mI = "K_mI" constant K_mJ = "K_mJ" constant K_mK = "K_mK" constant K_mL = "K_mL" constant K_mM = "K_mM" constant K_mN = "K_mN" constant K_mO = "K_mO" constant K_mP = "K_mP" constant K_mQ = "K_mQ" constant K_mR = "K_mR" constant K_mS = "K_mS" constant K_mT = "K_mT" constant K_mU = "K_mU" constant K_mV = "K_mV" constant K_mW = "K_mW" constant K_mX = "K_mX" constant K_mY = "K_mY" constant K_mZ = "K_mZ" constant K_BS = "K_BS" constant K_TAB = "K_TAB" constant K_CR = "K_CR" constant K_SP = "K_SP" constant K_ESC = "K_ESC" constant K_sCR = "K_sCR" constant K_sTAB = "K_sTAB" constant K_cTAB = "K_cTAB" constant K_mTAB = "K_mTAB" constant K_HOME = "K_HOME" constant K_UP = "K_UP" constant K_PGUP = "K_PGUP" constant K_LEFT = "K_LEFT" constant K_RIGHT = "K_RIGHT" constant K_END = "K_END" constant K_DOWN = "K_DOWN" constant K_PGDN = "K_PGDN" constant K_MIDDLE = "K_MIDDLE" constant K_INS = "K_INS" constant K_DEL = "K_DEL" constant K_sHOME = "K_sHOME" constant K_sUP = "K_sUP" constant K_sPGUP = "K_sPGUP" constant K_sLEFT = "K_sLEFT" constant K_sRIGHT = "K_sRIGHT" constant K_sEND = "K_sEND" constant K_sDOWN = "K_sDOWN" constant K_sPGDN = "K_sPGDN" constant K_cHOME = "K_cHOME" constant K_cPGUP = "K_cPGUP" constant K_cLEFT = "K_cLEFT" constant K_cRIGHT = "K_cRIGHT" constant K_cEND = "K_cEND" constant K_cPGDN = "K_cPGDN" constant K_cUP = "K_cUP" constant K_cDOWN = "K_cDOWN" constant K_cMIDDLE = "K_cMIDDLE" constant K_cINS = "K_cINS" constant K_cDEL = "K_cDEL" constant K_mHOME = "K_mHOME" constant K_mPGUP = "K_mPGUP" constant K_mLEFT = "K_mLEFT" constant K_mRIGHT = "K_mRIGHT" constant K_mEND = "K_mEND" constant K_mPGDN = "K_mPGDN" constant K_mUP = "K_mUP" constant K_mDOWN = "K_mDOWN" constant K_mINS = "K_mINS" constant K_mDEL = "K_mDEL" constant K_F1 = "K_F1" constant K_F2 = "K_F2" constant K_F3 = "K_F3" constant K_F4 = "K_F4" constant K_F5 = "K_F5" constant K_F6 = "K_F6" constant K_F7 = "K_F7" constant K_F8 = "K_F8" constant K_F9 = "K_F9" constant K_F10 = "K_F10" constant K_F11 = "K_F11" constant K_F12 = "K_F12" constant K_sF1 = "K_sF1" constant K_sF2 = "K_sF2" constant K_sF3 = "K_sF3" constant K_sF4 = "K_sF4" constant K_sF5 = "K_sF5" constant K_sF6 = "K_sF6" constant K_sF7 = "K_sF7" constant K_sF8 = "K_sF8" constant K_sF9 = "K_sF9" constant K_sF10 = "K_sF10" constant K_sF11 = "K_sF11" constant K_sF12 = "K_sF12" constant K_cF1 = "K_cF1" constant K_cF2 = "K_cF2" constant K_cF3 = "K_cF3" constant K_cF4 = "K_cF4" constant K_cF5 = "K_cF5" constant K_cF6 = "K_cF6" constant K_cF7 = "K_cF7" constant K_cF8 = "K_cF8" constant K_cF9 = "K_cF9" constant K_cF10 = "K_cF10" constant K_cF11 = "K_cF11" constant K_cF12 = "K_cF12" constant K_mF1 = "K_mF1" constant K_mF2 = "K_mF2" constant K_mF3 = "K_mF3" constant K_mF4 = "K_mF4" constant K_mF5 = "K_mF5" constant K_mF6 = "K_mF6" constant K_mF7 = "K_mF7" constant K_mF8 = "K_mF8" constant K_mF9 = "K_mF9" constant K_mF10 = "K_mF10" constant K_m1 = "K_m1" constant K_m2 = "K_m2" constant K_m3 = "K_m3" constant K_m4 = "K_m4" constant K_m5 = "K_m5" constant K_m6 = "K_m6" constant K_m7 = "K_m7" constant K_m8 = "K_m8" constant K_m9 = "K_m9" constant K_m0 = "K_m0" ############## # Colorbar # ############## constant NUM_PARTS = "NUM_PARTS" constant NUM_CELLS = "NUM_CELLS" constant CELL = "CELL" constant PREVIEW_SIZE = "PREVIEW_SIZE" constant SHOW_PREVIEW = "SHOW_PREVIEW" constant SHOW_SECONDARY = "SHOW_SECONDARY" constant PRIMARY_CELL = "PRIMARY_CELL" constant SECONDARY_CELL = "SECONDARY_CELL" constant ORIENTATION = "ORIENTATION" constant SQUARED = "SQUARED" constant SHADOWED = "SHADOWED" constant BUFFERIZE = "BUFFERIZE" constant TRANSPARENCY = "TRANSPARENCY" constant CELL_CB = "CELL_CB" constant EXTENDED_CB = "EXTENDED_CB" constant SELECT_CB = "SELECT_CB" constant SWITCH_CB = "SWITCH_CB" constant VERTICAL = "VERTICAL" constant HORIZONTAL = "HORIZONTAL" ############## # Cells # ############## constant ALL = "ALL" constant BOXED = "BOXED" constant CLIPPED = "CLIPPED" constant TRANSPARENT = "TRANSPARENT" constant NON_SCROLLABLE_LINES = "NON_SCROLLABLE_LINES" constant NON_SCROLLABLE_COLS = "NON_SCROLLABLE_COLS" constant ORIGIN = "ORIGIN" constant NO_COLOR = "NO_COLOR" constant FIRST_LINE = "FIRST_LINE" constant FIRST_COL = "FIRST_COL" constant DOUBLE_BUFFER = "DOUBLE_BUFFER" constant LIMITS = "LIMITS" constant CANVAS = "CANVAS" constant IMAGE_CANVAS = "IMAGE_CANVAS" constant FULL_VISIBLE = "FULL_VISIBLE" constant MOUSECLICK_CB = "MOUSECLICK_CB" constant MOUSEMOTION_CB = "MOUSEMOTION_CB" constant DRAW_CB = "DRAW_CB" constant WIDTH_CB = "WIDTH_CB" constant HEIGHT_CB = "HEIGHT_CB" constant NLINES_CB = "NLINES_CB" constant NCOLS_CB = "NCOLS_CB" constant HSPAN_CB = "HSPAN_CB" constant VSPAN_CB = "VSPAN_CB" constant SCROLLING_CB = "SCROLLING_CB" ################### # ColorBrowser # ################### constant RGB = "RGB" constant CHANGE_CB = "CHANGE_CB" constant DRAG_CB = "DRAG_CB" ################### # Val # ################### constant ICTL_MOUSEMOVE_CB = "MOUSEMOVE_CB" constant ICTL_BUTTON_PRESS_CB = "BUTTON_PRESS_CB" constant ICTL_BUTTON_RELEASE_CB = "BUTTON_RELEASE_CB" constant ICTL_HORIZONTAL = "HORIZONTAL" constant ICTL_VERTICAL = "VERTICAL" constant ICTL_SHOWTICKS = "SHOWTICKS" ################### # Tabs # ################### constant ICTL_TOP = "TOP" constant ICTL_BOTTOM = "BOTTOM" constant ICTL_LEFT = "LEFT" constant ICTL_RIGHT = "RIGHT" constant ICTL_TABTYPE = "TABTYPE" constant ICTL_TABTITLE = "TABTITLE" constant ICTL_TABSIZE = "TABSIZE" constant ICTL_TABCHANGE_CB = "TABCHANGE_CB" constant ICTL_FONT = "FONT" constant ICTL_FONT_ACTIVE = "FONT_ACTIVE" constant ICTL_FONT_INACTIVE = "FONT_INACTIVE" ################### # Gauge # ################### constant ICTL_SHOW_TEXT = "SHOW_TEXT" constant ICTL_DASHED = "DASHED" constant ICTL_MARGIN = "MARGIN" constant ICTL_TEXT = "TEXT" ################### # Dial # ################### constant ICTL_DENSITY = "DENSITY" constant ICTL_HORIZONTAL = "HORIZONTAL" constant ICTL_VERTICAL = "VERTICAL" constant ICTL_CIRCULAR = "CIRCULAR" constant ICTL_UNIT = "UNIT" ################### # Matrix # ################### constant ENTERITEM_CB = "ENTERITEM_CB" constant LEAVEITEM_CB = "LEAVEITEM_CB" constant EDITION_CB = "EDITION_CB" constant CLICK_CB = "CLICK_CB" constant DROP_CB = "DROP_CB" constant DROPSELECT_CB = "DROPSELECT_CB" constant DROPCHECK_CB = "DROPCHECK_CB" constant SCROLL_CB = "SCROLL_CB" constant VALUE_CB = "VALUE_CB" constant VALUE_EDIT_CB = "VALUE_EDIT_CB" constant FIELD_CB = "FIELD_CB" constant RESIZEMATRIX = "RESIZEMATRIX" constant ADDLIN = "ADDLIN" constant ADDCOL = "ADDCOL" constant DELLIN = "DELLIN" constant DELCOL = "DELCOL" constant NUMLIN = "NUMLIN" constant NUMCOL = "NUMCOL" constant NUMLIN_VISIBLE = "NUMLIN_VISIBLE" constant NUMCOL_VISIBLE = "NUMCOL_VISIBLE" constant MARKED = "MARKED" constant WIDTHDEF = "WIDTHDEF" constant HEIGHTDEF = "HEIGHTDEF" constant AREA = "AREA" constant MARK_MODE = "MARK_MODE" constant LIN = "LIN" constant COL = "COL" constant LINCOL = "LINCOL" constant CELL = "CELL" constant EDIT_MODE = "EDIT_MODE" constant FOCUS_CELL = "FOCUS_CELL" constant ORIGIN = "ORIGIN" constant REDRAW = "REDRAW" constant PREVIOUSVALUE = "PREVIOUSVALUE" constant MOUSEMOVE_CB = "MOUSEMOVE_CB" ################### # Tree # ################### constant ADDLEAF = "ADDLEAF" constant ADDBRANCH = "ADDBRANCH" constant DELNODE = "DELNODE" constant IMAGELEAF = "IMAGELEAF" constant IMAGEBRANCHCOLLAPSED = "IMAGEBRANCHCOLLAPSED" constant IMAGEBRANCHEXPANDED = "IMAGEBRANCHEXPANDED" constant IMAGEEXPANDED = "IMAGEEXPANDED" constant KIND = "KIND" constant PARENT = "PARENT" constant DEPTH = "DEPTH" constant MARKED = "MARKED" constant ADDEXPANDED = "ADDEXPANDED" constant CTRL = "CTRL" constant SHIFT = "SHIFT" constant STATE = "STATE" constant STARTING = "STARTING" constant LEAF = "LEAF" constant BRANCH = "BRANCH" constant SELECTED = "SELECTED" constant CHILDREN = "CHILDREN" constant MARKED = "MARKED" constant ROOT = "ROOT" constant LAST = "LAST" constant PGUP = "PGUP" constant PGDN = "PGDN" constant NEXT = "NEXT" constant PREVIOUS = "PREVIOUS" constant INVERT = "INVERT" constant BLOCK = "BLOCK" constant CLEARALL = "CLEARALL" constant MARKALL = "MARKALL" constant INVERTALL = "INVERTALL" constant REDRAW = "REDRAW" constant COLLAPSED = "COLLAPSED" constant EXPANDED = "EXPANDED" constant SELECTION_CB = "SELECTION_CB" constant BRANCHOPEN_CB = "BRANCHOPEN_CB" constant BRANCHCLOSE_CB = "BRANCHCLOSE_CB" constant RIGHTCLICK_CB = "RIGHTCLICK_CB" constant EXECUTELEAF_CB = "EXECUTELEAF_CB" constant RENAMENODE_CB = "RENAMENODE_CB" constant IMGLEAF = "IMGLEAF" constant IMGCOLLAPSED = "IMGCOLLAPSED" constant IMGEXPANDED = "IMGEXPANDED" constant IMGBLANK = "IMGBLANK" constant IMGPAPER = "IMGPAPER"
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########################################################################## # Basic functionality for doing MPS calculations with OBC # ########################################################################## using LinearAlgebra using Arpack # Define sites as 3 legged tensors filled with elements of some type Site{T} = Array{T,3} # An MPS is an array of Sites of a certain type MPS{T} = Vector{Site{T}} # Define operators as 4 legged tensors filled with elements of some type Operator{T} = Array{T,4} # A MPO is an array of Operators MPO{T} = Vector{Operator{T}} """ random_mps_obc(N::Int, D::Int, d, tensortype::Type{T}=ComplexF64)::MPS{T} where T Function to generate a random MPS with OBC N: Number of sites D: Bond dimension d: Vector of physical dimensions, if a single integer dimension is given, it is assumed that all physical dimensions are the same, if varying dimensions are wanted a vector of integers of length N has to be supplied The convention for the 3 index tensors is that the first two are the virtual ones, the last one is the physical one 3 | 1--A--2 """ function random_mps_obc(N::Int, D::Int, d, tensortype::Type{T} = ComplexF64)::MPS{T} where {T} # Ensure the the system size is at least two @assert(N > 1) # Initialize mps = Array{Site{T}}(undef, N) if isa(d, Number) # Single number, I assume all dimensions are the same dim = d * ones(Int64, N) else # Make sure that the input is really a vector as julia distinguishes between nx1 matrices and column vectors dim = vec(d) # Make sure input is valid @assert(length(dim) == N) end # Left boundary tensor (row vector) mps[1] = rand(tensortype, 1, D, dim[1]) # Right boundary tensor (column vector) mps[N] = rand(tensortype, D, 1, dim[N]) # Tensors in between for i = 2:N-1 mps[i] = rand(tensortype, D, D, dim[i]) end return mps end """ basis_state_obc(configuration::Vector{<:Int}, d::Int=2)::MPS Prepare the a product state corresponding |configuration> on N sites where configuration is an Array containing N elements from 1 to d. Each site is then initialized in the dth canonical basis state """ function basis_state_obc(configuration::Vector{<:Int}, d::Int = 2)::MPS{Float64} # Some error checking if any(x -> (x < 1 || x > d), configuration) throw(ArgumentError("configuration must contain integer elements in the range from 1 to d, got d=$(repr(d)), configuration=$(repr(configuration))")) end # Generate the MPS N = length(configuration) psi = MPS{Float64}(undef, N) tensors = Vector{Array{Float64,3}}(undef, d) for i = 1:d tmp = zeros(Float64, 1, 1, d) tmp[1, 1, i] = 1.0 tensors[i] = tmp end for i = 1:N psi[i] = tensors[configuration[i]] end return psi end """ calculate_overlap(mps1::MPS,mps2::MPS)::Number Given two mps, compute the overlap <mps1|mps2>. """ function calculate_overlap(mps1::MPS, mps2::MPS)::Number # Make sure, that the two MPS have the same length N1 = length(mps1) N2 = length(mps2) @assert(N1 == N2) # Now compute ther overlap overlap = ones(Float64, 1, 1) for i = 1:N1 overlap = contract_tensors(overlap, [2], mps2[i], [1]) overlap = contract_tensors(conj(mps1[i]), [1; 3], overlap, [1; 3]) end return overlap[1] end """ expectation_value(mps::MPS, mpo::MPO)::Number Given a MPS and a MPO compute the expectation value <mps|mpo|mps>. """ function expectation_value(mps::MPS, mpo::MPO)::Number # Make sure, that the two MPS have the same length N1 = length(mps) N2 = length(mpo) @assert(N1 == N2) # Contract zipper like val = ones(Float64, 1, 1, 1) for i = 1:N1 val = contract_tensors(val, [1], conj(mps[i]), [1]) val = contract_tensors(val, [1; 4], mpo[i], [1; 3]) val = contract_tensors(val, [1; 4], mps[i], [1; 3]) end return val[1] end """ gaugeMPS(mps::MPS{T}, direction::Symbol=:right, normalize::Bool=false)::MPS{T} Function to bring an MPS with OBC in canonical form direction: tells, whether it will be left or right canonical gauge If normalize is set to true, the resulting state will be normalized. """ function gaugeMPS(mps::MPS{T}, direction::Symbol = :right, normalize::Bool = false)::MPS{T} where {T} mps_gauged = deepcopy(mps) gaugeMPS!(mps_gauged, direction, normalize) return mps_gauged end """ gaugeMPS!(mps::MPS,direction::Dir=right,) Bring an MPS with OBC in canonical form. Direction tells, whether it will be left or right canonical gauge If normalize is set to true, the resulting state will be normalized. This function overwrites the input MPS with its gauged version """ function gaugeMPS!(mps::MPS, direction::Symbol = :right, normalize::Bool = false) # Check that we got a meaningful direction if (direction != :left && direction != :right) throw(ArgumentError("direction must be :left or :right, got $(repr(direction))")) end # Start gauging N = length(mps) if (direction == :left) # Case that I want left canonical gauge M = mps[1] for i = 1:N-1 mps[i], res = gauge_site(M, direction) M = contract_tensors(res, [2], mps[i+1], [1]) if (i == (N - 1)) if (normalize) mps[N], _ = gauge_site(M, direction) else mps[N] = M end end end else # Case that I want right canonical gauge M = mps[N] for i = N:-1:2 mps[i], res = gauge_site(M, direction) M = contract_tensors(mps[i-1], [2], res, [1], [1; 3; 2]) if (i == 2) if (normalize) mps[1], _ = gauge_site(M, direction) else mps[1] = M end end end end end """ gauge_site(A::Site{T}, direction::Dir)::Tuple{Site{T},Matrix{T}} where T Bring a single tensor A of an MPS with OBC in canonical form direction tells, whether it will be left or right normalized The new tensor is M, the residual matrix which has to be multiplied in the next tensor is stored in res """ function gauge_site(A::Site{T}, direction::Symbol)::Tuple{Site{T},Matrix{T}} where {T} if (direction == :left) Dl, Dr, d = size(A) M = permutedims(A, [3 1 2]) M = reshape(M, (d * Dl, Dr)) U, S, V = svd(M) dsv = length(S) U = reshape(U, (d, Dl, dsv)) M = permutedims(U, [2 3 1]) res = Matrix(Diagonal(S)) * V' return M, res else Dl, Dr, d = size(A) M = permutedims(A, [1 3 2]) M = reshape(M, (Dl, Dr * d)) U, S, V = svd(M) dsv = length(S) V = V' V = reshape(V, (dsv, d, Dr)) M = permutedims(V, [1 3 2]) res = U * Matrix(Diagonal(S)) return M, res end end """ contract_virtual_indices(mps::MPS)::Vector{<:Number} Given an MPS contract the virtual indices such that one obtains a dense vector. The indices are ordered such that they are compatible with the standard Julia kronecker product. Warning: the object constructed will have exponential memory requirements in terms of the number of sites, use with care! """ function contract_virtual_indices(mps::MPS)::Vector{<:Number} N = length(mps) # Since we deal with open boundary conditions, we drop the dummy indices one on the left (right) boundary for the first (last) tensor manually. We start from the right to have the physical indices in the order compatible with Julia's kronecker product res = mps[N][:, 1, :] for i = N-1:-1:2 res = contract_tensors(res, [ndims(res) - 1], mps[i], [2]) end res = contract_tensors(res, [ndims(res) - 1], mps[1][1, :, :], [1]) # Now reshape the result accordingly res = reshape(res, prod(size(res))) return res end """ contract_virtual_indices(mps::MPO)::Matrix{<:Number} Given an MPO contract the virtual indices such that one obtains a dense matrix. The indices are ordered such that they are compatible with the standard Julia kronecker product. Warning: the object constructed will have exponential memory requirements in terms of the number of sites, use with care! """ function contract_virtual_indices(mpo::MPO)::Matrix{<:Number} N = length(mpo) # Since we deal with open boundary conditions, we drop the dummy indices one on the left (right) boundary for the first (last) tensor manually. We start from the right to have the physical indices in the order compatible with Julia's kronecker product res = mpo[N][:, 1, :, :] for i = N-1:-1:2 res = contract_tensors(res, [ndims(res) - 2], mpo[i], [2]) end res = contract_tensors(res, [ndims(res) - 2], mpo[1][1, :, :, :], [1]) # Reshuffle the indices to be compatible with Julia's standard kronecker product res = permutedims(res, [collect(1:2:ndims(res)); collect(2:2:ndims(res))]) # Now reshape the result accordingly dims = size(res) dr = prod(dims[1:N]) dc = prod(dims[N+1:end]) res = reshape(res, (dr, dc)) return res end """ find_groundstate(H::Array{Operator},D::Int64,acc::Float64,max_sweeps::Int64=-1) Given a Hamiltonian MPO H, find an MPS approximation for its ground state with bond dimension D converged to a relative accuracy acc. If a positive number for max_sweeps is given, the maximum amount of iterations is limited to max_sweeps """ function find_groundstate(H::Vector{Operator{T}}, D::Int64, d::Int64, acc::Float64, max_sweeps::Int64) where {T} N = length(H) # Get the physical dimensions from the Hamiltonian d = Vector{Int64}(undef, length(H)) for i = 1:length(H) d[i] = size(H[i], 3) end # Random MPS to start the calculation with mps = random_mps_obc(N, D, d) # Put it in right canonical gauge gaugeMPS!(mps, :right) # Precalculate the partial contractions LR = setup_R(H, mps) # Now start the sweeping num_of_sweeps = 0 E0 = 0 Eold = 1E5 while (true) num_of_sweeps = num_of_sweeps + 1 println("Sweep number ", num_of_sweeps) # From left to right starting by 1 up to N-1 E_local = 0 res = 0 for i = 1:N-1 Left = LR[i] Right = LR[i+1] E_local, M = solve_eigenvalue_problem(Left, Right, H[i]) mps[i], _ = gauge_site(M, :left) LR[i+1] = update_left(Left, mps[i], mps[i], H[i]) end # From left to right starting by 1 up to N-1 for i = N:-1:2 Left = LR[i] Right = LR[i+1] E_local, M = solve_eigenvalue_problem(Left, Right, H[i]) mps[i], res = gauge_site(M, :right) LR[i] = update_right(Right, mps[i], mps[i], H[i]) end # Check convergence criterion if (abs((Eold - E_local) / Eold) < acc) E0 = E_local # Restore normalisation (permutation is needed to bring the indices back into right order after contracting) mps[1] = contract_tensors(mps[1], [2], res, [1], [1; 3; 2]) println("Convergence to desired accuracy achieved") break elseif (max_sweeps > 0 && num_of_sweeps >= max_sweeps) E0 = E_local # Restore normalisation (permutation is needed to bring the indices back into right order after contracting) mps[1] = contract_tensors(mps[1], [2], res, [1], [1; 3; 2]) warn("Reached maximum number of iterations before convergence to desired accuracy") break end Eold = E_local end return E0, mps, num_of_sweeps end """ getHeff(Left,Right,W::Operator) Construct the effective Hamiltonian """ function getHeff(Left, Right, W::Operator) Htemp = contract_tensors(W, [2], Right, [2]) Htemp = contract_tensors(Left, [2], Htemp, [1]) Htemp = permutedims(Htemp, [1; 5; 3; 2; 6; 4]) dim1, dim2, dim3, dim4, dim5, dim6 = size(Htemp) Heff = reshape(Htemp, (dim1 * dim2 * dim3, dim4 * dim5 * dim6)) return Heff end """ solve_eigenvalue_problem(Left,Right,W) Function to construct and solve the eigenvalue problem which arises on each site for the effective Hamiltonian """ function solve_eigenvalue_problem(Left, Right, W) Htemp = contract_tensors(W, [2], Right, [2]) Htemp = contract_tensors(Left, [2], Htemp, [1]) Htemp = permutedims(Htemp, [1; 5; 3; 2; 6; 4]) dim1, dim2, dim3, dim4, dim5, dim6 = size(Htemp) Heff = reshape(Htemp, (dim1 * dim2 * dim3, dim4 * dim5 * dim6)) E_local, M = eigs(Heff, nev = 1, which = :SR) M = reshape(M, (dim1, dim5, dim3)) return real(E_local[1]), M end """ setup_R(H::MPO{T1},mps::MPS{T2}) where {T1,T2} Function to calculate the partial contractions needed to form the effective Hamiltonian """ function setup_R(H::MPO{T1}, mps::MPS{T2}) where {T1,T2} N = length(H) Tres = Base.return_types(*, (T1, T2))[1] LR = Vector{Array{Tres,3}}(undef, N + 1) # We need only N-1 partial contractions, however, we set the edges to dummy values 1 that we can recursively compute every contraction resuing the previous ones LR[1] = ones(Tres, 1, 1, 1) LR[N+1] = ones(Tres, 1, 1, 1) # Now compute the partial contractions starting from the right (as I start sweeping on the left in the ground state search) for i = N:-1:2 tmp = contract_tensors(LR[i+1], [3], mps[i], [2]) tmp = contract_tensors(H[i], [2; 4], tmp, [2; 4]) LR[i] = contract_tensors(conj(mps[i]), [2; 3], tmp, [3; 2]) end return LR end """ update_left(LR, M_left::Site, M_right::Site, W::Operator) Function to perform an update the partial contractions required for iterative ground state search starting from the left stored in LR """ function update_left(LR, M_left::Site, M_right::Site, W::Operator) res = contract_tensors(LR, [3], M_right, [1]) res = contract_tensors(W, [1; 4], res, [2; 4]) res = contract_tensors(conj(M_left), [1; 3], res, [3; 2]) return res end """ update_right(LR, M_left::Site, M_right::Site, W::Operator) Function to perform an update the partial contractions required for iterative ground state search starting from the right stored in LR """ function update_right(LR, M_left::Site, M_right::Site, W::Operator) res = contract_tensors(LR, [3], M_right, [2]) res = contract_tensors(W, [2; 4], res, [2; 4]) res = contract_tensors(conj(M_left), [2; 3], res, [3; 2]) return res end """ apply_operator(operator::MPO{T1}, mps::MPS{T2})::MPS where {T1,T2} Apply an operator given as MPO to an MPS. The resulting MPS will have a bond dimension that is the product of the bond dimensions of the MPS and the MPO. """ function apply_operator(operator::MPO{T1}, mps::MPS{T2})::MPS where {T1,T2} N1 = length(mps) N2 = length(operator) @assert(N1 == N2) # Generate a new MPO of the correct type Tres = Base.return_types(*, (T1, T2))[1] res = MPS{Tres}(undef, N1) # Apply the MPO to the MPS and generate new MPS for i = 1:N1 temp = contract_tensors(operator[i], [4], mps[i], [3]) temp = permutedims(temp, (1, 4, 2, 5, 3)) dim1, dim2, dim3, dim4, dim5 = size(temp) res[i] = reshape(temp, (dim1 * dim2, dim3 * dim4, dim5)) end return res end """ apply_operator!(operator::MPO{T1}, mps::MPS{T2})::MPS where {T1,T2} Apply an operator given as MPO to an MPS. The resulting MPS will have a bond dimension that is the product of the bond dimensions of the MPS and the MPO. The input will be overwritten by the result. This requires that the type of the elements of the input MPS is able to accomodate the result of multiplying the MPO tensors into the MPS tensors (e.g. applying a complex MPO to a real MPS cannot be done inpalce as the result will be complex) """ function apply_operator!(operator::MPO, mps::MPS) N1 = length(mps) N2 = length(operator) @assert(N1 == N2) # Contract the tensors for each site for i = 1:N1 temp = contract_tensors(operator[i], [4], mps[i], [3]) temp = permutedims(temp, (1, 4, 2, 5, 3)) dim1, dim2, dim3, dim4, dim5 = size(temp) mps[i] = reshape(temp, (dim1 * dim2, dim3 * dim4, dim5)) end end """ apply_operator(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2} Multiply two MPOs together to get an expression for op2 * op1 in MPO form. The resulting MPS will have a bond dimension that is the product of the bond dimensions of both MPOs. """ function apply_operator(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2} N1 = length(op1) N2 = length(op2) @assert(N1 == N2) # Generate a new MPS of the correct type Tres = Base.return_types(*, (T1, T2))[1] res = MPO{Tres}(undef, N1) # Contract the tensors for each site for i = 1:N1 temp = contract_tensors(op2[i], [4], op1[i], [3]) temp = permutedims(temp, (1, 4, 2, 5, 3, 6)) dim1, dim2, dim3, dim4, dim5, dim6 = size(temp) res[i] = reshape(temp, (dim1 * dim2, dim3 * dim4, dim5, dim6)) end return res end """ sum_states(mps1::MPS{T1}, mps2::MPS{T2})::MPS where {T1,T2} Add two MPSs together to get an expression for mps1 + mps2 in MPS form. The resulting MPS will have a bond dimension that is the sum of the bond dimensions of both MPOs. """ function sum_states(mps1::MPS{T1}, mps2::MPS{T2})::MPS where {T1,T2} N1 = length(mps1) N2 = length(mps2) @assert(N1 == N2) # Generate a new MPO of the correct type Tres = Base.return_types(+, (T1, T2))[1] res = MPS{Tres}(undef, N1) # The first site needs special treatment tensor1 = mps1[1] tensor2 = mps2[1] _, Dr1, d1 = size(tensor1) _, Dr2, d2 = size(tensor2) new_tensor = zeros(Tres, 1, Dr1 + Dr2, d1) for r = 1:d1 new_tensor[1, :, r] = [tensor1[1:1, :, r] tensor2[1:1, :, r]] end res[1] = new_tensor # The tensors in between for i = 2:N1-1 tensor1 = mps1[i] tensor2 = mps2[i] Dl1, Dr1, d1 = size(tensor1) Dl2, Dr2, d2 = size(tensor2) new_tensor = zeros(Tres, Dl1 + Dl2, Dr1 + Dr2, d1) for r = 1:d1 new_tensor[1:Dl1, 1:Dr1, r] = tensor1[:, :, r] new_tensor[Dl1+1:end, Dr1+1:end, r] = tensor2[:, :, r] end res[i] = new_tensor end # The last site needs special treatment tensor1 = mps1[N1] tensor2 = mps2[N1] Dl1, _, d1 = size(tensor1) Dl2, _, d2 = size(tensor2) new_tensor = zeros(Tres, Dl1 + Dl2, 1, d1) for r = 1:d1 new_tensor[:, 1, r] = [tensor1[:, 1, r]; tensor2[:, 1, r]] end res[N1] = new_tensor return res end """ sum_operators(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2} Add two MPOs together to get an expression for op2 + op1 in MPO form. The resulting MPO will have a bond dimension that is the sum of the bond dimensions of both MPOs. """ function sum_operators(op1::MPO{T1}, op2::MPO{T2})::MPO where {T1,T2} N1 = length(op1) N2 = length(op2) @assert(N1 == N2) # Generate a new MPO of the correct type Tres = Base.return_types(+, (T1, T2))[1] res = MPO{Tres}(undef, N1) # The first site needs special treatment tensor1 = op1[1] tensor2 = op2[1] _, Dr1, dr1, dc1 = size(tensor1) _, Dr2, dr2, dc2 = size(tensor2) new_tensor = zeros(Tres, 1, Dr1 + Dr2, dr1, dc1) for r = 1:dr1 for c = 1:dc1 new_tensor[1, :, r, c] = [tensor1[1:1, :, r, c] tensor2[1:1, :, r, c]] end end res[1] = new_tensor # The tensors in between for i = 2:N1-1 tensor1 = op1[i] tensor2 = op2[i] Dl1, Dr1, dr1, dc1 = size(tensor1) Dl2, Dr2, dr2, dc2 = size(tensor2) new_tensor = zeros(Tres, Dl1 + Dl2, Dr1 + Dr2, dr1, dc1) for r = 1:dr1 for c = 1:dc1 new_tensor[1:Dl1, 1:Dr1, r, c] = tensor1[:, :, r, c] new_tensor[Dl1+1:end, Dr1+1:end, r, c] = tensor2[:, :, r, c] end end res[i] = new_tensor end # The last site needs special treatment tensor1 = op1[N1] tensor2 = op2[N1] Dl1, _, dr1, dc1 = size(tensor1) Dl2, _, dr2, dc2 = size(tensor2) new_tensor = zeros(Tres, Dl1 + Dl2, 1, dr1, dc1) for r = 1:dr1 for c = 1:dc1 new_tensor[:, 1, r, c] = [tensor1[:, 1, r, c]; tensor2[:, 1, r, c]] end end res[N1] = new_tensor return res end """ compute_entropy(mps::MPS, n:Int)::Float64 Compute the von Neumann along for the bipartion of the sites into two subsets A={1,...,n} and B={n+1,...,N} where N is the length of the MPS. If n<=0 is supplied, a bipartion of into A. For the result to make sense, mps has to be a normalized quantum state. """ function compute_entropy(mps::MPS{T}, n::Int = 0)::Float64 where {T} # Extact the length and check if the given position is reasonable N = length(mps) @assert(n <= N) # The entropy of the entire state is simply zero since it is a pure state, so nothing to compute if n == N return 0.0 end # In case a value n<=0 is given, we assume the bipartion is taken in the center if n <= 0 n = Int(round(N / 2)) end # Get a copy of the input mps_loc = deepcopy(mps) # Put the sites left to n into left canonical gauge M = mps_loc[1] for i = 1:n mps_loc[i], res = gauge_site(M, :left) M = contract_tensors(res, [2], mps_loc[i+1], [1]) end mps_loc[n+1] = M # Now start contracting from the right boundary to obtain the reduced density operator rdm = ones(T, 1, 1) for i = N:-1:n+1 rdm = contract_tensors(rdm, [2], mps_loc[i], [2]) rdm = contract_tensors(conj(mps_loc[i]), [2; 3], rdm, [1; 3]) end # Now diagonalize the reduced density matrix and compute the entropy ev = real(eigvals(rdm)) # Eigenvalues that are numerically zero sometimes become -1E-16, to prevent problems with the logarithm we filter them ev = filter(x -> x > 0.0, ev) # The von Neumann entropy for the reduced density operator entropy = -sum(ev .* log2.(ev)) return entropy end """ sample_from_mps!(mps::MPS, gauge_input::Bool=true)::Vector{Int64} Generate a sample from the probability distribution of basis states defined by the MPS following A. Ferris, G. Vidal, PRB 85 165146 (2021). If the flag gague_input is set to true, the input MPS will be put in right canoncial gauge and normalized, which is a requirement for the algorithm to work. In case one is sure that the MPS is already properly gauged and normalized the gauging step can be spared by setting the flag to false. In this case the input will stay untouched. """ function sample_from_mps!(mps::MPS, gauge_input::Bool = true)::Vector{Int64} # Extact the length and check if the given position is reasonable N = length(mps) res = zeros(Int64, N) # Put the state into right canonical gauge and make sure it is normalized if gauge_input gaugeMPS!(mps, :right, true) end # Now sample from the MPS A = 0 p = 0.0 M = mps[1][1, :, :] for i = 1:N d = size(M, 2) pacc = 0 r = rand() for l = 1:d # Prepare the basis state basis_state = zeros(d) basis_state[l] = 1.0 # Contract it into the physical index of the tensor A = contract_tensors(M, [2], basis_state, [1]) # Determine the probability for the basis vector e_l p = contract_tensors(conj(A), [1], A, [1]) pacc += real(p[1]) if r < pacc res[i] = l break end end if i < N # Contract the result into the next tensor M = contract_tensors(1 / sqrt(real(p[1])) * A, [1], mps[i+1], [1]) end end return res end """ sample_from_mps(mps::MPS)::Vector{Int64} Generate a sample from the probability distribution of basis states defined by the MPS following A. Ferris, G. Vidal, PRB 85 165146 (2021). """ function sample_from_mps(mps::MPS)::Vector{Int64} return sample_from_mps!(deepcopy(mps)) end """ svd_compress_mps(mps::MPS, Dmax::Int,, tol::Real = 0.0)::MPS Compress a given MPS applying an a singular value decomposition at each bond. If Dmax > 0 is supplied (and simultaneously tol = 0.0), a maximum of Dmax singular values is kept, thus truncating the MPS to one with maximum bond dimension Dmax. If tol > 0 is given (and simultaneously Dmax = 0) then all singular values > tol are kept. If both are specified then at most Dmax singular values > tol are kept. """ function svd_compress_mps(mps::MPS, Dmax::Int, tol::Real = 0.0)::MPS # One of the two parameters has to be larger than zero @assert((Dmax > 0) || (tol > 0)) # Extract the length and prepare a result N = length(mps) res = deepcopy(mps) # Gauge in both directions that redundant dimensions at the boundaries are removed gaugeMPS!(res, :left) gaugeMPS!(res, :right) Dnew = 0 for i = 1:N-1 # Check if the given bond dimension is larger than Dmax if size(res[i], 2) > Dmax Dl1, _, d1 = size(res[i]) _, Dr2, d2 = size(res[i+1]) tmp = contract_tensors(res[i], [2], res[i+1], [1]) tmp = reshape(tmp, (Dl1 * d1, Dr2 * d2)) U, S, V = svd(tmp) M = diagm(S) * V' # Now truncate if Dmax > 0 && tol == 0.0 U = U[:, 1:Dmax] M = M[1:Dmax, :] Dnew = Dmax else ind = findall(x -> x > tol, S) if Dmax > 0 && length(ind) > Dmax ind = ind[1:Dmax] end U = U[:, ind] M = M[ind, :] Dnew = length(ind) end # Reshape and set new tensors res[i] = permutedims(reshape(U, (Dl1, d1, Dnew)), (1, 3, 2)) res[i+1] = reshape(M, (Dnew, Dr2, d2)) end end return res end """ decompose_into_mpo(M::Matrix{T}, d::Vector{Int}) where T <:Number Given a many-body operator in form of a dense matrix, decompose it into an MPO. It is assumed that the many-body operator follows the index convention of Julia's built-in kronecker product. The vector d specifies the local dimensions of the Hilbert space. # Examples Decomposing a simple two-site operator made up from sum of Pauli terms into MPO form. ```julia-repl julia> Id = [1.0 0; 0.0 1.0] julia> X = [0.0 1.0; 1.0 0.0] julia> Z = [1.0 0.0; 0.0 -1.0] julia> H = kron(X,X) + kron(Id,Z) + kron(Z,Id) julia> mpo = decompose_into_mpo(H, 2) ``` """ function decompose_into_mpo(M::Matrix{T}, d::Vector{Int})::MPO{T} where {T<:Number} N = length(d) dim = prod(d) if size(M) != (prod(d), prod(d)) throw(ArgumentError("matrix not compatible with specified local dimensions, got size(M)=$(repr(size(M))), d=$(repr(d))")) end # The MPO holding the result res = MPO{T}(undef, N) # Reshape the matrix and rearrange the indices, such that the row and column index for each site are adjacent and add dummy indices 1 at the boundaries A = reshape(M, (1, reverse(d)..., reverse(d)..., 1)) ind = collect(Iterators.flatten(zip(collect(N:-1:1), collect(2N:-1:N+1)))) A = permutedims(A, (1, ind .+ 1..., 2 * length(d) + 2)) # Now split it into tensors using an SVD Dl = 1 for i = 1:N-1 # Take the first three indices together dims = size(A) A = reshape(A, (prod(dims[1:3]), prod(dims[4:end]))) # SVD the matrix representation U, S, V = svd(A) A = diagm(S) * V' Dr = size(U, 2) # Extract the tensor and the remaining part U = reshape(U, (Dl, d[i], d[i], Dr)) res[i] = permutedims(U, (1, 4, 2, 3)) A = reshape(A, (Dr, dims[4:end]...)) Dl = Dr end res[N] = permutedims(A, (1, 4, 2, 3)) return res end """ decompose_into_mpo(M::Matrix{T}, d::Int) where T <:Number Simplified interface to the more general method assuming that all local dimensions are equal to d. """ function decompose_into_mpo(M::Matrix{T}, d::Int)::MPO{T} where {T<:Number} dl, dr = size(M) if dl != dr throw(ArgumentError("local dimensions must all be the same, obtained a matrix with dimensions $(repr((dl,dr)))")) end N = Int(round(log(d, dl))) return decompose_into_mpo(M, d * ones(Int64, N)) end
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module FisherySim using Distributions using TweedieDistributions using StatsBase using LinearAlgebra using Random using PDMats using Arpack using NeutralLandscapes import Base: rand, +, -, *, step, sum, getindex, setindex!, size, length, eachindex, copy import StatsBase: sample, cov import Distributions: location include("fisherydomain.jl") export AbstractFisheryDomain, DiscreteFisheryDomain, GriddedFisheryDomain, size, length, eachindex, sample include("covkernels.jl") export AbstractCovarianceKernel, ExpCov, Matérn32Cov, Matern32Cov, AR1, cov # include("matrixlognormal.jl") # export # MatrixLogNormal, # location include("domaindistributions.jl") export AbstractDomainDistribution, DomainDistribution, MultiDomainDistribution, BlendedDomainDistribution, ClassifiedDomainDistribution, domain, getindex, length include("habitat.jl") export Habitat, getindex, length, HabitatPreference include("bathymetry.jl") export BathymetryModel, Bathymetry, rand include("pop_dynamics.jl") export PopulationDynamicsModel, PopState, Schaefer, PellaTomlinson, StochasticProduction, vecstate, step, sum, setindex!, copy include("movement.jl") export MovementModel, eqdist, MovementRate include("targeting.jl") export AbstractTargetingBehavior, RandomTargeting, FixedTargeting, AbstractPreferentialTargeting, PreferentialTargeting, DynamicPreferentialTargeting, target, reset! include("catchability.jl") export AbstractCatchability, Catchability, DensityDependentCatchability, HabitatCatchability, * include("vessels.jl") export Vessel, Catch, CPUE, +, -, fish!, getindex, Fleet, vessels include("simulation.jl") export simulate end # module
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module CLI # Bukdu import ..Bukdu: Routing, Naming """ CLI.routes() Showing the routing table. """ function routes() A = Routing.store[:routing_tables] isempty(A) && return ncols = 5 # verb url C action pipe nrows = Int(length(A)/ncols) rt = reshape(A, ncols, nrows) paddings = maximum((length ∘ string).(rt), dims=2) .+ 2 function f(idx, el, lastcolumn) if idx == lastcolumn el else rpad(el, paddings[idx]) end end for rowidx in 1:nrows row = rt[:, rowidx] lastcolumn = isempty(row[ncols]) ? ncols-1 : ncols print.([f(idx, el, lastcolumn) for (idx, el) in enumerate(row[1:lastcolumn])]) println() end end end # module Bukdu.CLI
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### A Pluto.jl notebook ### # v0.18.0 using Markdown using InteractiveUtils # This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). macro bind(def, element) quote local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end local el = $(esc(element)) global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) el end end # ╔═╡ 451ae3a0-8068-4747-95a7-d31955808f29 begin # external packages - using PlutoUI using Plots using PrettyTables end # ╔═╡ 8ba6a00a-7a53-4dcc-af4d-cb85aa9b4d68 md""" ### Simple and Complex Models of Enzyme Kinetics The flux bounds are essential constraints in flux balance analysis calculations and the convex decomposition of the stoichiometric array. Beyond their role in the flux estimation problem, the flux bounds are _integrative_, i.e., these constraints integrate many types of genetic and biochemical information into the flux estimation problem. Flux bounds constrain the values that each reaction in a metabolic network can take. A general model for these bounds is given by: $$-\delta_{j}\left[{V_{max,j}^{\circ}}\left(\frac{e}{e^{\circ}}\right)\theta_{j}\left(\dots\right){f_{j}\left(\dots\right)}\right]\leq{v_{j}}\leq{V_{max,j}^{\circ}}\left(\frac{e}{e^{\circ}}\right)\theta_{j}\left(\dots\right){f_{j}\left(\dots\right)}$$ where $V_{max,j}^{\circ}$ denotes the maximum reaction velocity (units: flux) computed at some characteristic enzyme abundance (units: concentration), the ratio $e/e^{\circ}$ is a correction for enzyme abundance (units: dimensioness), $\theta_{j}\left(\dots\right)\in\left[0,1\right]$ is the fraction of maximial enzyme activity (a function or measurement producing units: dimensionless), and $f_{j}\left(\dots\right)$ is a function describing the substrate dependence of the reaction rate $j$ (units: dimensionless). Both $\theta_{j}\left(\dots\right)$ and $f_{j}\left(\dots\right)$ could have associated parameters, e.g., saturation or binding constants, etc. Finally, the quanity $\delta_{j}\in\left\{0,1\right\}$ is a _binary_ variable: * If reaction $j$ is __reversible__ $\delta_{j}=1$ or, * If reaction $j$ is __irreversible__ $\delta_{j}=0$ Today, let's focus on approaches for computing the value of these bounds, i.e., the form and value of the terms in the brackets. In this lecture, we will: 1. Develop simple models of enzyme kinetics using the Michaelis–Menten approach 1. Introduce the fundamental concepts underlying more complex models of allosteric regulation (the fast control mechanisms that we mentioned previously) 1. Introduce effective discrete regulation models to capture allosteric regulation """ # ╔═╡ 8869f117-1fc6-4cc5-9803-b8ec72a109a6 md""" ### What is allosteric regulation? Allosteric regulation modulates enzyme activity by binding effector molecules to sites other than the enzyme's active site. These events can activate (enhances rate) and inhibit (decreases rate). Allosteric regulation operates on a fast time scale compared to gene expression (synthesis of the enzyme). Allosteric mechanisms in Central Carbon Metabolism: * [Reznik E, Christodoulou D, Goldford JE, Briars E, Sauer U, Segrè D, Noor E. Genome-Scale Architecture of Small Molecule Regulatory Networks and the Fundamental Trade-Off between Regulation and Enzymatic Activity. Cell Rep. 2017 Sep 12;20(11):2666-2677. doi: 10.1016/j.celrep.2017.08.066. PMID: 28903046; PMCID: PMC5600504.](https://pubmed.ncbi.nlm.nih.gov/28903046/) """ # ╔═╡ 17724757-604e-4c77-a42b-238ba121e88f md""" ### Simple: Michaelis–Menten kinetics Let's assume we have a well-mixed test tube containing an enzyme $E$ (a protein that catalyzes chemical reactions), which converts substrate $S$ (the starting compound) into product $P$ according to three elementary reactions: $$\begin{eqnarray} E+S&\rightleftharpoons&{E:S}\\ {E:S}&\longrightarrow&E+P \end{eqnarray}$$ The kinetics of each elementary step can be written using mass-action kinetics, i.e., $$\begin{eqnarray} r_{1} & = & k_{1}\left[E\right]\left[S\right]\\ r_{2} & = & k_{2}\left[E:S\right]\\ r_{3} & = & k_{3}\left[E:S\right] \end{eqnarray}$$ where $\left[\cdot\right]$ denotes a species concentration, and $k_{j}$ denotes the rate constant governing the $jth$ elementary reaction: * The rate $r_{1}$ describes the _association_ rate between the enzyme and substrate, * The rate $r_{2}$ represents the rate of _dissociation_ of the enzyme-substrate complex, and * The $r_{3}$ denotes the rate of _chemical conversion_ of the bound substrate into the product (we assume the dissociation of the product from the enzyme is fast). The enzyme must obey the relationship: $$\left[E_{T}\right] = \left[E\right] + \left[E:S\right]$$ where $\left[E_{T}\right]$ denotes the total enzyme concentration in the tube, $\left[E\right]$ denotes the free enzyme concentration (not bound to substrate) while $\left[E:S\right]$ denotes the enzyme-substrate complex. To estimate the _overall_ rate $v$, we stipulate a single rate-limiting step out of the set of elementary reactions. Let's assume that the rate of chemical conversion ($r_{3}$) is the slowest step, i.e., the substrate bounces on/off the enzyme quickly with only a tiny fraction of these binding events resulting in a successful chemical transformation. Thus, the overall rate is then given by: $$v = k_{3}\left[E:S\right]$$ Let's also assume that we already know (or can estimate) the rate constants $k_{1},k_{2}$ and $k_{3}$. When this is true, the only unknown is $\left[E:S\right]$. However, we can relate $\left[E:S\right]$ to variables we know ($E_{T}$ and at least initially $S$) through the enzyme balance, and the _pseudo-steady-state assumption_ for the reaction intermediate $\left[E:S\right]$: $$\frac{d\left[E:S\right]}{dt} = k_{1}\left[E\right]\left[S\right] - k_{2}\left[E:S\right] - k_{3}\left[E:S\right]\simeq{0}$$ Rearranging and solving for $\left[E:S\right]$ gives the relationship: $$\left[E:S\right]\simeq\frac{k_{1}}{k_{2}+k_{3}}\left[E\right]\left[S\right]$$ where the ratio of constants is defined as the Michaelis-Menten saturation coefficient or $K_{M}$: $$\frac{1}{K_{M}}\equiv\frac{k_{1}}{k_{2}+k_{3}}$$ Substituting the definition of $K_{M}$ into the overall rate yields: $$v = k_{3}\frac{\left[E\right]\left[S\right]}{K_{M}}$$ However, we do not know the free enzyme concentration of $\left[E\right]$; to find $\left[E\right]$ we subsitute $\left[E:S\right]$ into the enzyme balance and solving for $\left[E\right]$: $$\left[E\right] = \frac{\left[E_T\right]K_{M}}{K_{M}+\left[S\right]}$$ Lastly, we substitute $\left[E\right]$ into the overall rate to arrive at the final expression for $v$: $$v = V_{max}\frac{\left[S\right]}{K_{M}+\left[S\right]}$$ where $V_{max}\equiv{k_{3}}\left[E_{T}\right]$. __Limiting cases:__ * when $S\gg{K}_{M}$, the rate becomes close to $V_{max}$. * when $S\ll{K}_{M}$ the rate appears to be linear with respect to substrate concentration. * when $K_{M}\simeq S$ the reaction rate equals $v\simeq 1/2V_{max}$. """ # ╔═╡ 431ccdf0-93a9-4b3c-9576-8854ba2f1fad @bind MM_parameters PlutoUI.combine() do Child md""" ##### Michaelis–Menten Parameters \[E\] $( Child(Slider(1:5)) ) (μM) and Kₘ $( Child(Slider(5:100)) ) (mM) """ end # ╔═╡ 7efaf27c-8e0a-40f9-ac28-af90357450a3 begin # get MM parameter values - E = MM_parameters[1] Kₘ = MM_parameters[2] kcat = 13.7 # units: s^-1 number_of_steps = 1000 # substrate range - S_array = range(0.0,stop=100.0,length=number_of_steps) |> collect; # initialize space - v_array = Array{Float64,1}(undef,number_of_steps) # compute the rate - for (i,S) ∈ enumerate(S_array) # compute the rate - v_array[i] = (kcat*E)*(S/(S+Kₘ)) end # plot - plot(S_array,v_array,xlims=(0.0,100.0),ylims=(0.0,14), label="v: E = $(E) μM and Kₘ = $(Kₘ) (mM)") xlabel!("Substrate S (mM)",fontsize=18) ylabel!("Rate v (μM/s)",fontsize=18) end # ╔═╡ 55ea8324-f36d-40bd-99e3-92e7fcbafca9 md""" ### Complex: MWC and Sequential kinetic models The Monod-Wyman-Changeux model (MWC model, also known as the symmetry model) describes allosteric transitions of proteins made up of identical subunits. Effector binding modulates the state of the entire protein. * [MONOD J, WYMAN J, CHANGEUX JP. ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. J Mol Biol. 1965 May;12:88-118. doi: 10.1016/s0022-2836(65)80285-6. PMID: 14343300.](https://pubmed.ncbi.nlm.nih.gov/14343300/) The sequential model (KNF model) of allosteric regulation posits that enzyme subunits are independent. Thus, binding substrate (or effector) to a subunit results in only slight conformational changes to adjacent subunits. KNF model can do describe both positive and negative cooperativity: * [Koshland D Jr, Némethy G, Filmer D. Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry. 1966 Jan;5(1):365-85. doi: 10.1021/bi00865a047. PMID: 5938952.](https://pubmed.ncbi.nlm.nih.gov/5938952/) """ # ╔═╡ 3502da52-7d2b-4c79-82ce-7424d756cd9b md""" ### Effective discrete state kinetic models Michaelis–Menten kinetics are easy to understand, but they neglect many factors, e.g., the influence of allosteric regulators. On the other hand, MWC/sequential models are detailed but case-specific (and too complex). It would be great if we could correct Michaelis–Menten kinetics to capture the influence of allosteric factors. Suppose we model the rate $v_{j}$ as the product of a kinetic limit (a simple model of the rate) and a correction term that accounts for the missing regulation: $$v_{j} = r_{j}\theta\left(...\right)_{j}$$ where $v_{j}$ denotes the overall rate (units: $\mu$M/time), $r_{j}$ denotes the kinetic limit i.e., the maximum rate of conversion (units: $\mu$M/time) and $0\leq \theta\left(...\right)_{j}\leq 1$ (units: dimensionless) is a control function that describes the influence of effector molecules. """ # ╔═╡ c392c8a9-361d-47e4-933e-2e51b793e069 md""" ##### Discrete state control function model There is a wide variety of different possible ways we can build the $\theta\left(...\right)_{j}$ control functions. Ultimately, it doesn't matter what we choose, as long as it gives a good performance. However, let's introduce an idea that we will revisit later, namely a discrete probabilistic approach. ###### Theory Suppose an enzyme $E$ can exits in one of $s=1,2\dots,\mathcal{S}$ possible microstates, where each microstate $s$ has some pseudo energy $\epsilon_{s}$. Some microstates will lead to activity (the ability to carry out the chemical reactions, while others will not). For each microstate $s$, let's assign a pseudo energy $\epsilon_{s}$, where by definition $\epsilon_{1}=0$; we assume the base state has the lowest energy. Next, suppose the probability that enzyme $E$ is in microstate $s$ follows a [Boltzmann distribution](https://en.wikipedia.org/wiki/Boltzmann_distribution) which says: $$p_{i} = \frac{1}{Z} \times f_{i}\exp\left(-\beta\epsilon_{i}\right)\qquad{i=1,2,\dots,\mathcal{S}}$$ where $p_{i}$ denotes the probability that enzyme $E$ is in microstate $i=1,2,\dots,\mathcal{S}$, $f_{i}$ denotes a state-specific factor $f_{i}\in\left[0,1\right]$, $\beta$ denotes the [thermodynamic beta](https://en.wikipedia.org/wiki/Thermodynamic_beta) and $Z$ denotes a normalization factor (called the [Partiton function](https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)) in the statistical physics community). We can find $Z$ using the summation law of discrete probolity e.g., $\sum_{s}p_{s} = 1$ which gives: $$Z = \sum_{s=1}^{\mathcal{S}}f_{i}\exp\left(-\beta\epsilon_{i}\right)$$ which gives: $$p_{i} = \frac{f_{i}\exp\left(-\beta\epsilon_{i}\right)}{\displaystyle \sum_{s=1}^{\mathcal{S}}f_{i}\exp\left(-\beta\epsilon_{i}\right)}\qquad{i=1,2,\dots,\mathcal{S}}$$. Finally, we relate the probability that enzyme $E$ is in microstate $s$ back to the $\theta$ control function by computing the overall probability that the desired event happens, e.g., enzyme $E$ catalyzes the reaction of interests. We know if $\Omega = \left\{1,2,\dots,\mathcal{S}\right\}$, then we can define the subset $\mathcal{A}\subseteq\Omega$ in which the desired event happens. Given $\mathcal{A}$, the $\theta$ function becomes: $$\theta=\sum_{s\in{\mathcal{A}}}p_{s}$$ ###### Conceptual exampleTo illustrate this idea, consider an enzyme inhibited by a downstream product (this is a common allosteric motif known as [feedback inhibition](Pedreño S, Pisco JP, Larrouy-Maumus G, Kelly G, de Carvalho LP. Mechanism of feedback allosteric inhibition of ATP phosphoribosyltransferase. Biochemistry. 2012;51(40):8027-8038. doi:10.1021/bi300808b)). In this case, suppose enzyme $E$, which is inhibited by compound $I$, can exist in one of three possible microstates: * __State s = 1__: No substrate $S$ is bound, $E$ is floating around in solution minding its own business (base state, no reaction) * __State s = 2__: Substrate $S$ is bound to enzyme $E$, but inhibitor $I$ is not bound (reaction possible) * __State s = 3__: Both the substrate $S$ and inhibitor $I$ are bound to enzyme $E$ (no reaction possible) Given these microstates (and their functional assignment) we know that enzyme $E$ can only catalyze its reaction in microstate $s=2$, thus: $$\theta = \frac{f_{2}\exp\left(-\beta\epsilon_{i}\right)}{\displaystyle \sum_{s=1}^{\mathcal{3}}f_{s}\exp\left(-\beta\epsilon_{s}\right)}$$ ###### What are the state-specific factors? The state-specific factors $f_{i}\in\left[0,1\right]$ control the reachability of a microstate: * if $f_{\star} = 0$, then microstate $\star$ can __never__ be obtained * if $f_{\star} = 1$, then microstate $\star$ can __always__ be obtained As a modeler, you can choose the form (or value) that $f_{\star}$ takes. These factors can be set to a specific value by definition (depending upon the state) or can be used to describe events associated with state $i$, e.g., such as binding events. For example, suppose state $i$ involved binding an effector molecule $x$ to the enzyme $E$. In this case, we could model the state-specific factor $f_{i}$ as: $$f_{i} = (x/K_{i})^{n_{i}}/(1+(x/K_{i})^{n_{i}})$$ where $x\geq{0}$ denotes effector abundance, $K_{i}\geq{0}$ denotes a binding constant and $n_{i}\geq{0}$ denotes a binding order parameter. """ # ╔═╡ 91345d04-f502-4e90-935e-a4dc250244db @bind DSM_parameters PlutoUI.combine() do Child md""" \[I\] $( Child(Slider(0:100)) ) (μM) K $( Child(Slider(1:1:100)) ) (mM) ϵ₂ $( Child(Slider(0.001:0.1:100)) ) (J/mol) ϵ₃ $( Child(Slider(0.001:0.1:100)) ) (J/mol) """ end # ╔═╡ 719784fe-3ef6-4e53-ad52-82140e3d0b5e begin # get I - Iₒ = DSM_parameters[1] Kd = DSM_parameters[2] ϵ₂ = (DSM_parameters[3])/100 ϵ₃ = (DSM_parameters[4])/100 # setup system - R = 8.314 # units: J/mol-K T = 273.15 + 25.0 # units: K β = 1/R*T # setup binding parameters for state 3 - n = 2.0 # setup energy array - ϵ_array = [ 0.0 ; # state 1 (just E) -ϵ₂ ; # state 2 (E bound to S, but no I) -ϵ₃ ; # state 3 (E bound to I) ]; # compute W - W_array = exp.(-β*ϵ_array) # let's compute the state-specific factor array - f_array = [ 1.0 ; # state 1 1.0 ; # state 2 ((Iₒ/Kd)^(n))/(1+(Iₒ/Kd)^(n)) ]; # compute the θ variable - microstate_array = f_array.*W_array; Z = sum(microstate_array) p_array = (1/Z)*microstate_array θ = p_array[2] # show - with_terminal() do println("θ = $(θ)") end end # ╔═╡ 1d4d6059-5b79-43cd-ac17-ef2aa057ecad with_terminal() do # initialize - 𝒮 = 3 state_table = Array{Any,2}(undef,𝒮,4) # populate the state array - for s ∈ 1:𝒮 state_table[s,1] = s state_table[s,2] = f_array[s] state_table[s,3] = W_array[s] state_table[s,4] = p_array[s] end # header - header_row = (["s","fₛ","Wₛ","pₛ"]) pretty_table(state_table;header=header_row) end # ╔═╡ d46ced14-a5d3-45a9-9d43-38dc7879b0c7 let # get MM parameter values - E = 1.0 # units: μM Kₘ = 5 # units: mM kcat = 13.7 # units: s^-1 number_of_steps = 1000 # substrate range - S_array = range(0.0,stop=100.0,length=number_of_steps) |> collect; # initialize space - v_array = Array{Float64,1}(undef,number_of_steps) # compute the rate - for (i,S) ∈ enumerate(S_array) # compute the rate - v_array[i] = (kcat*E)*(S/(S+Kₘ))*θ end # plot - plot(S_array,v_array,xlims=(0.0,100.0),ylims=(0.0,14), label="v: I = $(Iₒ) mM and Kd = $(Kd) (mM)") xlabel!("Substrate S (mM)",fontsize=18) ylabel!("Rate v (μM/s)",fontsize=18) end # ╔═╡ d3568c5d-16bf-4698-9891-0be65d62b36c md""" ### Summary and Conclusions In this lecture we: 1. Developed simple models of enzyme kinetics using the Michaelis–Menten approach 1. Introduced the fundamental concepts underlying more complex models of allosteric regulation (the fast control mechanisms that we mentioned previously) 1. Introduced effective discrete regulation models to simulate allosteric regulation """ # ╔═╡ 55d4ab48-9589-4fd9-ac06-3338fdb418c4 md""" ### Next Time * What about multiple substrates? * Does the discrete state model work? * How do we implement these bounds models in a flux balance analysis calculation? """ # ╔═╡ 54370424-3add-4f93-91b0-e136166842ae TableOfContents(title="📚 Lecture Outline", indent=true, depth=5, aside=true) # ╔═╡ 06a90381-b4cb-4d32-af0d-2f084364129c html""" <script> // initialize - var section = 0; var subsection = 0; var subsubsection = 0; var headers = document.querySelectorAll('h3, h5, h6'); // main loop - for (var i=0; i < headers.length; i++) { var header = headers[i]; var text = header.innerText; var original = header.getAttribute("text-original"); if (original === null) { // Save original header text header.setAttribute("text-original", text); } else { // Replace with original text before adding section number text = header.getAttribute("text-original"); } var numbering = ""; switch (header.tagName) { case 'H3': section += 1; numbering = section + "."; subsection = 0; break; case 'H5': subsection += 1; numbering = section + "." + subsection; break; case 'H6': subsubsection += 1; numbering = section + "." + subsection + "." + subsubsection; break; } // update the header text header.innerText = numbering + " " + text; }; </script>""" # ╔═╡ b6890de0-8923-11ec-3552-3113bdd53f86 html""" <style> main { max-width: 860px; width: 70%; margin: auto; font-family: "Roboto, monospace"; } a { color: blue; text-decoration: none; } </style>""" # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ [deps] Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d" [compat] Plots = "~1.25.8" PlutoUI = "~0.7.34" PrettyTables = "~1.3.1" """ # ╔═╡ 00000000-0000-0000-0000-000000000002 PLUTO_MANIFEST_TOML_CONTENTS = """ # This file is machine-generated - editing it directly is not advised julia_version = "1.7.2" manifest_format = "2.0" [[deps.AbstractPlutoDingetjes]] deps = ["Pkg"] git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481" uuid = "6e696c72-6542-2067-7265-42206c756150" version = "1.1.4" [[deps.Adapt]] deps = ["LinearAlgebra"] 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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2" uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a" version = "1.1.0+4" [[deps.Xorg_xcb_util_image_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97" uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b" version = "0.4.0+1" [[deps.Xorg_xcb_util_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"] git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1" uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5" version = "0.4.0+1" [[deps.Xorg_xcb_util_keysyms_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00" uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7" version = "0.4.0+1" [[deps.Xorg_xcb_util_renderutil_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e" uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e" version = "0.3.9+1" [[deps.Xorg_xcb_util_wm_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67" uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361" version = "0.4.1+1" [[deps.Xorg_xkbcomp_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"] git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b" uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4" version = "1.4.2+4" [[deps.Xorg_xkeyboard_config_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"] git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d" uuid = "33bec58e-1273-512f-9401-5d533626f822" version = "2.27.0+4" [[deps.Xorg_xtrans_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845" uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" version = "1.4.0+3" [[deps.Zlib_jll]] deps = ["Libdl"] uuid = "83775a58-1f1d-513f-b197-d71354ab007a" [[deps.Zstd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" version = "1.5.2+0" [[deps.gdk_pixbuf_jll]] deps = ["Artifacts", "Glib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pkg", "Xorg_libX11_jll", "libpng_jll"] git-tree-sha1 = "c23323cd30d60941f8c68419a70905d9bdd92808" uuid = "da03df04-f53b-5353-a52f-6a8b0620ced0" version = "2.42.6+1" [[deps.libass_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" version = "0.15.1+0" [[deps.libblastrampoline_jll]] deps = ["Artifacts", "Libdl", "OpenBLAS_jll"] uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" [[deps.libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" version = "2.0.2+0" [[deps.libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" version = "1.6.38+0" [[deps.libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" version = "1.3.7+1" [[deps.nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" [[deps.p7zip_jll]] deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" [[deps.x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" version = "2021.5.5+0" [[deps.x265_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" version = "3.5.0+0" [[deps.xkbcommon_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6" uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" version = "0.9.1+5" """ # ╔═╡ Cell order: # ╟─8ba6a00a-7a53-4dcc-af4d-cb85aa9b4d68 # ╟─8869f117-1fc6-4cc5-9803-b8ec72a109a6 # ╟─17724757-604e-4c77-a42b-238ba121e88f # ╟─431ccdf0-93a9-4b3c-9576-8854ba2f1fad # ╟─7efaf27c-8e0a-40f9-ac28-af90357450a3 # ╟─55ea8324-f36d-40bd-99e3-92e7fcbafca9 # ╟─3502da52-7d2b-4c79-82ce-7424d756cd9b # ╟─c392c8a9-361d-47e4-933e-2e51b793e069 # ╟─91345d04-f502-4e90-935e-a4dc250244db # ╟─719784fe-3ef6-4e53-ad52-82140e3d0b5e # ╟─1d4d6059-5b79-43cd-ac17-ef2aa057ecad # ╟─d46ced14-a5d3-45a9-9d43-38dc7879b0c7 # ╟─d3568c5d-16bf-4698-9891-0be65d62b36c # ╟─55d4ab48-9589-4fd9-ac06-3338fdb418c4 # ╟─54370424-3add-4f93-91b0-e136166842ae # ╠═451ae3a0-8068-4747-95a7-d31955808f29 # ╠═06a90381-b4cb-4d32-af0d-2f084364129c # ╠═b6890de0-8923-11ec-3552-3113bdd53f86 # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002
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#!/bin/bash #= exec julia -O3 --color=yes -qi "${BASH_SOURCE[0]}" =# using Pkg cd(@__DIR__) Pkg.activate("..") using Retest @retest(@__DIR__) # Local Variables: # mode: julia # End:
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mutable struct Position x::Int y::Int end struct Size width::Int height::Int end s1 = Spaceship(Position(0,0), Size(30,5), Missile); s2 = Spaceship(Position(10,0), Size(30,5), Laser); a1 = Asteroid(Position(20,0), Size(20,20)); a2 = Asteroid(Position(0,20), Size(20,20)); struct Rectangle top::Int left::Int bottom::Int right::Int # return the upper-left and lower-right points Rectangle(p::Position, s::Size) = new(p.y + s.height, p.x, p.y, p.x+s.width) end # check if the 2 rectangles (A & B) overlap function overlap(A::Rectangle, B::Rectangle) return A.left < B.right && A.right > B.left && A.top > B.bottom && A.bottom < B.top end function collide(A::Thing, B::Thing) println("Checking collision of thing vs. thing") rectA = Rectangle(position(A), size(A)) rectB = Rectangle(position(B), size(B)) return overlap(rectA, rectB) end function collide(A::Spaceship, B::Spaceship) println("Checking collision of spaceship vs. spaceship") return true # just a test end # Randomly pick two things and check function check_randomly(things) for i in 1:5 two = rand(things, 2) collide(two...) end end
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############################################################ # judiWavefield ############################################## ############################################################ # Authors: Philipp Witte ([email protected]), Henryk Modzelewski ([email protected]) # Date: June 2017 export judiWavefield, fft, ifft ############################################################ mutable struct judiWavefield{T} <: judiMultiSourceVector{T} nsrc::Integer dt::Vector{T} data::Vector{<:Union{Array{T, N}, PyArray}} where N end ############################################################ ## outer constructors """ judiWavefield nsrc::Integer dt::AbstractFloat data Abstract vector for seismic wavefields. Constructors ============ Construct wavefield vector from an info structure, a cell array of wavefields and the computational \\ time step dt: judiWavefield(nsrc, dt, data) """ function judiWavefield(nsrc::Integer, dt::AbstractFloat, data::Array{T, N}) where {T<:Number, N} # length of vector dataCell = [convert(Array{Float32, N}, data) for j=1:nsrc] return judiWavefield{Float32}(nsrc, [Float32(dt) for i=1:nsrc], dataCell) end function judiWavefield(dt::AbstractFloat, data::Vector{Array{T, N}}) where {T, N} # length of vector nsrc = length(data) T != Float32 && (data = tof32.(data)) return judiWavefield{Float32}(nsrc, [Float32(dt) for i=1:nsrc], data) end judiWavefield(dt::AbstractFloat, nsrc::Integer, data::Array{T, N}) where {T<:Number, N} = judiWavefield(nsrc, dt, data) judiWavefield(dt::AbstractFloat, data::Vector{Any}) = judiWavefield(dt, tof32.(data)) judiWavefield(dt::AbstractFloat, data::Array{T, N}) where {T<:Number, N} = judiWavefield(1, dt, data) conj(w::judiWavefield{T}) where {T<:Complex} = judiWavefield{R}(w.nsrc, w.dt, conj(w.data)) ############################################################ ## overloaded multi_source functions time_sampling(jv::judiWavefield) = jv.dt #################################################################### # JOLI conversion jo_convert(::Type{T}, jw::judiWavefield{T}, ::Bool) where {T<:Number} = jw jo_convert(::Type{T}, jw::judiWavefield{vT}, B::Bool) where {T<:Number, vT} = judiWavefield{T}(jw.nsrc, jv.dt, jo_convert.(T, jw.data, B)) zero(::Type{T}, v::judiWavefield{vT}; nsrc::Integer=v.nsrc) where {T, vT} = judiWavefield{T}(nsrc, v.dt, T(0) .* v.data[1:nsrc]) zero(::Type{T}, v::judiWavefield{vT}; nsrc::Integer=v.nsrc) where {T<:AbstractFloat, vT<:Complex} = judiWavefield{T}(nsrc, v.dt, T(0) .* real(v.data[1:nsrc])) (w::judiWavefield)(x::Vector{<:Array}) = judiWavefield(w.dt, x) function copy!(jv::judiWavefield, jv2::judiWavefield) v.data .= jv2.data jv.dt = jv2.dt jv end copyto!(jv::judiWavefield, jv2::judiWavefield) = copy!(jv, jv2) make_input(w::judiWavefield) = w.data[1] check_compat(ms::Vararg{judiWavefield, N}) where N = all(y -> y.dt == first(ms).dt, ms) getindex(a::judiWavefield{T}, srcnum::RangeOrVec) where T = judiWavefield{T}(length(srcnum), a.dt[srcnum], a.data[srcnum]) #################################################################### function push!(a::judiWavefield{T}, b::judiWavefield{T}) where T append!(a.data, b.data) append!(a.dt, b.dt) a.nsrc += b.nsrc end # DFT operator for wavefields, acts along time dimension function fft(x_in::judiWavefield{T}) where T x = similar(x_in, Complex{Float32}) for i=1:x_in.nsrc x.data[i] = fft(x_in.data[i], 1)/sqrt(size(x_in.data[i], 1)) end return x end function ifft(x_in::judiWavefield{T}) where T x = similar(x_in, Float32) for i=1:x_in.nsrc x.data[i] = real(ifft(x_in.data[i], 1)) * sqrt(size(x_in.data[i], 1)) end return x end
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2.557613
1,458
export pswap, singlet_block, basis_rotor using YaoBlocks using YaoArrayRegister: mulrow!, u1rows! function Yao.apply!(reg::ArrayReg, pb::PutBlock{N,2,RotationGate{2,T,G}}) where {N,T,G<:SWAPGate} mask1 = bmask(pb.locs[1]) mask2 = bmask(pb.locs[2]) mask12 = mask1|mask2 a, c, b_, d = mat(Rx(pb.content.theta)) e = exp(-im/2*pb.content.theta) state = statevec(reg) for b in basis(reg) if b&mask1==0 i = b+1 i_ = b ⊻ mask12 + 1 if b&mask2==mask2 u1rows!(state, i, i_, a, b_, c, d) else mulrow!(state, i, e) mulrow!(state, i_, e) end end end return reg end mutable struct Bag{N}<:TagBlock{AbstractBlock, N} content::AbstractBlock{N} end Yao.content(bag) = bag.content Yao.chcontent(bag::Bag, content) = Bag(content) Yao.mat(bag::Bag) = mat(bag.content) Yao.apply!(reg::AbstractRegister, bag::Bag) = apply!(reg, bag.content) YaoBlocks.PreserveStyle(::Bag) = YaoBlocks.PreserveAll() setcontent!(bag::Bag, content) = (bag.content = content; bag) function YaoBlocks.print_annotation(io::IO, bag::Bag) printstyled(io, "[⊞] "; bold=true, color=:blue) end """parametrized swap gate.""" function pswap(nbit::Int, i::Int, j::Int) put(nbit, (i,j)=>rot(SWAP, 0.0)) end """block for generating singlets.""" function singlet_block(nbit::Int, i::Int, j::Int) unit = chain(nbit) push!(unit, put(nbit, i=>chain(X, H))) push!(unit, control(nbit, -i, j=>X)) end basis_rotor(::ZGate) = I2Gate() basis_rotor(::XGate) = Ry(-0.5π) basis_rotor(::YGate) = Rx(0.5π) basis_rotor(basis::PauliGate, nbit, locs) = repeat(nbit, basis_rotor(basis), locs)
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2.040476
840
# this takes a load of spikes and plots them on an animated graph function spiketrain(t, spikes) # get co-ordinates for the spikes spiked= findall(spikes) spcoords = (t .* ones(length(spiked)), spiked) sc = scatter!(spcoords,xlims=(0,1000),marker=1, legend=false) display(sc) end function spiketrain(t, matrix::Array{<:Any,2}, spikes::BitArray{1}) matrix[:,t] = spikes imshow(matrix) return(matrix) end function visualiseweights(weights) GR.imshow(repeat(weights)) end function dashboard(plt, t, weights, activation, spt, da, rec) plt.p1 = plotact!(plt.p1, activation) plt.p2 = plotspt!(plt.p2, spt, t) plt.p3 = plotda!(plt.p3, [da], [t]) plt.p4 = plotrec!(plt.p4, rec) p = plot(plt.p1, plt.p2, plt.p3, plt.p4, layout = grid(2,2), legend=false, show=true) display(p) end function dashboard(plt, t, l, m::MatrixTypes, da) plt.p1 = plotact!(plt.p1, m.activation.layers[l]) plt.p2 = plotspt!(plt.p2, m.spt.layers[l], t) plt.p3 = plotda!(plt.p3, [da], [t]) plt.p4 = plotrec!(plt.p4, m.rec.layers[l]) p = plot(plt.p1, plt.p2, plt.p3, plt.p4, layout = grid(2,2), legend=false, show=true) display(p) end mutable struct Dashplot p1::Plots.Plot{<:AbstractBackend} p2::Plots.Plot{<:AbstractBackend} p3::Plots.Plot{<:AbstractBackend} p4::Plots.Plot{<:AbstractBackend} Dashplot() = new(heatmap(),heatmap(), scatter(), heatmap()) end function initialiseplot(plottype::Function) return plottype() end function plotact!(p1, activation) heatmap!(p1, reshape(activation, length(activation), 1)) end function plotspt!(p2, spt, t) spiked = spt.==t heatmap!(p2, reshape(spiked, length(spiked),1)) end function plotda!(p3, t, da) scatter!(p3, da, t) end function plotrec!(p4, rec) heatmap!(p4, reshape(rec,length(rec),1)) end
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2.245839
781
using Escher using FactCheck using Compat include("macros.jl") include("interop.jl") FactCheck.exitstatus()
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3.027778
36
include("c-lib-p2f-test.jl") include("c-lib-f2p-test.jl") include("c-lib-add-test.jl") include("c-lib-mul-test.jl") include("c-lib-div-test.jl") include("c-lib-mode-test.jl")
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2.108434
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""" Cropbox Declarative crop modeling framework. https://github.com/cropbox/Cropbox.jl See also: [`@system`](@ref), [`@config`](@ref), [`simulate`](@ref), [`evaluate`](@ref), [`calibrate`](@ref), [`visualize`](@ref), [`manipulate`](@ref) """ module Cropbox include("system.jl") include("unit.jl") include("random.jl") include("graph.jl") include("macro.jl") include("state.jl") include("bundle.jl") include("config.jl") include("system/clock.jl") include("system/context.jl") include("system/controller.jl") include("system/calendar.jl") include("system/store.jl") include("system/thermaltime.jl") include("util/simulate.jl") include("util/calibrate.jl") include("util/evaluate.jl") include("util/gather.jl") include("util/color.jl") include("util/dive.jl") include("util/hierarchy.jl") include("util/plot.jl") include("util/visualize.jl") include("util/manipulate.jl") end
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function Log_LikeliHood(m::AbstractModel, om, leaves) if leaves #= if the animal has left we want the probability of this to happen at that omission, given that it has not left before. Since we assume that the events are independent the product of each likelihood should give me the total probability. Using the log we can simply sum them =# return log(cdf(m,om) - cdf(m,om-1)) else #= if the animal hasn't left we want the probability of not leaving until om =# # this is equivalent log(1-cdf(dist,om)) but it's safe when cdf is near 1 return log(1-cdf(m, om)) end end function nll_data(m::AbstractModel,cm::Dict) -sum(v*Log_LikeliHood(m, k...) for (k, v) in cm) end function Distributions.fit(::Type{T}, b::DataFrames.AbstractDataFrame) where T<:AbstractModel cm = countmap(StructArray((Omissions_plus_one = b.Omissions_plus_one, Leave = b.Leave))) p = init(T, cm) res = optimize(params(p)) do param all(param .> 1e-10) || return 1e10 params(p) .= param return nll_data(p, cm) end params(p) .= Optim.minimizer(res) return p end ### function simulate(m::AbstractModel,n_samples=1) w = [cdf(m,x)-cdf(m,x-1) for x in 1:maximum(m)] weights = StatsBase.weights(w) [sample(1:maximum(m),weights) for _ in 1:n_samples] end
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# implementation of the GPUCompiler interfaces for generating WASM code ## target export WASMCompilerTarget Base.@kwdef struct WASMCompilerTarget <: AbstractCompilerTarget end llvm_triple(::WASMCompilerTarget) = "wasm32-unknown-unknown" function llvm_machine(target::WASMCompilerTarget) triple = llvm_triple(target) t = Target(triple=triple) cpu = "" feat = "" tm = TargetMachine(t, triple, cpu, feat) asm_verbosity!(tm, true) return tm end function process_entry!(job::CompilerJob{WASMCompilerTarget}, mod::LLVM.Module, entry::LLVM.Function) push!(function_attributes(entry), StringAttribute("wasm-export-name", String(chop(LLVM.name(entry), tail=4)), context(mod))) invoke(process_entry!, Tuple{CompilerJob, LLVM.Module, LLVM.Function}, job, mod, entry) end ## job runtime_slug(job::CompilerJob{WASMCompilerTarget}) = "wasm"
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""" reproduce!(bact::Bacterium, model::ABM) Simulates reproduction of bacteria. Energy is halved after subtracting a cost. Inherited features are varied. """ function reproduce!(bact::Bacterium, model::ABM) add_agent!( bact.pos, Bacterium, model, bact.species, 0, (bact.energy - model.reproduction_energy_cost) / 2.0, inherit(bact.sensory_radius, model.rng, model.σ_sensory_radius), inherit(bact.reproduction_threshold, model.rng, model.σ_reproduction_threshold), inherit(bact.speed, model.rng, model.σ_speed), bact.food_target, ) bact.age = 0 bact.energy = (bact.energy - model.reproduction_energy_cost) / 2.0 bact.sensory_radius = inherit(bact.sensory_radius, model.rng, model.σ_sensory_radius) bact.reproduction_threshold = inherit(bact.reproduction_threshold, model.rng, model.σ_reproduction_threshold) bact.speed = inherit(bact.speed, model.rng, model.σ_speed) end function agent_step!(bact::Bacterium, model::ABM) # die of age or starvation (bact.age > model.lifetime || bact.energy <= 0) && (kill_agent!(bact, model); return) # grow older bact.age += 1 # reproduce if possible bact.energy >= bact.reproduction_threshold && reproduce!(bact, model) # if currently on a food source if model.food[bact.pos...] > 0.0 # eat eaten = min(model.food[bact.pos...], bact.speed * model.eat_rate_factor) model.food[bact.pos...] -= eaten bact.energy += eaten return else # can't eat, so look for something else bact.food_target = (-1, -1) end # if bact doesn't see any food if bact.food_target == (-1, -1) best_pos = (-1, -1) # look for the best food nearby for pos in nearby_positions(bact.pos, model, bact.sensory_radius) best_pos == (-1, -1) || model.food[best_pos...] < model.food[pos...] || continue best_pos = pos end best_pos != (-1, -1) && (bact.food_target = best_pos) end # if we found some food or already had eyes on it if bact.food_target != (-1, -1) # move toward target delta = bact.food_target .- bact.pos #move as many steps diagonally as possible diag = min(abs.(delta)..., bact.speed) steps = diag movement = sign.(delta) .* diag # move the rest steps axially, if possible delta = delta .- movement while steps < bact.speed && any(delta .> 0) movement = movement .+ sign.(delta) delta = delta .- sign.(delta) steps += 1 end else # move randomly if there's no food nearby movement = rand.(model.rng, (AXIAL_DIRECTIONS, AXIAL_DIRECTIONS)) .* bact.speed end # move move_agent!(bact, clamp.(bact.pos .+ movement, 1, size(model.space.s)), model) # subtract cost of movement and looking bact.energy -= model.sensory_radius_cost * bact.sensory_radius + model.distance_cost * max(abs.(movement)...) end
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include("Batcher.jl") include("ForwardBatcher.jl")
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3
17
@testset "chi-square-analysis" begin msr_path = joinpath(mktempdir(),"temp.csv") data = _PMD.parse_file(_PMDSE.get_enwl_dss_path(ntw, fdr)) if rm_transfo _PMDSE.rm_enwl_transformer!(data) end if rd_lines _PMDSE.reduce_enwl_lines_eng!(data) end data["settings"]["sbase_default"] = 100.0 # insert the load profiles _PMDSE.insert_profiles!(data, season, elm, pfs, t = time_step) # transform data model data = _PMD.transform_data_model(data); _PMDSE.reduce_single_phase_loadbuses!(data) # solve the power flow pf_result = _PMD.solve_mc_pf(data, _PMD.ACPUPowerModel, ipopt_solver) key = "1" # or "sourcebus" v_pu = data["settings"]["vbases_default"][key]* data["settings"]["voltage_scale_factor"] # divider [V] to get the voltage in per units. v_max_err = 1.15 # maximum error of voltage measurement = 0.5% or 1.15 V σ_v = 1/3*v_max_err/v_pu p_pu = data["settings"]["sbase"] # divider [kW] to get the power in per units. p_max_err = 0.01 # maximum error of power measurement = 10W, or 0.01 kW σ_p = 1/3*p_max_err/p_pu # sigma_dict σ_dict = Dict("load" => Dict("load" => σ_p, "bus" => σ_v), "gen" => Dict("gen" => σ_p/100, "bus" => σ_v/100) ) # write measurements based on power flow _PMDSE.write_measurements!(_PMD.ACPUPowerModel, data, pf_result, msr_path, exclude = ["vi","vr"], σ = σ_dict) # read-in measurement data and set initial values _PMDSE.add_measurements!(data, msr_path, actual_meas = true) data["se_settings"] = Dict{String,Any}("criterion" => "rwlav", "rescaler" => 1) se_result = _PMDSE.solve_acp_red_mc_se(data, ipopt_solver) @test _PMDSE.get_degrees_of_freedom(data) == 34 chi_result = _PMDSE.exceeds_chi_squares_threshold(se_result, data) @test chi_result[1] == false @test isapprox(chi_result[2], 0.0, atol = 1e-8) @test isapprox(chi_result[3], 48.60, atol = 1e-2) _PMDSE.add_measurements!(data, msr_path, actual_meas = false) se_result = _PMDSE.solve_acp_red_mc_se(data, ipopt_solver) chi_result = _PMDSE.exceeds_chi_squares_threshold(se_result, data) @test chi_result[1] == true #TODO: there's no real bad data, check whether there is a problem with write_meas @test isapprox(chi_result[2], 963.32, atol = 1e-2) @test isapprox(chi_result[3], 48.60, atol = 1e-2) end @testset "h_functions" begin # NB: the length (in terms of lines of code) of this sub-test could/should be significantly result but have no time now msr_path = joinpath(mktempdir(),"temp.csv") data = _PMD.parse_file(joinpath(BASE_DIR, "test/data/extra/networks/case3_unbalanced.dss"); data_model=MATHEMATICAL) #reduce grid [delete!(data["load"], l) for (l, load) in data["load"] if l!="1"] _PMDSE.reduce_single_phase_loadbuses!(data) pf_result = _PMD.solve_mc_pf(data, _PMD.ACPUPowerModel, ipopt_solver) _PMDSE.write_measurements!(_PMD.ACPUPowerModel, data, pf_result, msr_path, exclude = ["vr","vi"]) _PMDSE.add_measurements!(data, msr_path, actual_meas = true) # state is the result of the power flow vv = pf_result["solution"]["bus"] state = [ vv["4"]["vm"][1], vv["4"]["vm"][2], vv["4"]["vm"][3], vv["1"]["vm"][1], vv["1"]["vm"][2], vv["1"]["vm"][3], vv["2"]["vm"][1], vv["2"]["vm"][2], vv["2"]["vm"][3], vv["3"]["vm"][1], vv["1"]["va"][1], vv["1"]["va"][2], vv["1"]["va"][3], vv["2"]["va"][1], vv["2"]["va"][2], vv["2"]["va"][3], vv["3"]["va"][1] ] variable_dict = _PMDSE.build_variable_dictionary(data) state_array = _PMDSE.build_state_array(pf_result, variable_dict) @test state_array == state # push h functions functions = [] ref_bus = 4 _PMDSE.add_h_function!(:pd, "4", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:qd, "5", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:pg, "1", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:qg, "2", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:vm, "3", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:vm, "6", data, ref_bus, variable_dict, functions) @test isapprox( functions[1](state), -_DST.mean(data["meas"]["4"]["dst"][1]) ) #pd @test isapprox( functions[2](state), -_DST.mean(data["meas"]["5"]["dst"][1]) ) # qd @test isapprox( functions[3](state), pf_result["solution"]["gen"]["1"]["pg"][1], atol=1e-8 ) @test isapprox( functions[4](state), pf_result["solution"]["gen"]["1"]["pg"][2], atol=1e-8 ) @test isapprox( functions[5](state), pf_result["solution"]["gen"]["1"]["pg"][3], atol=1e-8 ) @test isapprox( functions[6](state), pf_result["solution"]["gen"]["1"]["qg"][1], atol=1e-8 ) @test isapprox( functions[7](state), pf_result["solution"]["gen"]["1"]["qg"][2], atol=1e-8 ) @test isapprox( functions[8](state), pf_result["solution"]["gen"]["1"]["qg"][3], atol=1e-8 ) @test isapprox( functions[9](state), pf_result["solution"]["bus"]["4"]["vm"][1] ) @test isapprox( functions[10](state), pf_result["solution"]["bus"]["4"]["vm"][2] ) @test isapprox( functions[11](state), pf_result["solution"]["bus"]["4"]["vm"][3] ) @test isapprox( functions[12](state), pf_result["solution"]["bus"]["3"]["vm"][1] ) _PMDSE.add_measurement!(data, :p, :branch, 1, pf_result["solution"]["branch"]["1"]["pt"], [0.0003]) _PMDSE.add_measurement!(data, :q, :branch, 3, pf_result["solution"]["branch"]["3"]["qf"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :q, :branch, 1, pf_result["solution"]["branch"]["1"]["qf"], [0.0003]) _PMDSE.add_h_function!(:p, "7", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:q, "8", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:q, "9", data, ref_bus, variable_dict, functions) cm3 = sqrt.(pf_result["solution"]["branch"]["3"]["pf"].^2+pf_result["solution"]["branch"]["3"]["qf"].^2)./(pf_result["solution"]["bus"]["4"]["vm"]) cm1 = sqrt(pf_result["solution"]["branch"]["1"]["pf"][1]^2+pf_result["solution"]["branch"]["1"]["qf"][1]^2)/(pf_result["solution"]["bus"]["1"]["vm"][2]) _PMDSE.add_measurement!(data, :cm, :branch, 3, cm3, [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :cm, :branch, 1, [cm1], [0.0003]) _PMDSE.add_measurement!(data, :va, :bus, 2, pf_result["solution"]["bus"]["2"]["va"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_h_function!(:cm, "10", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:cm, "11", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:va, "12", data, ref_bus, variable_dict, functions) @test isapprox( functions[13](state), pf_result["solution"]["branch"]["1"]["pf"][1] ) @test isapprox( functions[14](state), pf_result["solution"]["branch"]["3"]["qf"][1], atol=1e-8 ) @test isapprox( functions[15](state), pf_result["solution"]["branch"]["3"]["qf"][2], atol=1e-8 ) @test isapprox( functions[16](state), pf_result["solution"]["branch"]["3"]["qf"][3], atol=1e-8 ) @test isapprox( functions[17](state), pf_result["solution"]["branch"]["1"]["qf"][1] ) @test isapprox( functions[18](state), cm3[1] , atol=1e-8) @test isapprox( functions[19](state), cm3[2] , atol=1e-8) @test isapprox( functions[20](state), cm3[3], atol=1e-8 ) @test isapprox( functions[21](state), cm1 ) @test isapprox( functions[22](state), pf_result["solution"]["bus"]["2"]["va"][1]) @test isapprox( functions[23](state), pf_result["solution"]["bus"]["2"]["va"][2]) @test isapprox( functions[24](state), pf_result["solution"]["bus"]["2"]["va"][3]) pf_result_ivr = _PMD.solve_mc_pf(data, _PMD.IVRUPowerModel, ipopt_solver) _PMDSE.add_measurement!(data, :cr, :branch, 3, pf_result_ivr["solution"]["branch"]["3"]["cr_fr"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :ci, :branch, 3, pf_result_ivr["solution"]["branch"]["3"]["ci_fr"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :crd, :branch, 1, pf_result_ivr["solution"]["load"]["1"]["crd_bus"], [0.0003]) _PMDSE.add_measurement!(data, :cid, :branch, 1, pf_result_ivr["solution"]["load"]["1"]["cid_bus"], [0.0003]) _PMDSE.add_h_function!(:cr, "13", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:ci, "14", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:crd, "15", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:cid, "16", data, ref_bus, variable_dict, functions) @test isapprox( functions[25](state), pf_result_ivr["solution"]["branch"]["3"]["cr_fr"][1], atol=1e-8) @test isapprox( functions[26](state), pf_result_ivr["solution"]["branch"]["3"]["cr_fr"][2], atol=4e-5) @test isapprox( functions[27](state), pf_result_ivr["solution"]["branch"]["3"]["cr_fr"][3], atol=1e-8) @test isapprox( functions[28](state), pf_result_ivr["solution"]["branch"]["3"]["ci_fr"][1], atol=1e-5) @test isapprox( functions[29](state), pf_result_ivr["solution"]["branch"]["3"]["ci_fr"][2], atol=2e-5) @test isapprox( functions[30](state), pf_result_ivr["solution"]["branch"]["3"]["ci_fr"][3], atol=2e-5) @test isapprox( functions[31](state), -pf_result_ivr["solution"]["load"]["1"]["crd_bus"][1], atol=2e-4) @test isapprox( functions[32](state), -pf_result_ivr["solution"]["load"]["1"]["cid_bus"][1], atol=2e-4) _PMDSE.add_measurement!(data, :p, :branch, 2, pf_result["solution"]["branch"]["2"]["pf"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :q, :branch, 2, pf_result["solution"]["branch"]["2"]["qf"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :cr, :branch, 2, pf_result_ivr["solution"]["branch"]["2"]["cr_fr"], [0.0003, 0.0003, 0.0003]) _PMDSE.add_measurement!(data, :ci, :branch, 2, pf_result_ivr["solution"]["branch"]["2"]["ci_fr"], [0.0003, 0.0003, 0.0003]) cmfr = sqrt.(pf_result_ivr["solution"]["branch"]["2"]["cr_fr"].^2 + pf_result_ivr["solution"]["branch"]["2"]["ci_fr"].^2) _PMDSE.add_measurement!(data, :cm, :branch, 2, cmfr, [0.0003, 0.0003, 0.0003]) _PMDSE.add_h_function!(:p, "17", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:q, "18", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:cr, "19", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:ci, "20", data, ref_bus, variable_dict, functions) _PMDSE.add_h_function!(:cm, "21", data, ref_bus, variable_dict, functions) @test isapprox( functions[33](state), pf_result["solution"]["branch"]["2"]["pf"][1], atol=1e-8) @test isapprox( functions[34](state), pf_result["solution"]["branch"]["2"]["pf"][2], atol=1e-8) @test isapprox( functions[35](state), pf_result["solution"]["branch"]["2"]["pf"][3], atol=1e-8) @test isapprox( functions[36](state), pf_result["solution"]["branch"]["2"]["qf"][1], atol=1e-8) @test isapprox( functions[37](state), pf_result["solution"]["branch"]["2"]["qf"][2], atol=1e-8) @test isapprox( functions[38](state), pf_result["solution"]["branch"]["2"]["qf"][3], atol=1e-8) @test isapprox( functions[39](state), pf_result_ivr["solution"]["branch"]["2"]["cr_fr"][1], atol=1e-4) @test isapprox( functions[40](state), pf_result_ivr["solution"]["branch"]["2"]["cr_fr"][2], atol=1e-4) @test isapprox( functions[41](state), pf_result_ivr["solution"]["branch"]["2"]["cr_fr"][3], atol=1e-4) @test isapprox( functions[42](state), pf_result_ivr["solution"]["branch"]["2"]["ci_fr"][1], atol=1e-4) @test isapprox( functions[43](state), pf_result_ivr["solution"]["branch"]["2"]["ci_fr"][2], atol=1e-4) @test isapprox( functions[44](state), pf_result_ivr["solution"]["branch"]["2"]["ci_fr"][3], atol=1e-4) @test isapprox( functions[45](state), cmfr[1], atol=1e-6) @test isapprox( functions[46](state), cmfr[2], atol=1e-6) @test isapprox( functions[47](state), cmfr[3], atol=1e-6) end @testset "BadData_matrices_and_LNR" begin msr_path = joinpath(mktempdir(),"temp.csv") data = _PMD.parse_file(joinpath(BASE_DIR, "test/data/extra/networks/case3_unbalanced.dss"); data_model=MATHEMATICAL) #reduce grid [delete!(data["load"], l) for (l, load) in data["load"] if l!="1"] _PMDSE.reduce_single_phase_loadbuses!(data) pf_result = _PMD.solve_mc_pf(data, _PMD.ACPUPowerModel, ipopt_solver) _PMDSE.write_measurements!(_PMD.ACPUPowerModel, data, pf_result, msr_path, exclude = ["vr","vi"]) _PMDSE.add_measurements!(data, msr_path, actual_meas = true) _PMDSE.assign_start_to_variables!(data) data["se_settings"] = Dict{String,Any}("criterion" => "wls", "rescaler" => 1) se_result = _PMDSE.solve_acp_red_mc_se(data, ipopt_solver) _PMDSE.add_zib_virtual_meas!(data, 0.00000001, exclude = [2]) _PMDSE.add_zib_virtual_residuals!(se_result, data) variable_dict = _PMDSE.build_variable_dictionary(data) h_array = _PMDSE.build_measurement_function_array(data, variable_dict) state_array = _PMDSE.build_state_array(pf_result, variable_dict) stored_H_matrix = h5open(joinpath(BASE_DIR, "test/data/H_matrix.h5"), "r") do file read(file, "H") end stored_G_matrix = h5open(joinpath(BASE_DIR, "test/data/G_matrix.h5"), "r") do file read(file, "G") end stored_R_matrix = h5open(joinpath(BASE_DIR, "test/data/R_matrix.h5"), "r") do file read(file, "R") end stored_Ω_matrix = h5open(joinpath(BASE_DIR, "test/data/Ω_matrix.h5"), "r") do file read(file, "Ω") end H = _PMDSE.build_H_matrix(h_array, state_array) R = _PMDSE.build_R_matrix(data) G = _PMDSE.build_G_matrix(stored_H_matrix, R) Ω = _PMDSE.build_omega_matrix(R, stored_H_matrix, G) @test all(isapprox.(H, stored_H_matrix, atol=1)) @test all(isapprox.(R, stored_R_matrix, atol=1)) #@test all(isapprox.(G, stored_G_matrix, atol=1)) @test all(isapprox.(Ω, stored_Ω_matrix, atol=1)) id_val, exc = _PMDSE.normalized_residuals(data, se_result, Ω) #@test !exc #@test id_val[1] == "3" #@test isapprox(id_val[2], 0.11035175, atol=1e-8) _PMDSE.simple_normalized_residuals(data, se_result, R) @test haskey(se_result["solution"]["meas"]["5"], "nr") end
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2.067679
6,915
module CUDNN using CUDA include("../libcudnn-5/libcudnn.jl") include("../libcudnn-5/libcudnn_types.jl") @windows? ( begin const libcudnn = Libdl.find_library(["cudnn64_5"]) end : begin const libcudnn = Libdl.find_library(["libcudnn"]) end) isempty(libcudnn) && throw("CUDNN library cannot be found.") function checkstatus(status) if status != CUDNN_STATUS_SUCCESS Base.show_backtrace(STDOUT, backtrace()) throw(bytestring(cudnnGetErrorString(status))) end end datatype(::Type{Float32}) = CUDNN_DATA_FLOAT datatype(::Type{Float64}) = CUDNN_DATA_DOUBLE datatype(::Type{Float16}) = CUDNN_DATA_HALF include("handle.jl") include("tensor.jl") include("activation.jl") include("convolution.jl") include("filter.jl") include("softmax.jl") end
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2.453674
313
import Base: .+, .-, .*, ./, .^, max, min, .==, .>, .>=, .<, .<=, +, - # Broadcasting binary functions (uses the same list as same size arrays) cuda12 = cuda11 # Broadcast max/min haven't been defined: max(a::Array,b::Array)=broadcast(max,a,b) min(a::Array,b::Array)=broadcast(min,a,b) function vbroadcast_shape(x,y) nz = max(ndims(x),ndims(y)) dz = ones(Int,nz) xdims = ydims = xsame = ysame = xlast = ylast = 0; zlen = 1 for i=1:nz if size(x,i) > 1 xdims += 1; xlast = i dz[i] = size(x,i) end if size(y,i) > 1 ydims += 1; ylast = i if dz[i] == 1 dz[i] = size(y,i) else dz[i] == size(y,i) || throw(DimensionMismatch("arrays could not be broadcast to a common size")) end end xsame += (dz[i] == size(x,i)) ysame += (dz[i] == size(y,i)) zlen *= dz[i] end xsame == nz || xdims <= 1 || error("Only vector broadcasting supported") ysame == nz || ydims <= 1 || error("Only vector broadcasting supported") if xdims == 0 sx = zlen; nx = 1 elseif xdims == 1 sx = prod(dz[1:xlast-1]); nx=dz[xlast] elseif xsame == nz sx = 1; nx=zlen else error("Broadcasting error") end if ydims == 0 sy = zlen; ny = 1 elseif ydims == 1 sy = prod(dz[1:ylast-1]); ny=dz[ylast] elseif ysame == nz sy = 1; ny=zlen else error("Broadcasting error") end return (tuple(dz...), sx, nx, sy, ny) end function cuda12def(f, j=f, o...) J=Symbol(j) for S in (32,64) T = Symbol("Float$S") F11 = "$(f)_$(S)_11" F12 = "$(f)_$(S)_12" @eval begin function $J(x::KnetArray{$T},y::KnetArray{$T}) if size(x)==size(y) z = similar(x) ccall(($F11,$libknet8),Void,(Cint,$Ptr{$T},Ptr{$T},Ptr{$T}),length(z),x,y,z) return z else (dz,sx,nx,sy,ny) = vbroadcast_shape(x,y) z = similar(x,dz) ccall(($F12,$libknet8),Void,(Cint,$Ptr{$T},Cint,Cint,Ptr{$T},Cint,Cint,Ptr{$T}),length(z),x,sx,nx,y,sy,ny,z) return z end end end end end #if isdefined(:libknet8) for f in cuda12 isa(f,Tuple) || (f=(f,)) cuda12def(f...) end #end
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1.710306
1,436
@testset "8.8 Polylogarithm function" begin (F, a, b, c, d, e, f, g, h, m, n, p, q, x, ) = @variables F a b c d e f g h m n p q x #= ::Package:: =# #= ::Title:: =# #=Integration*Problems*Involving*the*Polylogarithm*Function=# #= ::Section::Closed:: =# #=Integrands*of*the*form*(d*x)^m*PolyLog(n, a*x^q)=# #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*PolyLog(n, a*x^q)=# #= ::Subsubsection::Closed:: =# #=q=1=# @test_int [x^4*PolyLog(2, a*x), x, 4, -(x/(25*a^4)) - x^2/(50*a^3) - x^3/(75*a^2) - x^4/(100*a) - x^5/125 - log(1 - a*x)/(25*a^5) + (1/25)*x^5*log(1 - a*x) + (1/5)*x^5*PolyLog(2, a*x)] @test_int [x^3*PolyLog(2, a*x), x, 4, -(x/(16*a^3)) - x^2/(32*a^2) - x^3/(48*a) - x^4/64 - log(1 - a*x)/(16*a^4) + (1/16)*x^4*log(1 - a*x) + (1/4)*x^4*PolyLog(2, a*x)] @test_int [x^2*PolyLog(2, a*x), x, 4, -(x/(9*a^2)) - x^2/(18*a) - x^3/27 - log(1 - a*x)/(9*a^3) + (1/9)*x^3*log(1 - a*x) + (1/3)*x^3*PolyLog(2, a*x)] @test_int [x^1*PolyLog(2, a*x), x, 4, -(x/(4*a)) - x^2/8 - log(1 - a*x)/(4*a^2) + (1/4)*x^2*log(1 - a*x) + (1/2)*x^2*PolyLog(2, a*x)] @test_int [x^0*PolyLog(2, a*x), x, 3, -x - ((1 - a*x)*log(1 - a*x))/a + x*PolyLog(2, a*x)] @test_int [PolyLog(2, a*x)/x^1, x, 1, PolyLog(3, a*x)] @test_int [PolyLog(2, a*x)/x^2, x, 5, a*log(x) - a*log(1 - a*x) + log(1 - a*x)/x - PolyLog(2, a*x)/x] @test_int [PolyLog(2, a*x)/x^3, x, 4, -(a/(4*x)) + (1/4)*a^2*log(x) - (1/4)*a^2*log(1 - a*x) + log(1 - a*x)/(4*x^2) - PolyLog(2, a*x)/(2*x^2)] @test_int [PolyLog(2, a*x)/x^4, x, 4, -(a/(18*x^2)) - a^2/(9*x) + (1/9)*a^3*log(x) - (1/9)*a^3*log(1 - a*x) + log(1 - a*x)/(9*x^3) - PolyLog(2, a*x)/(3*x^3)] @test_int [PolyLog(2, a*x)/x^5, x, 4, -(a/(48*x^3)) - a^2/(32*x^2) - a^3/(16*x) + (1/16)*a^4*log(x) - (1/16)*a^4*log(1 - a*x) + log(1 - a*x)/(16*x^4) - PolyLog(2, a*x)/(4*x^4)] @test_int [x^3*PolyLog(3, a*x), x, 5, x/(64*a^3) + x^2/(128*a^2) + x^3/(192*a) + x^4/256 + log(1 - a*x)/(64*a^4) - (1/64)*x^4*log(1 - a*x) - (1/16)*x^4*PolyLog(2, a*x) + (1/4)*x^4*PolyLog(3, a*x)] @test_int [x^2*PolyLog(3, a*x), x, 5, x/(27*a^2) + x^2/(54*a) + x^3/81 + log(1 - a*x)/(27*a^3) - (1/27)*x^3*log(1 - a*x) - (1/9)*x^3*PolyLog(2, a*x) + (1/3)*x^3*PolyLog(3, a*x)] @test_int [x^1*PolyLog(3, a*x), x, 5, x/(8*a) + x^2/16 + log(1 - a*x)/(8*a^2) - (1/8)*x^2*log(1 - a*x) - (1/4)*x^2*PolyLog(2, a*x) + (1/2)*x^2*PolyLog(3, a*x)] @test_int [x^0*PolyLog(3, a*x), x, 4, x + ((1 - a*x)*log(1 - a*x))/a - x*PolyLog(2, a*x) + x*PolyLog(3, a*x)] @test_int [PolyLog(3, a*x)/x^1, x, 1, PolyLog(4, a*x)] @test_int [PolyLog(3, a*x)/x^2, x, 6, a*log(x) - a*log(1 - a*x) + log(1 - a*x)/x - PolyLog(2, a*x)/x - PolyLog(3, a*x)/x] @test_int [PolyLog(3, a*x)/x^3, x, 5, -(a/(8*x)) + (1/8)*a^2*log(x) - (1/8)*a^2*log(1 - a*x) + log(1 - a*x)/(8*x^2) - PolyLog(2, a*x)/(4*x^2) - PolyLog(3, a*x)/(2*x^2)] @test_int [PolyLog(3, a*x)/x^4, x, 5, -(a/(54*x^2)) - a^2/(27*x) + (1/27)*a^3*log(x) - (1/27)*a^3*log(1 - a*x) + log(1 - a*x)/(27*x^3) - PolyLog(2, a*x)/(9*x^3) - PolyLog(3, a*x)/(3*x^3)] #= ::Subsubsection::Closed:: =# #=q=2=# @test_int [x^5*PolyLog(2, a*x^2), x, 5, -(x^2/(18*a^2)) - x^4/(36*a) - x^6/54 - log(1 - a*x^2)/(18*a^3) + (1/18)*x^6*log(1 - a*x^2) + (1/6)*x^6*PolyLog(2, a*x^2)] @test_int [x^3*PolyLog(2, a*x^2), x, 5, -(x^2/(8*a)) - x^4/16 - log(1 - a*x^2)/(8*a^2) + (1/8)*x^4*log(1 - a*x^2) + (1/4)*x^4*PolyLog(2, a*x^2)] @test_int [x^1*PolyLog(2, a*x^2), x, 4, -(x^2/2) - ((1 - a*x^2)*log(1 - a*x^2))/(2*a) + (1/2)*x^2*PolyLog(2, a*x^2)] @test_int [PolyLog(2, a*x^2)/x^1, x, 1, (1/2)*PolyLog(3, a*x^2)] @test_int [PolyLog(2, a*x^2)/x^3, x, 6, a*log(x) - (1/2)*a*log(1 - a*x^2) + log(1 - a*x^2)/(2*x^2) - PolyLog(2, a*x^2)/(2*x^2)] @test_int [PolyLog(2, a*x^2)/x^5, x, 5, -(a/(8*x^2)) + (1/4)*a^2*log(x) - (1/8)*a^2*log(1 - a*x^2) + log(1 - a*x^2)/(8*x^4) - PolyLog(2, a*x^2)/(4*x^4)] @test_int [PolyLog(2, a*x^2)/x^7, x, 5, -(a/(36*x^4)) - a^2/(18*x^2) + (1/9)*a^3*log(x) - (1/18)*a^3*log(1 - a*x^2) + log(1 - a*x^2)/(18*x^6) - PolyLog(2, a*x^2)/(6*x^6)] @test_int [x^4*PolyLog(2, a*x^2), x, 5, -((4*x)/(25*a^2)) - (4*x^3)/(75*a) - (4*x^5)/125 + (4*atanh(sqrt(a)*x))/(25*a^(5/2)) + (2/25)*x^5*log(1 - a*x^2) + (1/5)*x^5*PolyLog(2, a*x^2)] @test_int [x^2*PolyLog(2, a*x^2), x, 5, -((4*x)/(9*a)) - (4*x^3)/27 + (4*atanh(sqrt(a)*x))/(9*a^(3/2)) + (2/9)*x^3*log(1 - a*x^2) + (1/3)*x^3*PolyLog(2, a*x^2)] @test_int [x^0*PolyLog(2, a*x^2), x, 4, -4*x + (4*atanh(sqrt(a)*x))/sqrt(a) + 2*x*log(1 - a*x^2) + x*PolyLog(2, a*x^2)] @test_int [PolyLog(2, a*x^2)/x^2, x, 3, 4*sqrt(a)*atanh(sqrt(a)*x) + (2*log(1 - a*x^2))/x - PolyLog(2, a*x^2)/x] @test_int [PolyLog(2, a*x^2)/x^4, x, 4, -((4*a)/(9*x)) + (4/9)*a^(3/2)*atanh(sqrt(a)*x) + (2*log(1 - a*x^2))/(9*x^3) - PolyLog(2, a*x^2)/(3*x^3)] @test_int [PolyLog(2, a*x^2)/x^6, x, 5, -((4*a)/(75*x^3)) - (4*a^2)/(25*x) + (4/25)*a^(5/2)*atanh(sqrt(a)*x) + (2*log(1 - a*x^2))/(25*x^5) - PolyLog(2, a*x^2)/(5*x^5)] @test_int [x^5*PolyLog(3, a*x^2), x, 6, x^2/(54*a^2) + x^4/(108*a) + x^6/162 + log(1 - a*x^2)/(54*a^3) - (1/54)*x^6*log(1 - a*x^2) - (1/18)*x^6*PolyLog(2, a*x^2) + (1/6)*x^6*PolyLog(3, a*x^2)] @test_int [x^3*PolyLog(3, a*x^2), x, 6, x^2/(16*a) + x^4/32 + log(1 - a*x^2)/(16*a^2) - (1/16)*x^4*log(1 - a*x^2) - (1/8)*x^4*PolyLog(2, a*x^2) + (1/4)*x^4*PolyLog(3, a*x^2)] @test_int [x^1*PolyLog(3, a*x^2), x, 5, x^2/2 + ((1 - a*x^2)*log(1 - a*x^2))/(2*a) - (1/2)*x^2*PolyLog(2, a*x^2) + (1/2)*x^2*PolyLog(3, a*x^2)] @test_int [PolyLog(3, a*x^2)/x^1, x, 1, (1/2)*PolyLog(4, a*x^2)] @test_int [PolyLog(3, a*x^2)/x^3, x, 7, a*log(x) - (1/2)*a*log(1 - a*x^2) + log(1 - a*x^2)/(2*x^2) - PolyLog(2, a*x^2)/(2*x^2) - PolyLog(3, a*x^2)/(2*x^2)] @test_int [PolyLog(3, a*x^2)/x^5, x, 6, -(a/(16*x^2)) + (1/8)*a^2*log(x) - (1/16)*a^2*log(1 - a*x^2) + log(1 - a*x^2)/(16*x^4) - PolyLog(2, a*x^2)/(8*x^4) - PolyLog(3, a*x^2)/(4*x^4)] @test_int [PolyLog(3, a*x^2)/x^7, x, 6, -(a/(108*x^4)) - a^2/(54*x^2) + (1/27)*a^3*log(x) - (1/54)*a^3*log(1 - a*x^2) + log(1 - a*x^2)/(54*x^6) - PolyLog(2, a*x^2)/(18*x^6) - PolyLog(3, a*x^2)/(6*x^6)] @test_int [x^4*PolyLog(3, a*x^2), x, 6, (8*x)/(125*a^2) + (8*x^3)/(375*a) + (8*x^5)/625 - (8*atanh(sqrt(a)*x))/(125*a^(5/2)) - (4/125)*x^5*log(1 - a*x^2) - (2/25)*x^5*PolyLog(2, a*x^2) + (1/5)*x^5*PolyLog(3, a*x^2)] @test_int [x^2*PolyLog(3, a*x^2), x, 6, (8*x)/(27*a) + (8*x^3)/81 - (8*atanh(sqrt(a)*x))/(27*a^(3/2)) - (4/27)*x^3*log(1 - a*x^2) - (2/9)*x^3*PolyLog(2, a*x^2) + (1/3)*x^3*PolyLog(3, a*x^2)] @test_int [x^0*PolyLog(3, a*x^2), x, 5, 8*x - (8*atanh(sqrt(a)*x))/sqrt(a) - 4*x*log(1 - a*x^2) - 2*x*PolyLog(2, a*x^2) + x*PolyLog(3, a*x^2)] @test_int [PolyLog(3, a*x^2)/x^2, x, 4, 8*sqrt(a)*atanh(sqrt(a)*x) + (4*log(1 - a*x^2))/x - (2*PolyLog(2, a*x^2))/x - PolyLog(3, a*x^2)/x] @test_int [PolyLog(3, a*x^2)/x^4, x, 5, -((8*a)/(27*x)) + (8/27)*a^(3/2)*atanh(sqrt(a)*x) + (4*log(1 - a*x^2))/(27*x^3) - (2*PolyLog(2, a*x^2))/(9*x^3) - PolyLog(3, a*x^2)/(3*x^3)] @test_int [PolyLog(3, a*x^2)/x^6, x, 6, -((8*a)/(375*x^3)) - (8*a^2)/(125*x) + (8/125)*a^(5/2)*atanh(sqrt(a)*x) + (4*log(1 - a*x^2))/(125*x^5) - (2*PolyLog(2, a*x^2))/(25*x^5) - PolyLog(3, a*x^2)/(5*x^5)] #= ::Subsubsection::Closed:: =# #=q*symbolic=# @test_int [x^2*PolyLog(2, a*x^q), x, 3, (a*q^2*x^(3 + q)*HypergeometricFunctions._₂F₁(1, (3 + q)/q, 2 + 3/q, a*x^q))/(9*(3 + q)) + (1/9)*q*x^3*log(1 - a*x^q) + (1/3)*x^3*PolyLog(2, a*x^q)] @test_int [x^1*PolyLog(2, a*x^q), x, 3, (a*q^2*x^(2 + q)*HypergeometricFunctions._₂F₁(1, (2 + q)/q, 2*(1 + 1/q), a*x^q))/(4*(2 + q)) + (1/4)*q*x^2*log(1 - a*x^q) + (1/2)*x^2*PolyLog(2, a*x^q)] @test_int [x^0*PolyLog(2, a*x^q), x, 3, (a*q^2*x^(1 + q)*HypergeometricFunctions._₂F₁(1, 1 + 1/q, 2 + 1/q, a*x^q))/(1 + q) + q*x*log(1 - a*x^q) + x*PolyLog(2, a*x^q)] @test_int [PolyLog(2, a*x^q)/x^1, x, 1, PolyLog(3, a*x^q)/q] @test_int [PolyLog(2, a*x^q)/x^2, x, 3, -((a*q^2*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, -((1 - q)/q), 2 - 1/q, a*x^q))/(1 - q)) + (q*log(1 - a*x^q))/x - PolyLog(2, a*x^q)/x] @test_int [PolyLog(2, a*x^q)/x^3, x, 3, -((a*q^2*x^(-2 + q)*HypergeometricFunctions._₂F₁(1, -((2 - q)/q), 2*(1 - 1/q), a*x^q))/(4*(2 - q))) + (q*log(1 - a*x^q))/(4*x^2) - PolyLog(2, a*x^q)/(2*x^2)] @test_int [PolyLog(2, a*x^q)/x^4, x, 3, -((a*q^2*x^(-3 + q)*HypergeometricFunctions._₂F₁(1, -((3 - q)/q), 2 - 3/q, a*x^q))/(9*(3 - q))) + (q*log(1 - a*x^q))/(9*x^3) - PolyLog(2, a*x^q)/(3*x^3)] @test_int [x^2*PolyLog(3, a*x^q), x, 4, -((a*q^3*x^(3 + q)*HypergeometricFunctions._₂F₁(1, (3 + q)/q, 2 + 3/q, a*x^q))/(27*(3 + q))) - (1/27)*q^2*x^3*log(1 - a*x^q) - (1/9)*q*x^3*PolyLog(2, a*x^q) + (1/3)*x^3*PolyLog(3, a*x^q)] @test_int [x^1*PolyLog(3, a*x^q), x, 4, -((a*q^3*x^(2 + q)*HypergeometricFunctions._₂F₁(1, (2 + q)/q, 2*(1 + 1/q), a*x^q))/(8*(2 + q))) - (1/8)*q^2*x^2*log(1 - a*x^q) - (1/4)*q*x^2*PolyLog(2, a*x^q) + (1/2)*x^2*PolyLog(3, a*x^q)] @test_int [x^0*PolyLog(3, a*x^q), x, 4, -((a*q^3*x^(1 + q)*HypergeometricFunctions._₂F₁(1, 1 + 1/q, 2 + 1/q, a*x^q))/(1 + q)) - q^2*x*log(1 - a*x^q) - q*x*PolyLog(2, a*x^q) + x*PolyLog(3, a*x^q)] @test_int [PolyLog(3, a*x^q)/x^1, x, 1, PolyLog(4, a*x^q)/q] @test_int [PolyLog(3, a*x^q)/x^2, x, 4, -((a*q^3*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, -((1 - q)/q), 2 - 1/q, a*x^q))/(1 - q)) + (q^2*log(1 - a*x^q))/x - (q*PolyLog(2, a*x^q))/x - PolyLog(3, a*x^q)/x] @test_int [PolyLog(3, a*x^q)/x^3, x, 4, -((a*q^3*x^(-2 + q)*HypergeometricFunctions._₂F₁(1, -((2 - q)/q), 2*(1 - 1/q), a*x^q))/(8*(2 - q))) + (q^2*log(1 - a*x^q))/(8*x^2) - (q*PolyLog(2, a*x^q))/(4*x^2) - PolyLog(3, a*x^q)/(2*x^2)] @test_int [PolyLog(3, a*x^q)/x^4, x, 4, -((a*q^3*x^(-3 + q)*HypergeometricFunctions._₂F₁(1, -((3 - q)/q), 2 - 3/q, a*x^q))/(27*(3 - q))) + (q^2*log(1 - a*x^q))/(27*x^3) - (q*PolyLog(2, a*x^q))/(9*x^3) - PolyLog(3, a*x^q)/(3*x^3)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*(d*x)^(m/2)*PolyLog(n, a*x^q)=# #= ::Subsubsection::Closed:: =# #=q=1=# @test_int [(d*x)^(3/2)*PolyLog(2, a*x), x, 7, -((8*d*sqrt(d*x))/(25*a^2)) - (8*(d*x)^(3/2))/(75*a) - (8*(d*x)^(5/2))/(125*d) + (8*d^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(25*a^(5/2)) + (4*(d*x)^(5/2)*log(1 - a*x))/(25*d) + (2*(d*x)^(5/2)*PolyLog(2, a*x))/(5*d)] @test_int [(d*x)^(1/2)*PolyLog(2, a*x), x, 6, -((8*sqrt(d*x))/(9*a)) - (8*(d*x)^(3/2))/(27*d) + (8*sqrt(d)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(9*a^(3/2)) + (4*(d*x)^(3/2)*log(1 - a*x))/(9*d) + (2*(d*x)^(3/2)*PolyLog(2, a*x))/(3*d)] @test_int [PolyLog(2, a*x)/(d*x)^(1/2), x, 5, -((8*sqrt(d*x))/d) + (8*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(sqrt(a)*sqrt(d)) + (4*sqrt(d*x)*log(1 - a*x))/d + (2*sqrt(d*x)*PolyLog(2, a*x))/d] @test_int [PolyLog(2, a*x)/(d*x)^(3/2), x, 4, (8*sqrt(a)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (4*log(1 - a*x))/(d*sqrt(d*x)) - (2*PolyLog(2, a*x))/(d*sqrt(d*x))] @test_int [PolyLog(2, a*x)/(d*x)^(5/2), x, 5, -((8*a)/(9*d^2*sqrt(d*x))) + (8*a^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(9*d^(5/2)) + (4*log(1 - a*x))/(9*d*(d*x)^(3/2)) - (2*PolyLog(2, a*x))/(3*d*(d*x)^(3/2))] @test_int [PolyLog(2, a*x)/(d*x)^(7/2), x, 6, -((8*a)/(75*d^2*(d*x)^(3/2))) - (8*a^2)/(25*d^3*sqrt(d*x)) + (8*a^(5/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(25*d^(7/2)) + (4*log(1 - a*x))/(25*d*(d*x)^(5/2)) - (2*PolyLog(2, a*x))/(5*d*(d*x)^(5/2))] @test_int [(d*x)^(5/2)*PolyLog(3, a*x), x, 9, (16*d^2*sqrt(d*x))/(343*a^3) + (16*d*(d*x)^(3/2))/(1029*a^2) + (16*(d*x)^(5/2))/(1715*a) + (16*(d*x)^(7/2))/(2401*d) - (16*d^(5/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(343*a^(7/2)) - (8*(d*x)^(7/2)*log(1 - a*x))/(343*d) - (4*(d*x)^(7/2)*PolyLog(2, a*x))/(49*d) + (2*(d*x)^(7/2)*PolyLog(3, a*x))/(7*d)] @test_int [(d*x)^(3/2)*PolyLog(3, a*x), x, 8, (16*d*sqrt(d*x))/(125*a^2) + (16*(d*x)^(3/2))/(375*a) + (16*(d*x)^(5/2))/(625*d) - (16*d^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(125*a^(5/2)) - (8*(d*x)^(5/2)*log(1 - a*x))/(125*d) - (4*(d*x)^(5/2)*PolyLog(2, a*x))/(25*d) + (2*(d*x)^(5/2)*PolyLog(3, a*x))/(5*d)] @test_int [(d*x)^(1/2)*PolyLog(3, a*x), x, 7, (16*sqrt(d*x))/(27*a) + (16*(d*x)^(3/2))/(81*d) - (16*sqrt(d)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(27*a^(3/2)) - (8*(d*x)^(3/2)*log(1 - a*x))/(27*d) - (4*(d*x)^(3/2)*PolyLog(2, a*x))/(9*d) + (2*(d*x)^(3/2)*PolyLog(3, a*x))/(3*d)] @test_int [PolyLog(3, a*x)/(d*x)^(1/2), x, 6, (16*sqrt(d*x))/d - (16*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(sqrt(a)*sqrt(d)) - (8*sqrt(d*x)*log(1 - a*x))/d - (4*sqrt(d*x)*PolyLog(2, a*x))/d + (2*sqrt(d*x)*PolyLog(3, a*x))/d] @test_int [PolyLog(3, a*x)/(d*x)^(3/2), x, 5, (16*sqrt(a)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (8*log(1 - a*x))/(d*sqrt(d*x)) - (4*PolyLog(2, a*x))/(d*sqrt(d*x)) - (2*PolyLog(3, a*x))/(d*sqrt(d*x))] @test_int [PolyLog(3, a*x)/(d*x)^(5/2), x, 6, -((16*a)/(27*d^2*sqrt(d*x))) + (16*a^(3/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(27*d^(5/2)) + (8*log(1 - a*x))/(27*d*(d*x)^(3/2)) - (4*PolyLog(2, a*x))/(9*d*(d*x)^(3/2)) - (2*PolyLog(3, a*x))/(3*d*(d*x)^(3/2))] @test_int [PolyLog(3, a*x)/(d*x)^(7/2), x, 7, -((16*a)/(375*d^2*(d*x)^(3/2))) - (16*a^2)/(125*d^3*sqrt(d*x)) + (16*a^(5/2)*atanh((sqrt(a)*sqrt(d*x))/sqrt(d)))/(125*d^(7/2)) + (8*log(1 - a*x))/(125*d*(d*x)^(5/2)) - (4*PolyLog(2, a*x))/(25*d*(d*x)^(5/2)) - (2*PolyLog(3, a*x))/(5*d*(d*x)^(5/2))] #= ::Subsubsection::Closed:: =# #=q=2=# @test_int [(d*x)^(3/2)*PolyLog(2, a*x^2), x, 9, -((32*d*sqrt(d*x))/(25*a)) - (32*(d*x)^(5/2))/(125*d) + (16*d^(3/2)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*a^(5/4)) + (16*d^(3/2)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*a^(5/4)) + (8*(d*x)^(5/2)*log(1 - a*x^2))/(25*d) + (2*(d*x)^(5/2)*PolyLog(2, a*x^2))/(5*d)] @test_int [(d*x)^(1/2)*PolyLog(2, a*x^2), x, 8, -((32*(d*x)^(3/2))/(27*d)) - (16*sqrt(d)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*a^(3/4)) + (16*sqrt(d)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*a^(3/4)) + (8*(d*x)^(3/2)*log(1 - a*x^2))/(9*d) + (2*(d*x)^(3/2)*PolyLog(2, a*x^2))/(3*d)] @test_int [PolyLog(2, a*x^2)/(d*x)^(1/2), x, 8, -((32*sqrt(d*x))/d) + (16*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) + (16*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) + (8*sqrt(d*x)*log(1 - a*x^2))/d + (2*sqrt(d*x)*PolyLog(2, a*x^2))/d] @test_int [PolyLog(2, a*x^2)/(d*x)^(3/2), x, 7, -((16*a^(1/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2)) + (16*a^(1/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (8*log(1 - a*x^2))/(d*sqrt(d*x)) - (2*PolyLog(2, a*x^2))/(d*sqrt(d*x))] @test_int [PolyLog(2, a*x^2)/(d*x)^(5/2), x, 7, (16*a^(3/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*d^(5/2)) + (16*a^(3/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(9*d^(5/2)) + (8*log(1 - a*x^2))/(9*d*(d*x)^(3/2)) - (2*PolyLog(2, a*x^2))/(3*d*(d*x)^(3/2))] @test_int [PolyLog(2, a*x^2)/(d*x)^(7/2), x, 8, -((32*a)/(25*d^3*sqrt(d*x))) - (16*a^(5/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*d^(7/2)) + (16*a^(5/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(25*d^(7/2)) + (8*log(1 - a*x^2))/(25*d*(d*x)^(5/2)) - (2*PolyLog(2, a*x^2))/(5*d*(d*x)^(5/2))] @test_int [(d*x)^(5/2)*PolyLog(3, a*x^2), x, 10, (128*d*(d*x)^(3/2))/(1029*a) + (128*(d*x)^(7/2))/(2401*d) + (64*d^(5/2)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*a^(7/4)) - (64*d^(5/2)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*a^(7/4)) - (32*(d*x)^(7/2)*log(1 - a*x^2))/(343*d) - (8*(d*x)^(7/2)*PolyLog(2, a*x^2))/(49*d) + (2*(d*x)^(7/2)*PolyLog(3, a*x^2))/(7*d)] @test_int [(d*x)^(3/2)*PolyLog(3, a*x^2), x, 10, (128*d*sqrt(d*x))/(125*a) + (128*(d*x)^(5/2))/(625*d) - (64*d^(3/2)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*a^(5/4)) - (64*d^(3/2)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*a^(5/4)) - (32*(d*x)^(5/2)*log(1 - a*x^2))/(125*d) - (8*(d*x)^(5/2)*PolyLog(2, a*x^2))/(25*d) + (2*(d*x)^(5/2)*PolyLog(3, a*x^2))/(5*d)] @test_int [(d*x)^(1/2)*PolyLog(3, a*x^2), x, 9, (128*(d*x)^(3/2))/(81*d) + (64*sqrt(d)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*a^(3/4)) - (64*sqrt(d)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*a^(3/4)) - (32*(d*x)^(3/2)*log(1 - a*x^2))/(27*d) - (8*(d*x)^(3/2)*PolyLog(2, a*x^2))/(9*d) + (2*(d*x)^(3/2)*PolyLog(3, a*x^2))/(3*d)] @test_int [PolyLog(3, a*x^2)/(d*x)^(1/2), x, 9, (128*sqrt(d*x))/d - (64*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) - (64*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(a^(1/4)*sqrt(d)) - (32*sqrt(d*x)*log(1 - a*x^2))/d - (8*sqrt(d*x)*PolyLog(2, a*x^2))/d + (2*sqrt(d*x)*PolyLog(3, a*x^2))/d] @test_int [PolyLog(3, a*x^2)/(d*x)^(3/2), x, 8, -((64*a^(1/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2)) + (64*a^(1/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/d^(3/2) + (32*log(1 - a*x^2))/(d*sqrt(d*x)) - (8*PolyLog(2, a*x^2))/(d*sqrt(d*x)) - (2*PolyLog(3, a*x^2))/(d*sqrt(d*x))] @test_int [PolyLog(3, a*x^2)/(d*x)^(5/2), x, 8, (64*a^(3/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*d^(5/2)) + (64*a^(3/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(27*d^(5/2)) + (32*log(1 - a*x^2))/(27*d*(d*x)^(3/2)) - (8*PolyLog(2, a*x^2))/(9*d*(d*x)^(3/2)) - (2*PolyLog(3, a*x^2))/(3*d*(d*x)^(3/2))] @test_int [PolyLog(3, a*x^2)/(d*x)^(7/2), x, 9, -((128*a)/(125*d^3*sqrt(d*x))) - (64*a^(5/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*d^(7/2)) + (64*a^(5/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(125*d^(7/2)) + (32*log(1 - a*x^2))/(125*d*(d*x)^(5/2)) - (8*PolyLog(2, a*x^2))/(25*d*(d*x)^(5/2)) - (2*PolyLog(3, a*x^2))/(5*d*(d*x)^(5/2))] @test_int [PolyLog(3, a*x^2)/(d*x)^(9/2), x, 9, -((128*a)/(1029*d^3*(d*x)^(3/2))) + (64*a^(7/4)*atan((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*d^(9/2)) + (64*a^(7/4)*atanh((a^(1/4)*sqrt(d*x))/sqrt(d)))/(343*d^(9/2)) + (32*log(1 - a*x^2))/(343*d*(d*x)^(7/2)) - (8*PolyLog(2, a*x^2))/(49*d*(d*x)^(7/2)) - (2*PolyLog(3, a*x^2))/(7*d*(d*x)^(7/2))] #= ::Subsubsection::Closed:: =# #=q*symbolic=# @test_int [(d*x)^(3/2)*PolyLog(2, a*x^q), x, 4, (8*a*d*q^2*x^(2 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (5/2 + q)/q, (1/2)*(4 + 5/q), a*x^q))/(25*(5 + 2*q)) + (4*q*(d*x)^(5/2)*log(1 - a*x^q))/(25*d) + (2*(d*x)^(5/2)*PolyLog(2, a*x^q))/(5*d)] @test_int [(d*x)^(1/2)*PolyLog(2, a*x^q), x, 4, (8*a*q^2*x^(1 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (3/2 + q)/q, (1/2)*(4 + 3/q), a*x^q))/(9*(3 + 2*q)) + (4*q*(d*x)^(3/2)*log(1 - a*x^q))/(9*d) + (2*(d*x)^(3/2)*PolyLog(2, a*x^q))/(3*d)] @test_int [PolyLog(2, a*x^q)/(d*x)^(1/2), x, 4, (8*a*q^2*x^q*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (1/2 + q)/q, (1/2)*(4 + 1/q), a*x^q))/(d*(1 + 2*q)) + (4*q*sqrt(d*x)*log(1 - a*x^q))/d + (2*sqrt(d*x)*PolyLog(2, a*x^q))/d] @test_int [PolyLog(2, a*x^q)/(d*x)^(3/2), x, 4, -((8*a*q^2*x^q*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 1/q), (1/2)*(4 - 1/q), a*x^q))/(d*(1 - 2*q)*sqrt(d*x))) + (4*q*log(1 - a*x^q))/(d*sqrt(d*x)) - (2*PolyLog(2, a*x^q))/(d*sqrt(d*x))] @test_int [PolyLog(2, a*x^q)/(d*x)^(5/2), x, 4, -((8*a*q^2*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 3/q), (1/2)*(4 - 3/q), a*x^q))/(9*d^2*(3 - 2*q)*sqrt(d*x))) + (4*q*log(1 - a*x^q))/(9*d*(d*x)^(3/2)) - (2*PolyLog(2, a*x^q))/(3*d*(d*x)^(3/2))] @test_int [(d*x)^(3/2)*PolyLog(3, a*x^q), x, 5, -((16*a*d*q^3*x^(2 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (5/2 + q)/q, (1/2)*(4 + 5/q), a*x^q))/(125*(5 + 2*q))) - (8*q^2*(d*x)^(5/2)*log(1 - a*x^q))/(125*d) - (4*q*(d*x)^(5/2)*PolyLog(2, a*x^q))/(25*d) + (2*(d*x)^(5/2)*PolyLog(3, a*x^q))/(5*d)] @test_int [(d*x)^(1/2)*PolyLog(3, a*x^q), x, 5, -((16*a*q^3*x^(1 + q)*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (3/2 + q)/q, (1/2)*(4 + 3/q), a*x^q))/(27*(3 + 2*q))) - (8*q^2*(d*x)^(3/2)*log(1 - a*x^q))/(27*d) - (4*q*(d*x)^(3/2)*PolyLog(2, a*x^q))/(9*d) + (2*(d*x)^(3/2)*PolyLog(3, a*x^q))/(3*d)] @test_int [PolyLog(3, a*x^q)/(d*x)^(1/2), x, 5, -((16*a*q^3*x^q*sqrt(d*x)*HypergeometricFunctions._₂F₁(1, (1/2 + q)/q, (1/2)*(4 + 1/q), a*x^q))/(d*(1 + 2*q))) - (8*q^2*sqrt(d*x)*log(1 - a*x^q))/d - (4*q*sqrt(d*x)*PolyLog(2, a*x^q))/d + (2*sqrt(d*x)*PolyLog(3, a*x^q))/d] @test_int [PolyLog(3, a*x^q)/(d*x)^(3/2), x, 5, -((16*a*q^3*x^q*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 1/q), (1/2)*(4 - 1/q), a*x^q))/(d*(1 - 2*q)*sqrt(d*x))) + (8*q^2*log(1 - a*x^q))/(d*sqrt(d*x)) - (4*q*PolyLog(2, a*x^q))/(d*sqrt(d*x)) - (2*PolyLog(3, a*x^q))/(d*sqrt(d*x))] @test_int [PolyLog(3, a*x^q)/(d*x)^(5/2), x, 5, -((16*a*q^3*x^(-1 + q)*HypergeometricFunctions._₂F₁(1, (1/2)*(2 - 3/q), (1/2)*(4 - 3/q), a*x^q))/(27*d^2*(3 - 2*q)*sqrt(d*x))) + (8*q^2*log(1 - a*x^q))/(27*d*(d*x)^(3/2)) - (4*q*PolyLog(2, a*x^q))/(9*d*(d*x)^(3/2)) - (2*PolyLog(3, a*x^q))/(3*d*(d*x)^(3/2))] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*PolyLog(n/2, a*x^q)=# @test_int [PolyLog(3/2, a*x), x, 2, (-x)*PolyLog(1/2, a*x) + x*PolyLog(3/2, a*x) + Unintegrable(PolyLog(-(1/2), a*x), x)] @test_int [PolyLog(1/2, a*x), x, 1, x*PolyLog(1/2, a*x) - Unintegrable(PolyLog(-(1/2), a*x), x)] @test_int [PolyLog(-1/2, a*x), x, 0, Unintegrable(PolyLog(-(1/2), a*x), x)] @test_int [PolyLog(-3/2, a*x), x, 1, x*PolyLog(-(1/2), a*x) - Unintegrable(PolyLog(-(1/2), a*x), x)] @test_int [PolyLog(-5/2, a*x), x, 2, x*PolyLog(-(3/2), a*x) - x*PolyLog(-(1/2), a*x) + Unintegrable(PolyLog(-(1/2), a*x), x)] @test_int [PolyLog(-3/2, a*x) + PolyLog(-1/2, a*x), x, 2, x*PolyLog(-1/2, a*x)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*(d*x)^m*PolyLog(n, a*x^q)*with*m*symbolic=# @test_int [(d*x)^m*PolyLog(2, a*x), x, 3, (a*(d*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, a*x))/(d^2*(1 + m)^2*(2 + m)) + ((d*x)^(1 + m)*log(1 - a*x))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(3, a*x), x, 4, -((a*(d*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, a*x))/(d^2*(1 + m)^3*(2 + m))) - ((d*x)^(1 + m)*log(1 - a*x))/(d*(1 + m)^3) - ((d*x)^(1 + m)*PolyLog(2, a*x))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(4, a*x), x, 5, (a*(d*x)^(2 + m)*HypergeometricFunctions._₂F₁(1, 2 + m, 3 + m, a*x))/(d^2*(1 + m)^4*(2 + m)) + ((d*x)^(1 + m)*log(1 - a*x))/(d*(1 + m)^4) + ((d*x)^(1 + m)*PolyLog(2, a*x))/(d*(1 + m)^3) - ((d*x)^(1 + m)*PolyLog(3, a*x))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(2, a*x^2), x, 4, (4*a*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (5 + m)/2, a*x^2))/(d^3*(1 + m)^2*(3 + m)) + (2*(d*x)^(1 + m)*log(1 - a*x^2))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x^2))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(3, a*x^2), x, 5, -((8*a*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (5 + m)/2, a*x^2))/(d^3*(1 + m)^3*(3 + m))) - (4*(d*x)^(1 + m)*log(1 - a*x^2))/(d*(1 + m)^3) - (2*(d*x)^(1 + m)*PolyLog(2, a*x^2))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x^2))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(4, a*x^2), x, 6, (16*a*(d*x)^(3 + m)*HypergeometricFunctions._₂F₁(1, (3 + m)/2, (5 + m)/2, a*x^2))/(d^3*(1 + m)^4*(3 + m)) + (8*(d*x)^(1 + m)*log(1 - a*x^2))/(d*(1 + m)^4) + (4*(d*x)^(1 + m)*PolyLog(2, a*x^2))/(d*(1 + m)^3) - (2*(d*x)^(1 + m)*PolyLog(3, a*x^2))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x^2))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(2, a*x^3), x, 4, (9*a*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/3, (7 + m)/3, a*x^3))/(d^4*(1 + m)^2*(4 + m)) + (3*(d*x)^(1 + m)*log(1 - a*x^3))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x^3))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(3, a*x^3), x, 5, -((27*a*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/3, (7 + m)/3, a*x^3))/(d^4*(1 + m)^3*(4 + m))) - (9*(d*x)^(1 + m)*log(1 - a*x^3))/(d*(1 + m)^3) - (3*(d*x)^(1 + m)*PolyLog(2, a*x^3))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x^3))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(4, a*x^3), x, 6, (81*a*(d*x)^(4 + m)*HypergeometricFunctions._₂F₁(1, (4 + m)/3, (7 + m)/3, a*x^3))/(d^4*(1 + m)^4*(4 + m)) + (27*(d*x)^(1 + m)*log(1 - a*x^3))/(d*(1 + m)^4) + (9*(d*x)^(1 + m)*PolyLog(2, a*x^3))/(d*(1 + m)^3) - (3*(d*x)^(1 + m)*PolyLog(3, a*x^3))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x^3))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(2, a*x^q), x, 4, (a*q^2*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q))/((1 + m)^2*(1 + m + q)) + (q*(d*x)^(1 + m)*log(1 - a*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(2, a*x^q))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(3, a*x^q), x, 5, -((a*q^3*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q))/((1 + m)^3*(1 + m + q))) - (q^2*(d*x)^(1 + m)*log(1 - a*x^q))/(d*(1 + m)^3) - (q*(d*x)^(1 + m)*PolyLog(2, a*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(3, a*x^q))/(d*(1 + m))] @test_int [(d*x)^m*PolyLog(4, a*x^q), x, 6, (a*q^4*x^(1 + q)*(d*x)^m*HypergeometricFunctions._₂F₁(1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q))/((1 + m)^4*(1 + m + q)) + (q^3*(d*x)^(1 + m)*log(1 - a*x^q))/(d*(1 + m)^4) + (q^2*(d*x)^(1 + m)*PolyLog(2, a*x^q))/(d*(1 + m)^3) - (q*(d*x)^(1 + m)*PolyLog(3, a*x^q))/(d*(1 + m)^2) + ((d*x)^(1 + m)*PolyLog(4, a*x^q))/(d*(1 + m))] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*(d*x)^m*PolyLog(n, a*x^q)*with*n*symbolic=# @test_int [x^1*PolyLog(n, a*x), x, 0, Unintegrable(x*PolyLog(n, a*x), x)] @test_int [x^0*PolyLog(n, a*x), x, 0, Unintegrable(PolyLog(n, a*x), x)] @test_int [PolyLog(n, a*x)/x^1, x, 1, PolyLog(1 + n, a*x)] @test_int [PolyLog(n, a*x)/x^2, x, 0, Unintegrable(PolyLog(n, a*x)/x^2, x)] @test_int [PolyLog(n, a*x)/x^3, x, 0, Unintegrable(PolyLog(n, a*x)/x^3, x)] @test_int [x^1*PolyLog(n, a*x^q), x, 0, Unintegrable(x*PolyLog(n, a*x^q), x)] @test_int [x^0*PolyLog(n, a*x^q), x, 0, Unintegrable(PolyLog(n, a*x^q), x)] @test_int [PolyLog(n, a*x^q)/x^1, x, 1, PolyLog(1 + n, a*x^q)/q] @test_int [PolyLog(n, a*x^q)/x^2, x, 0, Unintegrable(PolyLog(n, a*x^q)/x^2, x)] @test_int [PolyLog(n, a*x^q)/x^3, x, 0, Unintegrable(PolyLog(n, a*x^q)/x^3, x)] #= ::Section::Closed:: =# #=Integrands*of*the*form*(d*x)^m*PolyLog(n, c*(a+b*x))=# #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*PolyLog(n, c*(a+b*x))=# @test_int [x^2*PolyLog(2, c*(a + b*x)), x, 13, -((a^2*x)/(3*b^2)) + (a*(1 - a*c)*x)/(6*b^2*c) - ((1 - a*c)^2*x)/(9*b^2*c^2) + (a*x^2)/(12*b) - ((1 - a*c)*x^2)/(18*b*c) - x^3/27 + (a*(1 - a*c)^2*log(1 - a*c - b*c*x))/(6*b^3*c^2) - ((1 - a*c)^3*log(1 - a*c - b*c*x))/(9*b^3*c^3) - (a*x^2*log(1 - a*c - b*c*x))/(6*b) + (1/9)*x^3*log(1 - a*c - b*c*x) - (a^2*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(3*b^3*c) + (a^3*PolyLog(2, c*(a + b*x)))/(3*b^3) + (1/3)*x^3*PolyLog(2, c*(a + b*x))] @test_int [x^1*PolyLog(2, c*(a + b*x)), x, 10, (a*x)/(2*b) - ((1 - a*c)*x)/(4*b*c) - x^2/8 - ((1 - a*c)^2*log(1 - a*c - b*c*x))/(4*b^2*c^2) + (1/4)*x^2*log(1 - a*c - b*c*x) + (a*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(2*b^2*c) - (a^2*PolyLog(2, c*(a + b*x)))/(2*b^2) + (1/2)*x^2*PolyLog(2, c*(a + b*x))] @test_int [x^0*PolyLog(2, c*(a + b*x)), x, 7, -x - ((1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (a*PolyLog(2, c*(a + b*x)))/b + x*PolyLog(2, c*(a + b*x))] @test_int [PolyLog(2, c*(a + b*x))/x^1, x, 3, log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)) + (1/2)*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2 + (1/2)*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2 + (log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)) + log(x)*PolyLog(2, c*(a + b*x)) + log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))) - log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))) + (log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)) - PolyLog(3, -((b*x)/a)) + PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))) - PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))) - PolyLog(3, 1 - c*(a + b*x))] @test_int [PolyLog(2, c*(a + b*x))/x^2, x, 7, -((b*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/a) - (b*PolyLog(2, c*(a + b*x)))/a - PolyLog(2, c*(a + b*x))/x - (b*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a] @test_int [PolyLog(2, c*(a + b*x))/x^3, x, 11, (b^2*c*log(x))/(2*a*(1 - a*c)) - (b^2*c*log(1 - a*c - b*c*x))/(2*a*(1 - a*c)) + (b*log(1 - a*c - b*c*x))/(2*a*x) + (b^2*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2) + (b^2*PolyLog(2, c*(a + b*x)))/(2*a^2) - PolyLog(2, c*(a + b*x))/(2*x^2) + (b^2*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2)] @test_int [PolyLog(2, c*(a + b*x))/x^4, x, 14, -((b^2*c)/(6*a*(1 - a*c)*x)) + (b^3*c^2*log(x))/(6*a*(1 - a*c)^2) - (b^3*c*log(x))/(3*a^2*(1 - a*c)) - (b^3*c^2*log(1 - a*c - b*c*x))/(6*a*(1 - a*c)^2) + (b^3*c*log(1 - a*c - b*c*x))/(3*a^2*(1 - a*c)) + (b*log(1 - a*c - b*c*x))/(6*a*x^2) - (b^2*log(1 - a*c - b*c*x))/(3*a^2*x) - (b^3*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(3*a^3) - (b^3*PolyLog(2, c*(a + b*x)))/(3*a^3) - PolyLog(2, c*(a + b*x))/(3*x^3) - (b^3*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3)] @test_int [x^2*PolyLog(3, c*(a + b*x)), x, 33, (11*a^2*x)/(18*b^2) - (5*a*(1 - a*c)*x)/(36*b^2*c) + ((1 - a*c)^2*x)/(27*b^2*c^2) - (5*a*x^2)/(72*b) + ((1 - a*c)*x^2)/(54*b*c) + x^3/81 - (5*a*(1 - a*c)^2*log(1 - a*c - b*c*x))/(36*b^3*c^2) + ((1 - a*c)^3*log(1 - a*c - b*c*x))/(27*b^3*c^3) + (5*a*x^2*log(1 - a*c - b*c*x))/(36*b) - (1/27)*x^3*log(1 - a*c - b*c*x) + (11*a^2*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(18*b^3*c) - (11*a^3*PolyLog(2, c*(a + b*x)))/(18*b^3) - (a^2*x*PolyLog(2, c*(a + b*x)))/(3*b^2) + (a*x^2*PolyLog(2, c*(a + b*x)))/(6*b) - (1/9)*x^3*PolyLog(2, c*(a + b*x)) + (2*a^3*PolyLog(3, c*(a + b*x)))/(3*b^3) - ((a^3 - b^3*x^3)*PolyLog(3, c*(a + b*x)))/(3*b^3)] @test_int [x^1*PolyLog(3, c*(a + b*x)), x, 19, -((3*a*x)/(4*b)) + ((1 - a*c)*x)/(8*b*c) + x^2/16 + ((1 - a*c)^2*log(1 - a*c - b*c*x))/(8*b^2*c^2) - (1/8)*x^2*log(1 - a*c - b*c*x) - (3*a*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b^2*c) + (3*a^2*PolyLog(2, c*(a + b*x)))/(4*b^2) + (a*x*PolyLog(2, c*(a + b*x)))/(2*b) - (1/4)*x^2*PolyLog(2, c*(a + b*x)) - ((a^2 - b^2*x^2)*PolyLog(3, c*(a + b*x)))/(2*b^2)] @test_int [x^0*PolyLog(3, c*(a + b*x)), x, 9, x + ((1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) - (a*PolyLog(2, c*(a + b*x)))/b - x*PolyLog(2, c*(a + b*x)) + (a*PolyLog(3, c*(a + b*x)))/b + x*PolyLog(3, c*(a + b*x))] @test_int [PolyLog(3, c*(a + b*x))/x^1, x, 1, Int(PolyLog(3, a*c + b*c*x)/x, x)] @test_int [PolyLog(3, c*(a + b*x))/x^2, x, 6, (b*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/a + (b*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(2*a) + (b*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(2*a) + (b*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/a + (b*log(x)*PolyLog(2, c*(a + b*x)))/a + (b*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/a - (b*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/a + (b*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/a - (b*PolyLog(3, -((b*x)/a)))/a - (2*b*PolyLog(3, c*(a + b*x)))/a + ((b - a/x)*PolyLog(3, c*(a + b*x)))/a + (b*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/a - (b*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/a - (b*PolyLog(3, 1 - c*(a + b*x)))/a] @test_int [PolyLog(3, c*(a + b*x))/x^3, x, 12, -((b^2*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2)) - (b^2*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/(2*a^2) - (b^2*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(4*a^2) - (b^2*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(4*a^2) - (b^2*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/(2*a^2) - (b^2*PolyLog(2, c*(a + b*x)))/(2*a^2) - (b*PolyLog(2, c*(a + b*x)))/(2*a*x) - (b^2*log(x)*PolyLog(2, c*(a + b*x)))/(2*a^2) - (b^2*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) - (b^2*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*a^2) + (b^2*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/(2*a^2) - (b^2*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/(2*a^2) + (b^2*PolyLog(3, -((b*x)/a)))/(2*a^2) + ((b^2 - a^2/x^2)*PolyLog(3, c*(a + b*x)))/(2*a^2) - (b^2*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*a^2) + (b^2*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/(2*a^2) + (b^2*PolyLog(3, 1 - c*(a + b*x)))/(2*a^2)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*(d+e*x)^m*PolyLog(n,c*(a+b*x))=# @test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^3, x, 16, -(((b*d - a*e)^3*x)/(4*b^3)) - ((b*d - a*e)^2*(b*c*d + e - a*c*e)*x)/(8*b^3*c) - ((b*d - a*e)*(b*c*d + e - a*c*e)^2*x)/(12*b^3*c^2) - ((b*c*d + e - a*c*e)^3*x)/(16*b^3*c^3) - ((b*d - a*e)^2*(d + e*x)^2)/(16*b^2*e) - ((b*d - a*e)*(b*c*d + e - a*c*e)*(d + e*x)^2)/(24*b^2*c*e) - ((b*c*d + e - a*c*e)^2*(d + e*x)^2)/(32*b^2*c^2*e) - ((b*d - a*e)*(d + e*x)^3)/(36*b*e) - ((b*c*d + e - a*c*e)*(d + e*x)^3)/(48*b*c*e) - (d + e*x)^4/(64*e) - ((b*d - a*e)^2*(b*c*d + e - a*c*e)^2*log(1 - a*c - b*c*x))/(8*b^4*c^2*e) - ((b*d - a*e)*(b*c*d + e - a*c*e)^3*log(1 - a*c - b*c*x))/(12*b^4*c^3*e) - ((b*c*d + e - a*c*e)^4*log(1 - a*c - b*c*x))/(16*b^4*c^4*e) - ((b*d - a*e)^3*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b^4*c) + ((b*d - a*e)^2*(d + e*x)^2*log(1 - a*c - b*c*x))/(8*b^2*e) + ((b*d - a*e)*(d + e*x)^3*log(1 - a*c - b*c*x))/(12*b*e) + ((d + e*x)^4*log(1 - a*c - b*c*x))/(16*e) - ((b*d - a*e)^4*PolyLog(2, c*(a + b*x)))/(4*b^4*e) + ((d + e*x)^4*PolyLog(2, c*(a + b*x)))/(4*e)] @test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^2, x, 13, -(((b*d - a*e)^2*x)/(3*b^2)) - ((b*d - a*e)*(b*c*d + e - a*c*e)*x)/(6*b^2*c) - ((b*c*d + e - a*c*e)^2*x)/(9*b^2*c^2) - ((b*d - a*e)*(d + e*x)^2)/(12*b*e) - ((b*c*d + e - a*c*e)*(d + e*x)^2)/(18*b*c*e) - (d + e*x)^3/(27*e) - ((b*d - a*e)*(b*c*d + e - a*c*e)^2*log(1 - a*c - b*c*x))/(6*b^3*c^2*e) - ((b*c*d + e - a*c*e)^3*log(1 - a*c - b*c*x))/(9*b^3*c^3*e) - ((b*d - a*e)^2*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(3*b^3*c) + ((b*d - a*e)*(d + e*x)^2*log(1 - a*c - b*c*x))/(6*b*e) + ((d + e*x)^3*log(1 - a*c - b*c*x))/(9*e) - ((b*d - a*e)^3*PolyLog(2, c*(a + b*x)))/(3*b^3*e) + ((d + e*x)^3*PolyLog(2, c*(a + b*x)))/(3*e)] @test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^1, x, 10, -(((b*d - a*e)*x)/(2*b)) - ((b*c*d + e - a*c*e)*x)/(4*b*c) - (d + e*x)^2/(8*e) - ((b*c*d + e - a*c*e)^2*log(1 - a*c - b*c*x))/(4*b^2*c^2*e) - ((b*d - a*e)*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(2*b^2*c) + ((d + e*x)^2*log(1 - a*c - b*c*x))/(4*e) - ((b*d - a*e)^2*PolyLog(2, c*(a + b*x)))/(2*b^2*e) + ((d + e*x)^2*PolyLog(2, c*(a + b*x)))/(2*e)] @test_int [PolyLog(2, c*(a + b*x))*(d + e*x)^0, x, 7, -x - ((1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (a*PolyLog(2, c*(a + b*x)))/b + x*PolyLog(2, c*(a + b*x))] @test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^1, x, 3, ((log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*e) + (log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/e - ((log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*e) + (log(d + e*x)*PolyLog(2, c*(a + b*x)))/e + ((log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/e + ((log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/e - (log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/e + (log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/e - PolyLog(3, (b*(d + e*x))/(b*d - a*e))/e - PolyLog(3, 1 - c*(a + b*x))/e - PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x))))/e + PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x)))/e] @test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^2, x, 8, (b*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(e*(b*d - a*e)) + (b*PolyLog(2, c*(a + b*x)))/(e*(b*d - a*e)) - PolyLog(2, c*(a + b*x))/(e*(d + e*x)) + (b*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(e*(b*d - a*e))] @test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^3, x, 12, (b^2*c*log(1 - a*c - b*c*x))/(2*e*(b*d - a*e)*(b*c*d + e - a*c*e)) - (b*log(1 - a*c - b*c*x))/(2*e*(b*d - a*e)*(d + e*x)) - (b^2*c*log(d + e*x))/(2*e*(b*d - a*e)*(b*c*d + e - a*c*e)) + (b^2*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*e*(b*d - a*e)^2) + (b^2*PolyLog(2, c*(a + b*x)))/(2*e*(b*d - a*e)^2) - PolyLog(2, c*(a + b*x))/(2*e*(d + e*x)^2) + (b^2*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(2*e*(b*d - a*e)^2)] @test_int [PolyLog(2, c*(a + b*x))/(d + e*x)^4, x, 15, (b^2*c)/(6*e*(b*d - a*e)*(b*c*d + e - a*c*e)*(d + e*x)) + (b^3*c^2*log(1 - a*c - b*c*x))/(6*e*(b*d - a*e)*(b*c*d + e - a*c*e)^2) + (b^3*c*log(1 - a*c - b*c*x))/(3*e*(b*d - a*e)^2*(b*c*d + e - a*c*e)) - (b*log(1 - a*c - b*c*x))/(6*e*(b*d - a*e)*(d + e*x)^2) - (b^2*log(1 - a*c - b*c*x))/(3*e*(b*d - a*e)^2*(d + e*x)) - (b^3*c^2*log(d + e*x))/(6*e*(b*d - a*e)*(b*c*d + e - a*c*e)^2) - (b^3*c*log(d + e*x))/(3*e*(b*d - a*e)^2*(b*c*d + e - a*c*e)) + (b^3*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*e*(b*d - a*e)^3) + (b^3*PolyLog(2, c*(a + b*x)))/(3*e*(b*d - a*e)^3) - PolyLog(2, c*(a + b*x))/(3*e*(d + e*x)^3) + (b^3*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(3*e*(b*d - a*e)^3)] #= Following*integrands*are*equal. =# @test_int [PolyLog(2, x)/(-1 + x), x, 5, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)] @test_int [-PolyLog(2, x)/(1 - x), x, 5, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)] @test_int [PolyLog(2, x)/((-1 + x)*x), x, 8, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)-PolyLog(3,x)] @test_int [-PolyLog(2, x)/((1 - x)*x), x, 8, log(1-x)^2*log(x)+2*log(1-x)*PolyLog(2,1-x)+log(1-x)*PolyLog(2,x)-2*PolyLog(3,1-x)-PolyLog(3,x)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*PolyLog(n, e*((a + b*x) / (c + d*x))^n) / ((a + b*x)*(c + d*x))=# @test_int [PolyLog(n, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(1 + n, e*((a + b*x)/(c + d*x))^n)/((b*c - a*d)*n)] @test_int [PolyLog(3, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(4, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))] @test_int [PolyLog(2, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(3, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))] @test_int [PolyLog(1, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 1, PolyLog(2, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))] @test_int [PolyLog(0, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 2, PolyLog(1, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))] @test_int [PolyLog(-1, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 2, 1/((b*c - a*d)*n*(1 - e*((a + b*x)/(c + d*x))^n))] @test_int [PolyLog(-2, e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)), x, 4, PolyLog(-1, e*((a + b*x)/(c + d*x))^n)/(n*(b*c - a*d))] #= ::Section::Closed:: =# #=Integrands*of*the*form*(d*x)^m*PolyLog(n, d*(F^(c*(a + b*x)))^p)=# @test_int [x^3*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 5, (x^3*PolyLog(1 + n, d*(F^(c*(a + b*x)))^p))/(b*c*p*log(F)) - (3*x^2*PolyLog(2 + n, d*(F^(c*(a + b*x)))^p))/(b^2*c^2*p^2*log(F)^2) + (6*x*PolyLog(3 + n, d*(F^(c*(a + b*x)))^p))/(b^3*c^3*p^3*log(F)^3) - (6*PolyLog(4 + n, d*(F^(c*(a + b*x)))^p))/(b^4*c^4*p^4*log(F)^4)] @test_int [x^2*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 4, (x^2*PolyLog(1 + n, d*(F^(c*(a + b*x)))^p))/(b*c*p*log(F)) - (2*x*PolyLog(2 + n, d*(F^(c*(a + b*x)))^p))/(b^2*c^2*p^2*log(F)^2) + (2*PolyLog(3 + n, d*(F^(c*(a + b*x)))^p))/(b^3*c^3*p^3*log(F)^3)] @test_int [x^1*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 3, (x*PolyLog(1 + n, d*(F^(c*(a + b*x)))^p))/(b*c*p*log(F)) - PolyLog(2 + n, d*(F^(c*(a + b*x)))^p)/(b^2*c^2*p^2*log(F)^2)] @test_int [x^0*PolyLog(n, d*(F^(c*(a + b*x)))^p), x, 2, PolyLog(1 + n, d*(F^(c*(a + b*x)))^p)/(b*c*p*log(F))] @test_int [PolyLog(n, d*(F^(c*(a + b*x)))^p)/x^1, x, 1, CannotIntegrate(PolyLog(n, d*(F^(a*c + b*c*x))^p)/x, x)] #= ::Section::Closed:: =# #=Integrands*of*the*form*(d*x)^m*P(x)*(g+h*log(f*(d+e*x)^n))*PolyLog(2, c*(a+b*x))=# #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*log(1-c*x)*PolyLog(2, c*x)=# @test_int [x^3*log(1 - c*x)*PolyLog(2, c*x), x, 38, (355*x)/(576*c^3) + (139*x^2)/(1152*c^2) + (67*x^3)/(1728*c) + (3*x^4)/256 + (139*log(1 - c*x))/(576*c^4) - (x^2*log(1 - c*x))/(8*c^2) - (5*x^3*log(1 - c*x))/(72*c) - (3/64)*x^4*log(1 - c*x) + (3*(1 - c*x)*log(1 - c*x))/(8*c^4) - log(1 - c*x)^2/(16*c^4) + (1/16)*x^4*log(1 - c*x)^2 - (log(c*x)*log(1 - c*x)^2)/(4*c^4) - (x*PolyLog(2, c*x))/(4*c^3) - (x^2*PolyLog(2, c*x))/(8*c^2) - (x^3*PolyLog(2, c*x))/(12*c) - (1/16)*x^4*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(4*c^4) + (1/4)*x^4*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, 1 - c*x))/(2*c^4) + PolyLog(3, 1 - c*x)/(2*c^4)] @test_int [x^2*log(1 - c*x)*PolyLog(2, c*x), x, 31, (31*x)/(36*c^2) + (11*x^2)/(72*c) + x^3/27 + (11*log(1 - c*x))/(36*c^3) - (7*x^2*log(1 - c*x))/(36*c) - (1/9)*x^3*log(1 - c*x) + (5*(1 - c*x)*log(1 - c*x))/(9*c^3) - log(1 - c*x)^2/(9*c^3) + (1/9)*x^3*log(1 - c*x)^2 - (log(c*x)*log(1 - c*x)^2)/(3*c^3) - (x*PolyLog(2, c*x))/(3*c^2) - (x^2*PolyLog(2, c*x))/(6*c) - (1/9)*x^3*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(3*c^3) + (1/3)*x^3*log(1 - c*x)*PolyLog(2, c*x) - (2*log(1 - c*x)*PolyLog(2, 1 - c*x))/(3*c^3) + (2*PolyLog(3, 1 - c*x))/(3*c^3)] @test_int [x^1*log(1 - c*x)*PolyLog(2, c*x), x, 22, (13*x)/(8*c) + x^2/16 + (1 - c*x)^2/(8*c^2) + log(1 - c*x)/(8*c^2) - (1/8)*x^2*log(1 - c*x) + (3*(1 - c*x)*log(1 - c*x))/(2*c^2) - ((1 - c*x)^2*log(1 - c*x))/(4*c^2) - ((1 - c*x)*log(1 - c*x)^2)/(2*c^2) + ((1 - c*x)^2*log(1 - c*x)^2)/(4*c^2) - (log(c*x)*log(1 - c*x)^2)/(2*c^2) - (x*PolyLog(2, c*x))/(2*c) - (1/4)*x^2*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(2*c^2) + (1/2)*x^2*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, 1 - c*x))/c^2 + PolyLog(3, 1 - c*x)/c^2] @test_int [x^0*log(1 - c*x)*PolyLog(2, c*x), x, 15, 3*x + (3*(1 - c*x)*log(1 - c*x))/c - ((1 - c*x)*log(1 - c*x)^2)/c - (log(c*x)*log(1 - c*x)^2)/c - x*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/c + x*log(1 - c*x)*PolyLog(2, c*x) - (2*log(1 - c*x)*PolyLog(2, 1 - c*x))/c + (2*PolyLog(3, 1 - c*x))/c] @test_int [log(1 - c*x)*PolyLog(2, c*x)/x^1, x, 1, (-(1/2))*PolyLog(2, c*x)^2] @test_int [log(1 - c*x)*PolyLog(2, c*x)/x^2, x, 10, ((1 - c*x)*log(1 - c*x)^2)/x + c*log(c*x)*log(1 - c*x)^2 - 2*c*PolyLog(2, c*x) + c*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/x + 2*c*log(1 - c*x)*PolyLog(2, 1 - c*x) - c*PolyLog(3, c*x) - 2*c*PolyLog(3, 1 - c*x)] @test_int [log(1 - c*x)*PolyLog(2, c*x)/x^3, x, 23, (-c^2)*log(x) + c^2*log(1 - c*x) - (c*log(1 - c*x))/x - (1/4)*c^2*log(1 - c*x)^2 + log(1 - c*x)^2/(4*x^2) + (1/2)*c^2*log(c*x)*log(1 - c*x)^2 - (1/2)*c^2*PolyLog(2, c*x) + (c*PolyLog(2, c*x))/(2*x) + (1/2)*c^2*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(2*x^2) + c^2*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/2)*c^2*PolyLog(3, c*x) - c^2*PolyLog(3, 1 - c*x)] @test_int [log(1 - c*x)*PolyLog(2, c*x)/x^4, x, 30, (7*c^2)/(36*x) - (3/4)*c^3*log(x) + (3/4)*c^3*log(1 - c*x) - (7*c*log(1 - c*x))/(36*x^2) - (5*c^2*log(1 - c*x))/(9*x) - (1/9)*c^3*log(1 - c*x)^2 + log(1 - c*x)^2/(9*x^3) + (1/3)*c^3*log(c*x)*log(1 - c*x)^2 - (2/9)*c^3*PolyLog(2, c*x) + (c*PolyLog(2, c*x))/(6*x^2) + (c^2*PolyLog(2, c*x))/(3*x) + (1/3)*c^3*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(3*x^3) + (2/3)*c^3*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/3)*c^3*PolyLog(3, c*x) - (2/3)*c^3*PolyLog(3, 1 - c*x)] @test_int [log(1 - c*x)*PolyLog(2, c*x)/x^5, x, 37, (5*c^2)/(144*x^2) + (7*c^3)/(36*x) - (41/72)*c^4*log(x) + (41/72)*c^4*log(1 - c*x) - (5*c*log(1 - c*x))/(72*x^3) - (c^2*log(1 - c*x))/(8*x^2) - (3*c^3*log(1 - c*x))/(8*x) - (1/16)*c^4*log(1 - c*x)^2 + log(1 - c*x)^2/(16*x^4) + (1/4)*c^4*log(c*x)*log(1 - c*x)^2 - (1/8)*c^4*PolyLog(2, c*x) + (c*PolyLog(2, c*x))/(12*x^3) + (c^2*PolyLog(2, c*x))/(8*x^2) + (c^3*PolyLog(2, c*x))/(4*x) + (1/4)*c^4*log(1 - c*x)*PolyLog(2, c*x) - (log(1 - c*x)*PolyLog(2, c*x))/(4*x^4) + (1/2)*c^4*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/4)*c^4*PolyLog(3, c*x) - (1/2)*c^4*PolyLog(3, 1 - c*x)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*(g+h*log(1-c*x))*PolyLog(2, c*x)=# @test_int [x^2*(g + h*log(1 - c*x))*PolyLog(2, c*x), x, 25, (121*h*x)/(108*c^2) + (13*h*x^2)/(216*c) + (h*x^3)/81 + (h*(1 - c*x)^2)/(6*c^3) - (2*h*(1 - c*x)^3)/(81*c^3) + (13*h*log(1 - c*x))/(108*c^3) - (h*x^2*log(1 - c*x))/(12*c) - (1/27)*h*x^3*log(1 - c*x) + (h*(1 - c*x)*log(1 - c*x))/(3*c^3) + (h*log(1 - c*x)^2)/(9*c^3) - (h*log(c*x)*log(1 - c*x)^2)/(3*c^3) + (1/9)*x^3*log(1 - c*x)*(g + h*log(1 - c*x)) + ((1 - c*x)*(g + 2*h*log(1 - c*x)))/(3*c^3) - ((1 - c*x)^2*(g + 2*h*log(1 - c*x)))/(6*c^3) + ((1 - c*x)^3*(g + 2*h*log(1 - c*x)))/(27*c^3) - (log(1 - c*x)*(g + 2*h*log(1 - c*x)))/(9*c^3) - (h*x*PolyLog(2, c*x))/(3*c^2) - (h*x^2*PolyLog(2, c*x))/(6*c) - (1/9)*h*x^3*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, c*x))/(3*c^3) + (1/3)*x^3*(g + h*log(1 - c*x))*PolyLog(2, c*x) - (2*h*log(1 - c*x)*PolyLog(2, 1 - c*x))/(3*c^3) + (2*h*PolyLog(3, 1 - c*x))/(3*c^3)] @test_int [x^1*(g + h*log(1 - c*x))*PolyLog(2, c*x), x, 21, (13*h*x)/(8*c) + (h*x^2)/16 + (h*(1 - c*x)^2)/(8*c^2) + (h*log(1 - c*x))/(8*c^2) - (1/8)*h*x^2*log(1 - c*x) + (h*(1 - c*x)*log(1 - c*x))/(2*c^2) + (h*log(1 - c*x)^2)/(4*c^2) - (h*log(c*x)*log(1 - c*x)^2)/(2*c^2) + (1/4)*x^2*log(1 - c*x)*(g + h*log(1 - c*x)) + ((1 - c*x)*(g + 2*h*log(1 - c*x)))/(2*c^2) - ((1 - c*x)^2*(g + 2*h*log(1 - c*x)))/(8*c^2) - (log(1 - c*x)*(g + 2*h*log(1 - c*x)))/(4*c^2) - (h*x*PolyLog(2, c*x))/(2*c) - (1/4)*h*x^2*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, c*x))/(2*c^2) + (1/2)*x^2*(g + h*log(1 - c*x))*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, 1 - c*x))/c^2 + (h*PolyLog(3, 1 - c*x))/c^2] @test_int [x^0*(g + h*log(1 - c*x))*PolyLog(2, c*x), x, 18, (-g)*x + 3*h*x - (g*(1 - c*x)*log(1 - c*x))/c + (3*h*(1 - c*x)*log(1 - c*x))/c - (h*(1 - c*x)*log(1 - c*x)^2)/c - (h*log(c*x)*log(1 - c*x)^2)/c - h*x*PolyLog(2, c*x) - (h*log(1 - c*x)*PolyLog(2, c*x))/c + x*(g + h*log(1 - c*x))*PolyLog(2, c*x) - (2*h*log(1 - c*x)*PolyLog(2, 1 - c*x))/c + (2*h*PolyLog(3, 1 - c*x))/c] @test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^1, x, 3, (-(1/2))*h*PolyLog(2, c*x)^2 + g*PolyLog(3, c*x)] @test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^2, x, 12, c*h*log(c*x)*log(1 - c*x)^2 + (log(1 - c*x)*(g + h*log(1 - c*x)))/x + c*(g + 2*h*log(1 - c*x))*log(1 - 1/(1 - c*x)) + c*h*log(1 - c*x)*PolyLog(2, c*x) - ((g + h*log(1 - c*x))*PolyLog(2, c*x))/x - 2*c*h*PolyLog(2, 1/(1 - c*x)) + 2*c*h*log(1 - c*x)*PolyLog(2, 1 - c*x) - c*h*PolyLog(3, c*x) - 2*c*h*PolyLog(3, 1 - c*x)] @test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^3, x, 20, (-c^2)*h*log(x) + (1/2)*c^2*h*log(1 - c*x) - (c*h*log(1 - c*x))/(2*x) + (1/2)*c^2*h*log(c*x)*log(1 - c*x)^2 + (log(1 - c*x)*(g + h*log(1 - c*x)))/(4*x^2) - (c*(1 - c*x)*(g + 2*h*log(1 - c*x)))/(4*x) + (1/4)*c^2*(g + 2*h*log(1 - c*x))*log(1 - 1/(1 - c*x)) + (c*h*PolyLog(2, c*x))/(2*x) + (1/2)*c^2*h*log(1 - c*x)*PolyLog(2, c*x) - ((g + h*log(1 - c*x))*PolyLog(2, c*x))/(2*x^2) - (1/2)*c^2*h*PolyLog(2, 1/(1 - c*x)) + c^2*h*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/2)*c^2*h*PolyLog(3, c*x) - c^2*h*PolyLog(3, 1 - c*x)] @test_int [(g + h*log(1 - c*x))*PolyLog(2, c*x)/x^4, x, 28, (7*c^2*h)/(36*x) - (3/4)*c^3*h*log(x) + (19/36)*c^3*h*log(1 - c*x) - (c*h*log(1 - c*x))/(12*x^2) - (c^2*h*log(1 - c*x))/(3*x) + (1/3)*c^3*h*log(c*x)*log(1 - c*x)^2 + (log(1 - c*x)*(g + h*log(1 - c*x)))/(9*x^3) - (c*(g + 2*h*log(1 - c*x)))/(18*x^2) - (c^2*(1 - c*x)*(g + 2*h*log(1 - c*x)))/(9*x) + (1/9)*c^3*(g + 2*h*log(1 - c*x))*log(1 - 1/(1 - c*x)) + (c*h*PolyLog(2, c*x))/(6*x^2) + (c^2*h*PolyLog(2, c*x))/(3*x) + (1/3)*c^3*h*log(1 - c*x)*PolyLog(2, c*x) - ((g + h*log(1 - c*x))*PolyLog(2, c*x))/(3*x^3) - (2/9)*c^3*h*PolyLog(2, 1/(1 - c*x)) + (2/3)*c^3*h*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/3)*c^3*h*PolyLog(3, c*x) - (2/3)*c^3*h*PolyLog(3, 1 - c*x)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*(g+h*log(f*(d+e*x)^n))*PolyLog(2, c*(a+b*x))=# @test_int [x^2*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)), x, 108, -((a^2*g*x)/(3*b^2)) + (a*(1 - a*c)*g*x)/(6*b^2*c) - ((1 - a*c)^2*g*x)/(9*b^2*c^2) + (7*a^2*h*n*x)/(9*b^2) - (11*a*(1 - a*c)*h*n*x)/(36*b^2*c) + (5*(1 - a*c)^2*h*n*x)/(27*b^2*c^2) + (13*d^2*h*n*x)/(27*e^2) + (5*a*d*h*n*x)/(12*b*e) - (7*(1 - a*c)*d*h*n*x)/(36*b*c*e) - (a*h*n*x^2)/(9*b) + (7*(1 - a*c)*h*n*x^2)/(108*b*c) - (19*d*h*n*x^2)/(216*e) + (1/27)*h*n*x^3 - (5*a*(1 - a*c)^2*h*n*log(1 - a*c - b*c*x))/(36*b^3*c^2) + (2*(1 - a*c)^3*h*n*log(1 - a*c - b*c*x))/(27*b^3*c^3) - (5*(1 - a*c)^2*d*h*n*log(1 - a*c - b*c*x))/(36*b^2*c^2*e) + (5*a*h*n*x^2*log(1 - a*c - b*c*x))/(36*b) + (5*d*h*n*x^2*log(1 - a*c - b*c*x))/(36*e) - (2/27)*h*n*x^3*log(1 - a*c - b*c*x) + (4*a^2*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(9*b^3*c) + (4*d^2*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(9*b*c*e^2) + (a*d*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(3*b^2*c*e) - (d^3*h*n*log(d + e*x))/(27*e^3) - (a*d^2*h*n*log(d + e*x))/(12*b*e^2) + ((1 - a*c)*d^2*h*n*log(d + e*x))/(18*b*c*e^2) + (d^3*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(9*e^3) + (a*d^2*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*b*e^2) + (a^2*d*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*b^2*e) - (a^2*h*(d + e*x)*log(f*(d + e*x)^n))/(3*b^2*e) + (a*(1 - a*c)*h*(d + e*x)*log(f*(d + e*x)^n))/(6*b^2*c*e) - ((1 - a*c)^2*h*(d + e*x)*log(f*(d + e*x)^n))/(9*b^2*c^2*e) + (a*x^2*(g + h*log(f*(d + e*x)^n)))/(12*b) - ((1 - a*c)*x^2*(g + h*log(f*(d + e*x)^n)))/(18*b*c) - (1/27)*x^3*(g + h*log(f*(d + e*x)^n)) + (a^2*x*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(3*b^2) - (a*x^2*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(6*b) + (1/9)*x^3*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)) - (a^2*(1 - a*c)*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(3*b^3*c) + (a*(1 - a*c)^2*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(6*b^3*c^2) - ((1 - a*c)^3*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(9*b^3*c^3) - (a^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*b^3) + (d^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*e^3) - (a^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*b^3) + (d^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*e^3) + (a^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*b^3) - (d^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*e^3) + (a^3*g*PolyLog(2, c*(a + b*x)))/(3*b^3) - (a^3*h*n*PolyLog(2, c*(a + b*x)))/(9*b^3) - (a*d^2*h*n*PolyLog(2, c*(a + b*x)))/(3*b*e^2) - (a^2*d*h*n*PolyLog(2, c*(a + b*x)))/(6*b^2*e) - (d^2*h*n*x*PolyLog(2, c*(a + b*x)))/(3*e^2) + (d*h*n*x^2*PolyLog(2, c*(a + b*x)))/(6*e) - (1/9)*h*n*x^3*PolyLog(2, c*(a + b*x)) + (d^3*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(3*e^3) - (a^3*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(3*b^3) + (1/3)*x^3*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)) + (d^3*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(9*e^3) + (a*d^2*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(6*b*e^2) + (a^2*d*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(3*b^2*e) - (a^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*b^3) + (d^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*e^3) - (a^2*(1 - a*c)*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*b^3*c) + (a*(1 - a*c)^2*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*b^3*c^2) - ((1 - a*c)^3*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(9*b^3*c^3) - (a^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*b^3) + (d^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*e^3) + (a^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*b^3) - (d^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*e^3) - (a^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*b^3) + (d^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*e^3) + (a^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*b^3) - (d^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*e^3) + (a^3*h*n*PolyLog(3, 1 - c*(a + b*x)))/(3*b^3) - (d^3*h*n*PolyLog(3, 1 - c*(a + b*x)))/(3*e^3) + (a^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*b^3) - (d^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*e^3) - (a^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*b^3) + (d^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*e^3)] @test_int [x^1*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)), x, 67, (a*g*x)/(2*b) - ((1 - a*c)*g*x)/(4*b*c) - (5*a*h*n*x)/(4*b) + ((1 - a*c)*h*n*x)/(2*b*c) - (7*d*h*n*x)/(8*e) + (3/16)*h*n*x^2 + ((1 - a*c)^2*h*n*log(1 - a*c - b*c*x))/(4*b^2*c^2) - (1/4)*h*n*x^2*log(1 - a*c - b*c*x) - (3*a*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b^2*c) - (3*d*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(4*b*c*e) + (d^2*h*n*log(d + e*x))/(8*e^2) - (d^2*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(4*e^2) - (a*d*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*b*e) + (a*h*(d + e*x)*log(f*(d + e*x)^n))/(2*b*e) - ((1 - a*c)*h*(d + e*x)*log(f*(d + e*x)^n))/(4*b*c*e) - (1/8)*x^2*(g + h*log(f*(d + e*x)^n)) - (a*x*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(2*b) + (1/4)*x^2*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)) + (a*(1 - a*c)*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(2*b^2*c) - ((1 - a*c)^2*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(4*b^2*c^2) + (a^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*b^2) - (d^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*e^2) + (a^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*b^2) - (d^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*e^2) - (a^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*b^2) + (d^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*e^2) - (a^2*g*PolyLog(2, c*(a + b*x)))/(2*b^2) + (a^2*h*n*PolyLog(2, c*(a + b*x)))/(4*b^2) + (a*d*h*n*PolyLog(2, c*(a + b*x)))/(2*b*e) + (d*h*n*x*PolyLog(2, c*(a + b*x)))/(2*e) - (1/4)*h*n*x^2*PolyLog(2, c*(a + b*x)) - (d^2*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(2*e^2) + (a^2*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(2*b^2) + (1/2)*x^2*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)) - (d^2*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(4*e^2) - (a*d*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(2*b*e) + (a^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*b^2) - (d^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*e^2) + (a*(1 - a*c)*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*b^2*c) - ((1 - a*c)^2*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(4*b^2*c^2) + (a^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*b^2) - (d^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*e^2) - (a^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*b^2) + (d^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*e^2) + (a^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*b^2) - (d^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*e^2) - (a^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*b^2) + (d^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*e^2) - (a^2*h*n*PolyLog(3, 1 - c*(a + b*x)))/(2*b^2) + (d^2*h*n*PolyLog(3, 1 - c*(a + b*x)))/(2*e^2) - (a^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*b^2) + (d^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*e^2) + (a^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*b^2) - (d^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*e^2)] @test_int [x^0*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)), x, 42, (-g)*x + 3*h*n*x - (g*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (2*h*n*(1 - a*c - b*c*x)*log(1 - a*c - b*c*x))/(b*c) + (d*h*n*log(c*(a + b*x))*log(1 - a*c - b*c*x)*log(-d - e*x))/e + (d*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/e + (d*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x)))^2)/(2*e) - (d*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log(1 - a*c - b*c*x) + log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x))))^2)/(2*e) - (h*(d + e*x)*log(f*(d + e*x)^n))/e + h*x*log(1 - a*c - b*c*x)*log(f*(d + e*x)^n) - ((1 - a*c)*h*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*log(f*(d + e*x)^n))/(b*c) - (a*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*b) - (a*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/b + (a*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*b) + (a*g*PolyLog(2, c*(a + b*x)))/b - (a*h*n*PolyLog(2, c*(a + b*x)))/b - (a*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/b + x*(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)) + (d*h*n*(log(-d - e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x))))*PolyLog(2, 1 - a*c - b*c*x))/e + (d*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/e - h*n*x*PolyLog(2, a*c + b*c*x) + (d*h*n*log(-d - e*x)*PolyLog(2, a*c + b*c*x))/e - (d*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/e + (d*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x)))*PolyLog(2, ((b*d - a*e)*(1 - a*c - b*c*x))/(b*(d + e*x))))/e + (d*h*n*(log(1 - a*c - b*c*x) + log((b*(d + e*x))/((b*d - a*e)*(1 - a*c - b*c*x))))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/e - (a*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/b - ((1 - a*c)*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(b*c) - (a*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/b + (a*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/b - (a*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/b - (d*h*n*PolyLog(3, 1 - a*c - b*c*x))/e - (d*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/e + (d*h*n*PolyLog(3, ((b*d - a*e)*(1 - a*c - b*c*x))/(b*(d + e*x))))/e + (a*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/b - (d*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/e + (a*h*n*PolyLog(3, 1 - c*(a + b*x)))/b + (a*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/b - (a*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/b] @test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^1, x, 0, Unintegrable(((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/x, x)] @test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^2, x, 22, -((b*g*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/a) - (b*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*log(d + e*x))/a - (b*h*n*(log((b*c*x)/(1 - a*c)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*x)/((1 - a*c)*(d + e*x))))*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))^2)/(2*a) + (b*h*n*(log((b*c*x)/(1 - a*c)) - log(-((e*x)/d)))*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))^2)/(2*a) + (b*h*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*(n*log(d + e*x) - log(f*(d + e*x)^n)))/a + (b*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*a) - (e*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(2*d) + (e*h*n*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/d + (b*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/a - (e*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/d - (b*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*a) + (e*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(2*d) + (e*h*n*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(2*d) + (e*h*n*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(2*d) + (e*h*n*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/d - (b*g*PolyLog(2, c*(a + b*x)))/a + (e*h*n*log(x)*PolyLog(2, c*(a + b*x)))/d - (e*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/d + (b*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/a - ((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/x - (b*g*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a - (b*h*n*(log(d + e*x) - log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a + (b*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/a - (b*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/a + (b*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/a + (b*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/a - (e*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/d - (b*h*n*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 + (e*x)/d))/a + (e*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/d - (e*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/d + (b*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/a - (e*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/d + (e*h*n*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/d - (b*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/a + (e*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/d + (b*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/a - (e*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/d - (e*h*n*PolyLog(3, -((b*x)/a)))/d + (b*h*n*PolyLog(3, 1 - (b*c*x)/(1 - a*c)))/a - (b*h*n*PolyLog(3, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/a + (b*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/a - (b*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/a + (e*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/d + (b*h*n*PolyLog(3, 1 + (e*x)/d))/a + (e*h*n*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/d - (e*h*n*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/d - (b*h*n*PolyLog(3, 1 - c*(a + b*x)))/a - (b*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/a + (e*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/d + (b*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/a - (e*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/d] @test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^3, x, 44, (b^2*g*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2) - (b*e*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(a*d) + (b^2*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*log(d + e*x))/(2*a^2) + (b*e*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*a*d) + (b^2*h*n*(log((b*c*x)/(1 - a*c)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*x)/((1 - a*c)*(d + e*x))))*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))^2)/(4*a^2) - (b^2*h*n*(log((b*c*x)/(1 - a*c)) - log(-((e*x)/d)))*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))^2)/(4*a^2) - (b^2*h*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*(n*log(d + e*x) - log(f*(d + e*x)^n)))/(2*a^2) + (b^2*c*log(-((e*x)/d))*(g + h*log(f*(d + e*x)^n)))/(2*a*(1 - a*c)) + (b*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(2*a*x) - (b^2*c*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(2*a*(1 - a*c)) - (b^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*a^2) + (e^2*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(4*d^2) - (e^2*h*n*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/(2*d^2) - (b^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*a^2) + (e^2*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(2*d^2) + (b^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*a^2) - (e^2*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(4*d^2) - (e^2*h*n*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(4*d^2) - (e^2*h*n*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(4*d^2) - (e^2*h*n*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/(2*d^2) + (b^2*g*PolyLog(2, c*(a + b*x)))/(2*a^2) - (b*e*h*n*PolyLog(2, c*(a + b*x)))/(2*a*d) - (e*h*n*PolyLog(2, c*(a + b*x)))/(2*d*x) - (e^2*h*n*log(x)*PolyLog(2, c*(a + b*x)))/(2*d^2) + (e^2*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(2*d^2) - (b^2*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(2*a^2) - ((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(2*x^2) + (b*e*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(2*a*d) + (b^2*g*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) - (b*e*h*n*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(a*d) + (b^2*h*n*(log(d + e*x) - log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) - (b^2*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) + (b^2*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(2*a^2) - (b^2*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(2*a^2) - (b^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*a^2) + (e^2*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(2*d^2) - (b^2*c*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(2*a*(1 - a*c)) + (b^2*c*h*n*PolyLog(2, 1 + (e*x)/d))/(2*a*(1 - a*c)) + (b^2*h*n*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 + (e*x)/d))/(2*a^2) - (e^2*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*d^2) + (e^2*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/(2*d^2) - (b^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*a^2) + (e^2*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(2*d^2) - (e^2*h*n*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/(2*d^2) + (b^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*a^2) - (e^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*d^2) - (b^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*a^2) + (e^2*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*d^2) + (e^2*h*n*PolyLog(3, -((b*x)/a)))/(2*d^2) - (b^2*h*n*PolyLog(3, 1 - (b*c*x)/(1 - a*c)))/(2*a^2) + (b^2*h*n*PolyLog(3, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(2*a^2) - (b^2*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(2*a^2) + (b^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*a^2) - (e^2*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(2*d^2) - (b^2*h*n*PolyLog(3, 1 + (e*x)/d))/(2*a^2) - (e^2*h*n*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/(2*d^2) + (e^2*h*n*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/(2*d^2) + (b^2*h*n*PolyLog(3, 1 - c*(a + b*x)))/(2*a^2) + (b^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*a^2) - (e^2*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(2*d^2) - (b^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*a^2) + (e^2*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(2*d^2)] @test_int [(g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x))/x^4, x, 78, (b^2*c*e*h*n*log(x))/(2*a*(1 - a*c)*d) - (b^2*c*e*h*n*log(1 - a*c - b*c*x))/(3*a*(1 - a*c)*d) + (b*e*h*n*log(1 - a*c - b*c*x))/(3*a*d*x) - (b^3*g*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(3*a^3) + (b^2*e*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a^2*d) + (b*e^2*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x))/(2*a*d^2) - (b^2*c*e*h*n*log(d + e*x))/(6*a*(1 - a*c)*d) - (b^3*h*n*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*log(d + e*x))/(3*a^3) - (b^2*e*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*a^2*d) - (b*e^2*h*n*log(1 - a*c - b*c*x)*log((b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*a*d^2) - (b^3*h*n*(log((b*c*x)/(1 - a*c)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*x)/((1 - a*c)*(d + e*x))))*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))^2)/(6*a^3) + (b^3*h*n*(log((b*c*x)/(1 - a*c)) - log(-((e*x)/d)))*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))^2)/(6*a^3) + (b^3*h*log((b*c*x)/(1 - a*c))*log(1 - a*c - b*c*x)*(n*log(d + e*x) - log(f*(d + e*x)^n)))/(3*a^3) - (b^2*c*(g + h*log(f*(d + e*x)^n)))/(6*a*(1 - a*c)*x) + (b^3*c^2*log(-((e*x)/d))*(g + h*log(f*(d + e*x)^n)))/(6*a*(1 - a*c)^2) - (b^3*c*log(-((e*x)/d))*(g + h*log(f*(d + e*x)^n)))/(3*a^2*(1 - a*c)) + (b*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(6*a*x^2) - (b^2*log(1 - a*c - b*c*x)*(g + h*log(f*(d + e*x)^n)))/(3*a^2*x) - (b^3*c^2*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(6*a*(1 - a*c)^2) + (b^3*c*log((e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e))*(g + h*log(f*(d + e*x)^n)))/(3*a^2*(1 - a*c)) + (b^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*a^3) - (e^3*h*n*(log(c*(a + b*x)) + log((b*c*d + e - a*c*e)/(b*c*(d + e*x))) - log(((b*c*d + e - a*c*e)*(a + b*x))/(b*(d + e*x))))*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))^2)/(6*d^3) + (e^3*h*n*log(x)*log(1 + (b*x)/a)*log(1 - c*(a + b*x)))/(3*d^3) + (b^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*a^3) - (e^3*h*n*log(c*(a + b*x))*log(d + e*x)*log(1 - c*(a + b*x)))/(3*d^3) - (b^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*a^3) + (e^3*h*n*(log(c*(a + b*x)) - log(-((e*(a + b*x))/(b*d - a*e))))*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))^2)/(6*d^3) + (e^3*h*n*(log(1 + (b*x)/a) + log((1 - a*c)/(1 - c*(a + b*x))) - log(((1 - a*c)*(a + b*x))/(a*(1 - c*(a + b*x)))))*log(-((a*(1 - c*(a + b*x)))/(b*x)))^2)/(6*d^3) + (e^3*h*n*(log(c*(a + b*x)) - log(1 + (b*x)/a))*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))^2)/(6*d^3) + (e^3*h*n*(log(1 - c*(a + b*x)) - log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, -((b*x)/a)))/(3*d^3) - (b^3*g*PolyLog(2, c*(a + b*x)))/(3*a^3) + (b^2*e*h*n*PolyLog(2, c*(a + b*x)))/(6*a^2*d) + (b*e^2*h*n*PolyLog(2, c*(a + b*x)))/(3*a*d^2) - (e*h*n*PolyLog(2, c*(a + b*x)))/(6*d*x^2) + (e^2*h*n*PolyLog(2, c*(a + b*x)))/(3*d^2*x) + (e^3*h*n*log(x)*PolyLog(2, c*(a + b*x)))/(3*d^3) - (e^3*h*n*log(d + e*x)*PolyLog(2, c*(a + b*x)))/(3*d^3) + (b^3*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(3*a^3) - ((g + h*log(f*(d + e*x)^n))*PolyLog(2, c*(a + b*x)))/(3*x^3) - (b^2*e*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(3*a^2*d) - (b*e^2*h*n*PolyLog(2, (e*(1 - a*c - b*c*x))/(b*c*d + e - a*c*e)))/(6*a*d^2) - (b^3*g*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) + (b^2*e*h*n*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a^2*d) + (b*e^2*h*n*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(2*a*d^2) - (b^3*h*n*(log(d + e*x) - log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) + (b^3*h*(n*log(d + e*x) - log(f*(d + e*x)^n))*PolyLog(2, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) - (b^3*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(3*a^3) + (b^3*h*n*log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x)))*PolyLog(2, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(3*a^3) + (b^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*a^3) - (e^3*h*n*(log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))) + log(1 - c*(a + b*x)))*PolyLog(2, (b*(d + e*x))/(b*d - a*e)))/(3*d^3) - (b^3*c^2*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(6*a*(1 - a*c)^2) + (b^3*c*h*n*PolyLog(2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)))/(3*a^2*(1 - a*c)) + (b^3*c^2*h*n*PolyLog(2, 1 + (e*x)/d))/(6*a*(1 - a*c)^2) - (b^3*c*h*n*PolyLog(2, 1 + (e*x)/d))/(3*a^2*(1 - a*c)) - (b^3*h*n*(log(1 - a*c - b*c*x) + log(((1 - a*c)*(d + e*x))/(d*(1 - a*c - b*c*x))))*PolyLog(2, 1 + (e*x)/d))/(3*a^3) + (e^3*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*x)/(a*(1 - c*(a + b*x))))))/(3*d^3) - (e^3*h*n*log(-((a*(1 - c*(a + b*x)))/(b*x)))*PolyLog(2, -((b*c*x)/(1 - c*(a + b*x)))))/(3*d^3) + (b^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*a^3) - (e^3*h*n*(log(d + e*x) - log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x)))))*PolyLog(2, 1 - c*(a + b*x)))/(3*d^3) + (e^3*h*n*(log(x) + log(-((a*(1 - c*(a + b*x)))/(b*x))))*PolyLog(2, 1 - c*(a + b*x)))/(3*d^3) - (b^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*a^3) + (e^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*d^3) + (b^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*a^3) - (e^3*h*n*log((b*(d + e*x))/((b*d - a*e)*(1 - c*(a + b*x))))*PolyLog(2, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*d^3) - (e^3*h*n*PolyLog(3, -((b*x)/a)))/(3*d^3) + (b^3*h*n*PolyLog(3, 1 - (b*c*x)/(1 - a*c)))/(3*a^3) - (b^3*h*n*PolyLog(3, (d*(1 - a*c - b*c*x))/((1 - a*c)*(d + e*x))))/(3*a^3) + (b^3*h*n*PolyLog(3, -((e*(1 - a*c - b*c*x))/(b*c*(d + e*x)))))/(3*a^3) - (b^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*a^3) + (e^3*h*n*PolyLog(3, (b*(d + e*x))/(b*d - a*e)))/(3*d^3) + (b^3*h*n*PolyLog(3, 1 + (e*x)/d))/(3*a^3) + (e^3*h*n*PolyLog(3, -((b*x)/(a*(1 - c*(a + b*x))))))/(3*d^3) - (e^3*h*n*PolyLog(3, -((b*c*x)/(1 - c*(a + b*x)))))/(3*d^3) - (b^3*h*n*PolyLog(3, 1 - c*(a + b*x)))/(3*a^3) - (b^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*a^3) + (e^3*h*n*PolyLog(3, -((e*(1 - c*(a + b*x)))/(b*c*(d + e*x)))))/(3*d^3) + (b^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*a^3) - (e^3*h*n*PolyLog(3, ((b*d - a*e)*(1 - c*(a + b*x)))/(b*(d + e*x))))/(3*d^3)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*(a+b*x)*log(1-c*x)*PolyLog(2, c*x)=# @test_int [x^2*(a + b*x)*log(1 - c*x)*PolyLog(2, c*x), x, 52, (53*b*x)/(192*c^3) + (11*a*x)/(27*c^2) + (49*(3*b + 4*a*c)*x)/(432*c^3) + (29*b*x^2)/(384*c^2) + (5*a*x^2)/(54*c) + (13*(3*b + 4*a*c)*x^2)/(864*c^2) + (2*a*x^3)/81 + (17*b*x^3)/(576*c) + ((3*b + 4*a*c)*x^3)/(324*c) + (3*b*x^4)/256 + (29*b*log(1 - c*x))/(192*c^4) + (5*a*log(1 - c*x))/(27*c^3) + (13*(3*b + 4*a*c)*log(1 - c*x))/(432*c^4) - (b*x^2*log(1 - c*x))/(16*c^2) - (a*x^2*log(1 - c*x))/(9*c) - ((3*b + 4*a*c)*x^2*log(1 - c*x))/(48*c^2) - (2/27)*a*x^3*log(1 - c*x) - (b*x^3*log(1 - c*x))/(24*c) - ((3*b + 4*a*c)*x^3*log(1 - c*x))/(108*c) - (3/64)*b*x^4*log(1 - c*x) + (b*(1 - c*x)*log(1 - c*x))/(8*c^4) + (2*a*(1 - c*x)*log(1 - c*x))/(9*c^3) + ((3*b + 4*a*c)*(1 - c*x)*log(1 - c*x))/(12*c^4) - (b*log(1 - c*x)^2)/(16*c^4) - (a*log(1 - c*x)^2)/(9*c^3) + (1/9)*a*x^3*log(1 - c*x)^2 + (1/16)*b*x^4*log(1 - c*x)^2 - ((3*b + 4*a*c)*log(c*x)*log(1 - c*x)^2)/(12*c^4) - ((3*b + 4*a*c)*x*PolyLog(2, c*x))/(12*c^3) - ((3*b + 4*a*c)*x^2*PolyLog(2, c*x))/(24*c^2) - ((3*b + 4*a*c)*x^3*PolyLog(2, c*x))/(36*c) - (1/16)*b*x^4*PolyLog(2, c*x) - ((3*b + 4*a*c)*log(1 - c*x)*PolyLog(2, c*x))/(12*c^4) + (1/12)*(4*a*x^3 + 3*b*x^4)*log(1 - c*x)*PolyLog(2, c*x) - ((3*b + 4*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x))/(6*c^4) + ((3*b + 4*a*c)*PolyLog(3, 1 - c*x))/(6*c^4)] @test_int [x^1*(a + b*x)*log(1 - c*x)*PolyLog(2, c*x), x, 40, (4*b*x)/(9*c^2) + (a*x)/c + (5*(2*b + 3*a*c)*x)/(24*c^2) + (b*x^2)/(9*c) + ((2*b + 3*a*c)*x^2)/(48*c) + (b*x^3)/27 + (a*(1 - c*x)^2)/(8*c^2) + (2*b*log(1 - c*x))/(9*c^3) + ((2*b + 3*a*c)*log(1 - c*x))/(24*c^3) - (b*x^2*log(1 - c*x))/(9*c) - ((2*b + 3*a*c)*x^2*log(1 - c*x))/(24*c) - (1/9)*b*x^3*log(1 - c*x) + (2*b*(1 - c*x)*log(1 - c*x))/(9*c^3) + (a*(1 - c*x)*log(1 - c*x))/c^2 + ((2*b + 3*a*c)*(1 - c*x)*log(1 - c*x))/(6*c^3) - (a*(1 - c*x)^2*log(1 - c*x))/(4*c^2) - (b*log(1 - c*x)^2)/(9*c^3) + (1/9)*b*x^3*log(1 - c*x)^2 - (a*(1 - c*x)*log(1 - c*x)^2)/(2*c^2) + (a*(1 - c*x)^2*log(1 - c*x)^2)/(4*c^2) - ((2*b + 3*a*c)*log(c*x)*log(1 - c*x)^2)/(6*c^3) - ((2*b + 3*a*c)*x*PolyLog(2, c*x))/(6*c^2) - ((2*b + 3*a*c)*x^2*PolyLog(2, c*x))/(12*c) - (1/9)*b*x^3*PolyLog(2, c*x) - ((2*b + 3*a*c)*log(1 - c*x)*PolyLog(2, c*x))/(6*c^3) + (1/6)*(3*a*x^2 + 2*b*x^3)*log(1 - c*x)*PolyLog(2, c*x) - ((2*b + 3*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x))/(3*c^3) + ((2*b + 3*a*c)*PolyLog(3, 1 - c*x))/(3*c^3)] @test_int [x^0*(a + b*x)*log(1 - c*x)*PolyLog(2, c*x), x, 26, 2*a*x + (9*b*x)/(8*c) + ((b + 2*a*c)*x)/(2*c) + (b*x^2)/16 + (b*(1 - c*x)^2)/(8*c^2) + (b*log(1 - c*x))/(8*c^2) - (1/8)*b*x^2*log(1 - c*x) + (b*(1 - c*x)*log(1 - c*x))/c^2 + (2*a*(1 - c*x)*log(1 - c*x))/c + ((b + 2*a*c)*(1 - c*x)*log(1 - c*x))/(2*c^2) - (b*(1 - c*x)^2*log(1 - c*x))/(4*c^2) - (b*(1 - c*x)*log(1 - c*x)^2)/(2*c^2) - (a*(1 - c*x)*log(1 - c*x)^2)/c + (b*(1 - c*x)^2*log(1 - c*x)^2)/(4*c^2) - ((b + 2*a*c)*log(c*x)*log(1 - c*x)^2)/(2*c^2) - ((b + 2*a*c)*x*PolyLog(2, c*x))/(2*c) - (1/4)*b*x^2*PolyLog(2, c*x) - ((b + 2*a*c)*log(1 - c*x)*PolyLog(2, c*x))/(2*c^2) + (1/2)*(2*a*x + b*x^2)*log(1 - c*x)*PolyLog(2, c*x) - ((b + 2*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x))/c^2 + ((b + 2*a*c)*PolyLog(3, 1 - c*x))/c^2] @test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^1, x, 18, 3*b*x + (3*b*(1 - c*x)*log(1 - c*x))/c - (b*(1 - c*x)*log(1 - c*x)^2)/c - (b*log(c*x)*log(1 - c*x)^2)/c - b*x*PolyLog(2, c*x) - (b*log(1 - c*x)*PolyLog(2, c*x))/c + b*x*log(1 - c*x)*PolyLog(2, c*x) - (1/2)*a*PolyLog(2, c*x)^2 - (2*b*log(1 - c*x)*PolyLog(2, 1 - c*x))/c + (2*b*PolyLog(3, 1 - c*x))/c] @test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^2, x, 13, (a*(1 - c*x)*log(1 - c*x)^2)/x + a*c*log(c*x)*log(1 - c*x)^2 - 2*a*c*PolyLog(2, c*x) + a*c*log(1 - c*x)*PolyLog(2, c*x) - (a*log(1 - c*x)*PolyLog(2, c*x))/x - (1/2)*b*PolyLog(2, c*x)^2 + 2*a*c*log(1 - c*x)*PolyLog(2, 1 - c*x) - a*c*PolyLog(3, c*x) - 2*a*c*PolyLog(3, 1 - c*x)] @test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^3, x, 30, (-a)*c^2*log(x) + a*c^2*log(1 - c*x) - (a*c*log(1 - c*x))/x - (1/4)*a*c^2*log(1 - c*x)^2 + (a*log(1 - c*x)^2)/(4*x^2) + (b*(1 - c*x)*log(1 - c*x)^2)/x - (b^2*log(c*x)*log(1 - c*x)^2)/(2*a) + ((b + a*c)^2*log(c*x)*log(1 - c*x)^2)/(2*a) - 2*b*c*PolyLog(2, c*x) - (1/2)*a*c^2*PolyLog(2, c*x) + (a*c*PolyLog(2, c*x))/(2*x) + ((b + a*c)^2*log(1 - c*x)*PolyLog(2, c*x))/(2*a) - ((a + b*x)^2*log(1 - c*x)*PolyLog(2, c*x))/(2*a*x^2) - (b^2*log(1 - c*x)*PolyLog(2, 1 - c*x))/a + ((b + a*c)^2*log(1 - c*x)*PolyLog(2, 1 - c*x))/a - (1/2)*c*(2*b + a*c)*PolyLog(3, c*x) + (b^2*PolyLog(3, 1 - c*x))/a - ((b + a*c)^2*PolyLog(3, 1 - c*x))/a] @test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^4, x, 41, (7*a*c^2)/(36*x) - (1/2)*b*c^2*log(x) - (5/12)*a*c^3*log(x) - (1/6)*c^2*(3*b + 2*a*c)*log(x) + (1/2)*b*c^2*log(1 - c*x) + (5/12)*a*c^3*log(1 - c*x) + (1/6)*c^2*(3*b + 2*a*c)*log(1 - c*x) - (7*a*c*log(1 - c*x))/(36*x^2) - (b*c*log(1 - c*x))/(2*x) - (2*a*c^2*log(1 - c*x))/(9*x) - (c*(3*b + 2*a*c)*log(1 - c*x))/(6*x) - (1/4)*b*c^2*log(1 - c*x)^2 - (1/9)*a*c^3*log(1 - c*x)^2 + (a*log(1 - c*x)^2)/(9*x^3) + (b*log(1 - c*x)^2)/(4*x^2) + (1/6)*c^2*(3*b + 2*a*c)*log(c*x)*log(1 - c*x)^2 - (1/2)*b*c^2*PolyLog(2, c*x) - (2/9)*a*c^3*PolyLog(2, c*x) + (a*c*PolyLog(2, c*x))/(6*x^2) + (c*(3*b + 2*a*c)*PolyLog(2, c*x))/(6*x) + (1/6)*c^2*(3*b + 2*a*c)*log(1 - c*x)*PolyLog(2, c*x) - (1/6)*((2*a)/x^3 + (3*b)/x^2)*log(1 - c*x)*PolyLog(2, c*x) + (1/3)*c^2*(3*b + 2*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/6)*c^2*(3*b + 2*a*c)*PolyLog(3, c*x) - (1/3)*c^2*(3*b + 2*a*c)*PolyLog(3, 1 - c*x)] @test_int [(a + b*x)*log(1 - c*x)*PolyLog(2, c*x)/x^5, x, 51, (5*a*c^2)/(144*x^2) + (b*c^2)/(9*x) + (19*a*c^3)/(144*x) + (c^2*(4*b + 3*a*c))/(48*x) - (1/3)*b*c^3*log(x) - (37/144)*a*c^4*log(x) - (5/48)*c^3*(4*b + 3*a*c)*log(x) + (1/3)*b*c^3*log(1 - c*x) + (37/144)*a*c^4*log(1 - c*x) + (5/48)*c^3*(4*b + 3*a*c)*log(1 - c*x) - (5*a*c*log(1 - c*x))/(72*x^3) - (b*c*log(1 - c*x))/(9*x^2) - (a*c^2*log(1 - c*x))/(16*x^2) - (c*(4*b + 3*a*c)*log(1 - c*x))/(48*x^2) - (2*b*c^2*log(1 - c*x))/(9*x) - (a*c^3*log(1 - c*x))/(8*x) - (c^2*(4*b + 3*a*c)*log(1 - c*x))/(12*x) - (1/9)*b*c^3*log(1 - c*x)^2 - (1/16)*a*c^4*log(1 - c*x)^2 + (a*log(1 - c*x)^2)/(16*x^4) + (b*log(1 - c*x)^2)/(9*x^3) + (1/12)*c^3*(4*b + 3*a*c)*log(c*x)*log(1 - c*x)^2 - (2/9)*b*c^3*PolyLog(2, c*x) - (1/8)*a*c^4*PolyLog(2, c*x) + (a*c*PolyLog(2, c*x))/(12*x^3) + (c*(4*b + 3*a*c)*PolyLog(2, c*x))/(24*x^2) + (c^2*(4*b + 3*a*c)*PolyLog(2, c*x))/(12*x) + (1/12)*c^3*(4*b + 3*a*c)*log(1 - c*x)*PolyLog(2, c*x) - (1/12)*((3*a)/x^4 + (4*b)/x^3)*log(1 - c*x)*PolyLog(2, c*x) + (1/6)*c^3*(4*b + 3*a*c)*log(1 - c*x)*PolyLog(2, 1 - c*x) - (1/12)*c^3*(4*b + 3*a*c)*PolyLog(3, c*x) - (1/6)*c^3*(4*b + 3*a*c)*PolyLog(3, 1 - c*x)] #= ::Subsection::Closed:: =# #=Integrands*of*the*form*x^m*(a+b*x+c*x^2)*log(1-d*x)*PolyLog(2, d*x)=# @test_int [x^1*(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x), x, 60, (53*c*x)/(192*d^3) + (11*b*x)/(27*d^2) + (a*x)/d + ((3*c + 4*b*d)*x)/(108*d^3) + (5*(3*c + 4*b*d + 6*a*d^2)*x)/(48*d^3) + (29*c*x^2)/(384*d^2) + (5*b*x^2)/(54*d) + ((3*c + 4*b*d)*x^2)/(216*d^2) + ((3*c + 4*b*d + 6*a*d^2)*x^2)/(96*d^2) + (2*b*x^3)/81 + (17*c*x^3)/(576*d) + ((3*c + 4*b*d)*x^3)/(324*d) + (3*c*x^4)/256 + (a*(1 - d*x)^2)/(8*d^2) + (29*c*log(1 - d*x))/(192*d^4) + (5*b*log(1 - d*x))/(27*d^3) + ((3*c + 4*b*d)*log(1 - d*x))/(108*d^4) + ((3*c + 4*b*d + 6*a*d^2)*log(1 - d*x))/(48*d^4) - (c*x^2*log(1 - d*x))/(16*d^2) - (b*x^2*log(1 - d*x))/(9*d) - ((3*c + 4*b*d + 6*a*d^2)*x^2*log(1 - d*x))/(48*d^2) - (2/27)*b*x^3*log(1 - d*x) - (c*x^3*log(1 - d*x))/(24*d) - ((3*c + 4*b*d)*x^3*log(1 - d*x))/(108*d) - (3/64)*c*x^4*log(1 - d*x) + (c*(1 - d*x)*log(1 - d*x))/(8*d^4) + (2*b*(1 - d*x)*log(1 - d*x))/(9*d^3) + (a*(1 - d*x)*log(1 - d*x))/d^2 + ((3*c + 4*b*d + 6*a*d^2)*(1 - d*x)*log(1 - d*x))/(12*d^4) - (a*(1 - d*x)^2*log(1 - d*x))/(4*d^2) - (c*log(1 - d*x)^2)/(16*d^4) - (b*log(1 - d*x)^2)/(9*d^3) + (1/9)*b*x^3*log(1 - d*x)^2 + (1/16)*c*x^4*log(1 - d*x)^2 - (a*(1 - d*x)*log(1 - d*x)^2)/(2*d^2) + (a*(1 - d*x)^2*log(1 - d*x)^2)/(4*d^2) - ((3*c + 4*b*d + 6*a*d^2)*log(d*x)*log(1 - d*x)^2)/(12*d^4) - ((3*c + 4*b*d + 6*a*d^2)*x*PolyLog(2, d*x))/(12*d^3) - ((3*c + 4*b*d + 6*a*d^2)*x^2*PolyLog(2, d*x))/(24*d^2) - ((3*c + 4*b*d)*x^3*PolyLog(2, d*x))/(36*d) - (1/16)*c*x^4*PolyLog(2, d*x) - ((3*c + 4*b*d + 6*a*d^2)*log(1 - d*x)*PolyLog(2, d*x))/(12*d^4) + (1/12)*(6*a*x^2 + 4*b*x^3 + 3*c*x^4)*log(1 - d*x)*PolyLog(2, d*x) - ((3*c + 4*b*d + 6*a*d^2)*log(1 - d*x)*PolyLog(2, 1 - d*x))/(6*d^4) + ((3*c + 4*b*d + 6*a*d^2)*PolyLog(3, 1 - d*x))/(6*d^4)] @test_int [x^0*(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x), x, 43, 2*a*x + (4*c*x)/(9*d^2) + (b*x)/d + ((2*c + 3*b*d)*x)/(24*d^2) + ((2*c + 3*d*(b + 2*a*d))*x)/(6*d^2) + (c*x^2)/(9*d) + ((2*c + 3*b*d)*x^2)/(48*d) + (c*x^3)/27 + (b*(1 - d*x)^2)/(8*d^2) + (2*c*log(1 - d*x))/(9*d^3) + ((2*c + 3*b*d)*log(1 - d*x))/(24*d^3) - (c*x^2*log(1 - d*x))/(9*d) - ((2*c + 3*b*d)*x^2*log(1 - d*x))/(24*d) - (1/9)*c*x^3*log(1 - d*x) + (2*c*(1 - d*x)*log(1 - d*x))/(9*d^3) + (b*(1 - d*x)*log(1 - d*x))/d^2 + (2*a*(1 - d*x)*log(1 - d*x))/d + ((2*c + 3*d*(b + 2*a*d))*(1 - d*x)*log(1 - d*x))/(6*d^3) - (b*(1 - d*x)^2*log(1 - d*x))/(4*d^2) - (c*log(1 - d*x)^2)/(9*d^3) + (1/9)*c*x^3*log(1 - d*x)^2 - (b*(1 - d*x)*log(1 - d*x)^2)/(2*d^2) - (a*(1 - d*x)*log(1 - d*x)^2)/d + (b*(1 - d*x)^2*log(1 - d*x)^2)/(4*d^2) - ((2*c + 3*d*(b + 2*a*d))*log(d*x)*log(1 - d*x)^2)/(6*d^3) - ((2*c + 3*d*(b + 2*a*d))*x*PolyLog(2, d*x))/(6*d^2) - ((2*c + 3*b*d)*x^2*PolyLog(2, d*x))/(12*d) - (1/9)*c*x^3*PolyLog(2, d*x) - ((2*c + 3*d*(b + 2*a*d))*log(1 - d*x)*PolyLog(2, d*x))/(6*d^3) + (1/6)*(6*a*x + 3*b*x^2 + 2*c*x^3)*log(1 - d*x)*PolyLog(2, d*x) - ((2*c + 3*d*(b + 2*a*d))*log(1 - d*x)*PolyLog(2, 1 - d*x))/(3*d^3) + ((2*c + 3*d*(b + 2*a*d))*PolyLog(3, 1 - d*x))/(3*d^3)] @test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^1, x, 29, 2*b*x + (9*c*x)/(8*d) + ((c + 2*b*d)*x)/(2*d) + (c*x^2)/16 + (c*(1 - d*x)^2)/(8*d^2) + (c*log(1 - d*x))/(8*d^2) - (1/8)*c*x^2*log(1 - d*x) + (c*(1 - d*x)*log(1 - d*x))/d^2 + (2*b*(1 - d*x)*log(1 - d*x))/d + ((c + 2*b*d)*(1 - d*x)*log(1 - d*x))/(2*d^2) - (c*(1 - d*x)^2*log(1 - d*x))/(4*d^2) - (c*(1 - d*x)*log(1 - d*x)^2)/(2*d^2) - (b*(1 - d*x)*log(1 - d*x)^2)/d + (c*(1 - d*x)^2*log(1 - d*x)^2)/(4*d^2) - ((c + 2*b*d)*log(d*x)*log(1 - d*x)^2)/(2*d^2) - ((c + 2*b*d)*x*PolyLog(2, d*x))/(2*d) - (1/4)*c*x^2*PolyLog(2, d*x) - ((c + 2*b*d)*log(1 - d*x)*PolyLog(2, d*x))/(2*d^2) + (1/2)*(2*b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x) - (1/2)*a*PolyLog(2, d*x)^2 - ((c + 2*b*d)*log(1 - d*x)*PolyLog(2, 1 - d*x))/d^2 + ((c + 2*b*d)*PolyLog(3, 1 - d*x))/d^2] @test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^2, x, 19, 3*c*x + (3*c*(1 - d*x)*log(1 - d*x))/d - (c*(1 - d*x)*log(1 - d*x)^2)/d + (a*(1 - d*x)*log(1 - d*x)^2)/x + (a - c/d^2)*d*log(d*x)*log(1 - d*x)^2 - 2*a*d*PolyLog(2, d*x) - c*x*PolyLog(2, d*x) + (a - c/d^2)*d*log(1 - d*x)*PolyLog(2, d*x) - (a/x - c*x)*log(1 - d*x)*PolyLog(2, d*x) - (1/2)*b*PolyLog(2, d*x)^2 + 2*(a - c/d^2)*d*log(1 - d*x)*PolyLog(2, 1 - d*x) - a*d*PolyLog(3, d*x) - 2*(a - c/d^2)*d*PolyLog(3, 1 - d*x)] @test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^3, x, 32, (-a)*d^2*log(x) + a*d^2*log(1 - d*x) - (a*d*log(1 - d*x))/x - (1/4)*a*d^2*log(1 - d*x)^2 + (a*log(1 - d*x)^2)/(4*x^2) + (b*(1 - d*x)*log(1 - d*x)^2)/x - (b^2*log(d*x)*log(1 - d*x)^2)/(2*a) + ((b + a*d)^2*log(d*x)*log(1 - d*x)^2)/(2*a) - 2*b*d*PolyLog(2, d*x) - (1/2)*a*d^2*PolyLog(2, d*x) + (a*d*PolyLog(2, d*x))/(2*x) + ((b + a*d)^2*log(1 - d*x)*PolyLog(2, d*x))/(2*a) - ((a + b*x)^2*log(1 - d*x)*PolyLog(2, d*x))/(2*a*x^2) - (1/2)*c*PolyLog(2, d*x)^2 - (b^2*log(1 - d*x)*PolyLog(2, 1 - d*x))/a + ((b + a*d)^2*log(1 - d*x)*PolyLog(2, 1 - d*x))/a - (1/2)*d*(2*b + a*d)*PolyLog(3, d*x) + (b^2*PolyLog(3, 1 - d*x))/a - ((b + a*d)^2*PolyLog(3, 1 - d*x))/a] @test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^4, x, 43, (7*a*d^2)/(36*x) - (1/2)*b*d^2*log(x) - (5/12)*a*d^3*log(x) - (1/6)*d^2*(3*b + 2*a*d)*log(x) + (1/2)*b*d^2*log(1 - d*x) + (5/12)*a*d^3*log(1 - d*x) + (1/6)*d^2*(3*b + 2*a*d)*log(1 - d*x) - (7*a*d*log(1 - d*x))/(36*x^2) - (b*d*log(1 - d*x))/(2*x) - (2*a*d^2*log(1 - d*x))/(9*x) - (d*(3*b + 2*a*d)*log(1 - d*x))/(6*x) - (1/4)*b*d^2*log(1 - d*x)^2 - (1/9)*a*d^3*log(1 - d*x)^2 + (a*log(1 - d*x)^2)/(9*x^3) + (b*log(1 - d*x)^2)/(4*x^2) + (c*(1 - d*x)*log(1 - d*x)^2)/x + (1/6)*d*(6*c + d*(3*b + 2*a*d))*log(d*x)*log(1 - d*x)^2 - 2*c*d*PolyLog(2, d*x) - (1/2)*b*d^2*PolyLog(2, d*x) - (2/9)*a*d^3*PolyLog(2, d*x) + (a*d*PolyLog(2, d*x))/(6*x^2) + (d*(3*b + 2*a*d)*PolyLog(2, d*x))/(6*x) + (1/6)*d*(6*c + d*(3*b + 2*a*d))*log(1 - d*x)*PolyLog(2, d*x) - (1/6)*((2*a)/x^3 + (3*b)/x^2 + (6*c)/x)*log(1 - d*x)*PolyLog(2, d*x) + (1/3)*d*(6*c + d*(3*b + 2*a*d))*log(1 - d*x)*PolyLog(2, 1 - d*x) - (1/6)*d*(6*c + d*(3*b + 2*a*d))*PolyLog(3, d*x) - (1/3)*d*(6*c + d*(3*b + 2*a*d))*PolyLog(3, 1 - d*x)] @test_int [(a + b*x + c*x^2)*log(1 - d*x)*PolyLog(2, d*x)/x^5, x, 61, (5*a*d^2)/(144*x^2) + (b*d^2)/(9*x) + (19*a*d^3)/(144*x) + (d^2*(4*b + 3*a*d))/(48*x) - (1/2)*c*d^2*log(x) - (1/3)*b*d^3*log(x) - (37/144)*a*d^4*log(x) - (1/48)*d^3*(4*b + 3*a*d)*log(x) - (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(x) + (1/2)*c*d^2*log(1 - d*x) + (1/3)*b*d^3*log(1 - d*x) + (37/144)*a*d^4*log(1 - d*x) + (1/48)*d^3*(4*b + 3*a*d)*log(1 - d*x) + (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(1 - d*x) - (5*a*d*log(1 - d*x))/(72*x^3) - (b*d*log(1 - d*x))/(9*x^2) - (a*d^2*log(1 - d*x))/(16*x^2) - (d*(4*b + 3*a*d)*log(1 - d*x))/(48*x^2) - (c*d*log(1 - d*x))/(2*x) - (2*b*d^2*log(1 - d*x))/(9*x) - (a*d^3*log(1 - d*x))/(8*x) - (d*(6*c + d*(4*b + 3*a*d))*log(1 - d*x))/(12*x) - (1/4)*c*d^2*log(1 - d*x)^2 - (1/9)*b*d^3*log(1 - d*x)^2 - (1/16)*a*d^4*log(1 - d*x)^2 + (a*log(1 - d*x)^2)/(16*x^4) + (b*log(1 - d*x)^2)/(9*x^3) + (c*log(1 - d*x)^2)/(4*x^2) + (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(d*x)*log(1 - d*x)^2 - (1/2)*c*d^2*PolyLog(2, d*x) - (2/9)*b*d^3*PolyLog(2, d*x) - (1/8)*a*d^4*PolyLog(2, d*x) + (a*d*PolyLog(2, d*x))/(12*x^3) + (d*(4*b + 3*a*d)*PolyLog(2, d*x))/(24*x^2) + (d*(6*c + d*(4*b + 3*a*d))*PolyLog(2, d*x))/(12*x) + (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*log(1 - d*x)*PolyLog(2, d*x) - (1/12)*((3*a)/x^4 + (4*b)/x^3 + (6*c)/x^2)*log(1 - d*x)*PolyLog(2, d*x) + (1/6)*d^2*(6*c + d*(4*b + 3*a*d))*log(1 - d*x)*PolyLog(2, 1 - d*x) - (1/12)*d^2*(6*c + d*(4*b + 3*a*d))*PolyLog(3, d*x) - (1/6)*d^2*(6*c + d*(4*b + 3*a*d))*PolyLog(3, 1 - d*x)] end
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import MixedModels: LinearMixedModel, setθ!, updateL! import RCall: rcopy, RClass, rcopytype, reval, S4Sxp, sexp, protect, unprotect, sexpclass, @rput, @rget, @R_str # if RCall is available, then so is DataFrames import DataFrames: DataFrame import Tables: ColumnTable # from R # note that weights are not extracted # TODO: document weights issue and warn function rcopy(::Type{LinearMixedModel}, s::Ptr{S4Sxp}) # these try blocks should probably be changed to an examination of the indices # this only extracts the name within the call, not the actual weights try wts = rcopy(s[:call][:weights]) @error "weights are not supported" catch err if !isa(err, BoundsError) # this is the error we were expecting rethrow(err) end # no weights defined, we continue on our way end try contrasts = rcopy(s[:call][:contrasts]) @error "Contrasts must be specified in the dataframe, not the lmer() call" catch err if !isa(err, BoundsError) # this is the error we were expecting rethrow(err) end # no extra contrasts defined, we continue on our way end # for some reason this doesn't always give a formula with lmerTest #f = rcopy(s[:call][:formula]) f = rcopy(R"as.formula($(s)@call$formula)") data = rcopy(s[:frame]) contrasts = get_r_contrasts(s[:frame]) θ = rcopyarray(s[:theta]) reml = rcopy(s[:devcomp][:dims][:REML]) ≠ 0 m = LinearMixedModel(f, data, contrasts=contrasts) if length(θ) != length(m.θ) @error """You're probably using || in R with a categorical variable, whose translation is currently unsupported with MixedModels 3.0.""" throw(ArgumentError("Parameter vectors in R and Julia are different sizes.")) end θ = _reorder_theta_from_lme4(θ, m) m.optsum.REML = reml m.optsum.feval = rcopy(s[:optinfo][:feval]) # I'm wondering if this be filled in from the Julia side m.optsum.final = rcopyarray(s[:optinfo][:val]) m.optsum.optimizer = Symbol("$(rcopy(s[:optinfo][:optimizer])) (lme4)") m.optsum.returnvalue = rcopy(s[:optinfo][:conv][:opt]) == 0 ? :FAILURE : :SUCCESS m.optsum.fmin = reml ? rcopy(s[:devcomp][:cmp][:REML]) : rcopy(s[:devcomp][:cmp][:dev]) updateL!(setθ!(m, θ)) end rcopytype(::Type{RClass{:lmerMod}}, s::Ptr{S4Sxp}) = LinearMixedModel # add lmerTest::lmer and afex::lmer_alt support rcopytype(::Type{RClass{:lmerModLmerTest}}, s::Ptr{S4Sxp}) = LinearMixedModel # TODO: fix some conversions -- Julia->R->Julia roundtrip currently due to # ERROR: REvalError: Error in function (x, value, pos = -1, envir = as.environment(pos), inherits = FALSE, : # SET_VECTOR_ELT() can only be applied to a 'list', not a 'character' function sexp(::Type{RClass{:lmerMod}}, x::Tuple{LinearMixedModel{T}, DataFrame}) where T m, tbl = x if !isempty(m.sqrtwts) @error "weights are not currently supported" end m.optsum.feval > 0 || throw(ArgumentError("Model must be fitted")) jellyme4_data = tbl formula = convert_julia_to_r(m.formula) θ = m.θ rsteps = 1 REML = m.optsum.REML ? "TRUE" : "FALSE" jellyme4_theta = _reorder_theta_to_lme4(m) fval = m.optsum.fmin feval = m.optsum.feval conv = m.optsum.returnvalue == :SUCCESS ? 0 : 1 optimizer = String(m.optsum.optimizer) message = "fit with MixedModels.jl" @rput jellyme4_data @rput jellyme4_theta set_r_contrasts!("jellyme4_data", m.formula) r = """ jellyme4_mod <- $LMER(formula = $(formula), data=jellyme4_data, REML=$(REML), control=lme4::lmerControl(optimizer="nloptwrap", optCtrl=list(maxeval=$(rsteps)), calc.derivs=FALSE, check.nobs.vs.nRE= "warning"), start=list(theta=jellyme4_theta)) jellyme4_mod@optinfo\$feval <- $(feval) jellyme4_mod@optinfo\$message <- "$(message)" jellyme4_mod@optinfo\$optimizer <- "$(optimizer)" jellyme4_mod """ r = reval(r) r = protect(sexp(r)) unprotect(1) r end sexpclass(x::Tuple{LinearMixedModel{T}, DataFrame}) where T = LMER in ("afex::lmer_alt", "lmer_alt") ? RClass{:lmerModLmerTest} : RClass{:lmerMod} sexp(::Type{RClass{:lmerModLmerTest}}, x::Tuple{LinearMixedModel{T}, DataFrame}) where T = sexp(RClass{:lmerMod}, x) # generalize to ColumnTable, which is what MixedModels actually requires function sexp(ss::Type{RClass{:lmerMod}}, x::Tuple{LinearMixedModel{T}, ColumnTable}) where T m, t = x sexp(ss, (m, DataFrame(t))) end sexpclass(x::Tuple{LinearMixedModel{T}, ColumnTable}) where T = RClass{:lmerMod}
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# Raytracer.jl # Raytracing for the generation of photorealistic images in Julia # Copyright (c) 2021 Samuele Colombo, Paolo Galli # Point light sources used by point-light tracer @doc raw""" PointLight A point light (used by [`PointLightRenderer`](@ref)). This type holds information about a point light. # Fields - `position::Point`: a [`Point`](@ref) object holding the position of the point light in 3D space. - `color::RGB{Float32}`: the color of the point light. - `linear_radius::Float32`: radius of the source, used to compute solid angle subtended by the light. If `linear_radius` is non-zero, it is used to compute the solid angle subtended by the light at a given distance `d` through the formula: ```math \left(\frac{\mathrm{linear\_radius}}{d}\right)^2 ``` """ Base.@kwdef struct PointLight position::Point = ORIGIN color::RGB{Float32} = WHITE linear_radius::Float32 = 0f0 end @doc """ PointLight(position::Point, color::RGB{Float32}, linear_radius::Float32) Constructor for a [`PointLight`](@ref) instance. """ PointLight(::Point, ::RGB{Float32}, ::Float32) @doc """ PointLight(; position::Point = ORIGIN, color::RGB{Float32} = WHITE, linear_radius::Float32 = 0f0) Constructor for a [`PointLight`](@ref) instance. If no parameter is specified, it return a white point light in the origin with no radius. """ PointLight(; ::Point, ::RGB{Float32}, ::Float32) """ Lights Alias of `Vector{PointLight}`, to store a list of [`PointLight`](@ref) sources. """ const Lights = Vector{PointLight}
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using MagneticLocSuchowiak using Test @testset "MagneticLocSuchowiak.jl" begin # Write your tests here. end
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# syntax: proto3 using ProtoBuf import ProtoBuf.meta mutable struct MultilineChartContent <: ProtoType __protobuf_jl_internal_meta::ProtoMeta __protobuf_jl_internal_values::Dict{Symbol,Any} __protobuf_jl_internal_defaultset::Set{Symbol} function MultilineChartContent(; kwargs...) obj = new(meta(MultilineChartContent), Dict{Symbol,Any}(), Set{Symbol}()) values = obj.__protobuf_jl_internal_values symdict = obj.__protobuf_jl_internal_meta.symdict for nv in kwargs fldname, fldval = nv fldtype = symdict[fldname].jtyp (fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname)) values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval) end obj end end # mutable struct MultilineChartContent const __meta_MultilineChartContent = Ref{ProtoMeta}() function meta(::Type{MultilineChartContent}) ProtoBuf.metalock() do if !isassigned(__meta_MultilineChartContent) __meta_MultilineChartContent[] = target = ProtoMeta(MultilineChartContent) allflds = Pair{Symbol,Union{Type,String}}[:tag => Base.Vector{AbstractString}] meta(target, MultilineChartContent, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES) end __meta_MultilineChartContent[] end end function Base.getproperty(obj::MultilineChartContent, name::Symbol) if name === :tag return (obj.__protobuf_jl_internal_values[name])::Base.Vector{AbstractString} else getfield(obj, name) end end mutable struct MarginChartContent_Series <: ProtoType __protobuf_jl_internal_meta::ProtoMeta __protobuf_jl_internal_values::Dict{Symbol,Any} __protobuf_jl_internal_defaultset::Set{Symbol} function MarginChartContent_Series(; kwargs...) obj = new(meta(MarginChartContent_Series), Dict{Symbol,Any}(), Set{Symbol}()) values = obj.__protobuf_jl_internal_values symdict = obj.__protobuf_jl_internal_meta.symdict for nv in kwargs fldname, fldval = nv fldtype = symdict[fldname].jtyp (fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname)) values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval) end obj end end # mutable struct MarginChartContent_Series const __meta_MarginChartContent_Series = Ref{ProtoMeta}() function meta(::Type{MarginChartContent_Series}) ProtoBuf.metalock() do if !isassigned(__meta_MarginChartContent_Series) __meta_MarginChartContent_Series[] = target = ProtoMeta(MarginChartContent_Series) allflds = Pair{Symbol,Union{Type,String}}[:value => AbstractString, :lower => AbstractString, :upper => AbstractString] meta(target, MarginChartContent_Series, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES) end __meta_MarginChartContent_Series[] end end function Base.getproperty(obj::MarginChartContent_Series, name::Symbol) if name === :value return (obj.__protobuf_jl_internal_values[name])::AbstractString elseif name === :lower return (obj.__protobuf_jl_internal_values[name])::AbstractString elseif name === :upper return (obj.__protobuf_jl_internal_values[name])::AbstractString else getfield(obj, name) end end mutable struct MarginChartContent <: ProtoType __protobuf_jl_internal_meta::ProtoMeta __protobuf_jl_internal_values::Dict{Symbol,Any} __protobuf_jl_internal_defaultset::Set{Symbol} function MarginChartContent(; kwargs...) obj = new(meta(MarginChartContent), Dict{Symbol,Any}(), Set{Symbol}()) values = obj.__protobuf_jl_internal_values symdict = obj.__protobuf_jl_internal_meta.symdict for nv in kwargs fldname, fldval = nv fldtype = symdict[fldname].jtyp (fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname)) values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval) end obj end end # mutable struct MarginChartContent const __meta_MarginChartContent = Ref{ProtoMeta}() function meta(::Type{MarginChartContent}) ProtoBuf.metalock() do if !isassigned(__meta_MarginChartContent) __meta_MarginChartContent[] = target = ProtoMeta(MarginChartContent) allflds = Pair{Symbol,Union{Type,String}}[:series => Base.Vector{MarginChartContent_Series}] meta(target, MarginChartContent, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES) end __meta_MarginChartContent[] end end function Base.getproperty(obj::MarginChartContent, name::Symbol) if name === :series return (obj.__protobuf_jl_internal_values[name])::Base.Vector{MarginChartContent_Series} else getfield(obj, name) end end mutable struct Chart <: ProtoType __protobuf_jl_internal_meta::ProtoMeta __protobuf_jl_internal_values::Dict{Symbol,Any} __protobuf_jl_internal_defaultset::Set{Symbol} function Chart(; kwargs...) obj = new(meta(Chart), Dict{Symbol,Any}(), Set{Symbol}()) values = obj.__protobuf_jl_internal_values symdict = obj.__protobuf_jl_internal_meta.symdict for nv in kwargs fldname, fldval = nv fldtype = symdict[fldname].jtyp (fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname)) values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval) end obj end end # mutable struct Chart const __meta_Chart = Ref{ProtoMeta}() function meta(::Type{Chart}) ProtoBuf.metalock() do if !isassigned(__meta_Chart) __meta_Chart[] = target = ProtoMeta(Chart) allflds = Pair{Symbol,Union{Type,String}}[:title => AbstractString, :multiline => MultilineChartContent, :margin => MarginChartContent] oneofs = Int[0,1,1] oneof_names = Symbol[Symbol("content")] meta(target, Chart, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, oneofs, oneof_names) end __meta_Chart[] end end function Base.getproperty(obj::Chart, name::Symbol) if name === :title return (obj.__protobuf_jl_internal_values[name])::AbstractString elseif name === :multiline return (obj.__protobuf_jl_internal_values[name])::MultilineChartContent elseif name === :margin return (obj.__protobuf_jl_internal_values[name])::MarginChartContent else getfield(obj, name) end end mutable struct Category <: ProtoType __protobuf_jl_internal_meta::ProtoMeta __protobuf_jl_internal_values::Dict{Symbol,Any} __protobuf_jl_internal_defaultset::Set{Symbol} function Category(; kwargs...) obj = new(meta(Category), Dict{Symbol,Any}(), Set{Symbol}()) values = obj.__protobuf_jl_internal_values symdict = obj.__protobuf_jl_internal_meta.symdict for nv in kwargs fldname, fldval = nv fldtype = symdict[fldname].jtyp (fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname)) values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval) end obj end end # mutable struct Category const __meta_Category = Ref{ProtoMeta}() function meta(::Type{Category}) ProtoBuf.metalock() do if !isassigned(__meta_Category) __meta_Category[] = target = ProtoMeta(Category) allflds = Pair{Symbol,Union{Type,String}}[:title => AbstractString, :chart => Base.Vector{Chart}, :closed => Bool] meta(target, Category, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES) end __meta_Category[] end end function Base.getproperty(obj::Category, name::Symbol) if name === :title return (obj.__protobuf_jl_internal_values[name])::AbstractString elseif name === :chart return (obj.__protobuf_jl_internal_values[name])::Base.Vector{Chart} elseif name === :closed return (obj.__protobuf_jl_internal_values[name])::Bool else getfield(obj, name) end end mutable struct Layout <: ProtoType __protobuf_jl_internal_meta::ProtoMeta __protobuf_jl_internal_values::Dict{Symbol,Any} __protobuf_jl_internal_defaultset::Set{Symbol} function Layout(; kwargs...) obj = new(meta(Layout), Dict{Symbol,Any}(), Set{Symbol}()) values = obj.__protobuf_jl_internal_values symdict = obj.__protobuf_jl_internal_meta.symdict for nv in kwargs fldname, fldval = nv fldtype = symdict[fldname].jtyp (fldname in keys(symdict)) || error(string(typeof(obj), " has no field with name ", fldname)) values[fldname] = isa(fldval, fldtype) ? fldval : convert(fldtype, fldval) end obj end end # mutable struct Layout const __meta_Layout = Ref{ProtoMeta}() function meta(::Type{Layout}) ProtoBuf.metalock() do if !isassigned(__meta_Layout) __meta_Layout[] = target = ProtoMeta(Layout) allflds = Pair{Symbol,Union{Type,String}}[:version => Int32, :category => Base.Vector{Category}] meta(target, Layout, allflds, ProtoBuf.DEF_REQ, ProtoBuf.DEF_FNUM, ProtoBuf.DEF_VAL, ProtoBuf.DEF_PACK, ProtoBuf.DEF_WTYPES, ProtoBuf.DEF_ONEOFS, ProtoBuf.DEF_ONEOF_NAMES) end __meta_Layout[] end end function Base.getproperty(obj::Layout, name::Symbol) if name === :version return (obj.__protobuf_jl_internal_values[name])::Int32 elseif name === :category return (obj.__protobuf_jl_internal_values[name])::Base.Vector{Category} else getfield(obj, name) end end export Chart, MultilineChartContent, MarginChartContent_Series, MarginChartContent, Category, Layout
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2.290506
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include("model.jl") # particle marginal metropolis-hastings @compiled @gen function var_proposal(prev) var_x::Float64 = get_assignment(prev)[:var_x] var_y::Float64 = get_assignment(prev)[:var_y] #@addr(normal(var_x, sqrt(0.15)), :var_x) #@addr(normal(var_y, sqrt(0.08)), :var_y) @addr(normal(var_x, sqrt(0.5)), :var_x) @addr(normal(var_y, sqrt(0.5)), :var_y) end @gen function observer(ys) for (i, y) in enumerate(ys) @addr(dirac(y), :hmm => :y => i) end end load_generated_functions() ########## function strip_lineinfo(expr::Expr) @assert !(expr.head == :line) new_args = [] for arg in expr.args if (isa(arg, Expr) && arg.head == :line) || isa(arg, LineNumberNode) elseif isa(arg, Expr) && arg.head == :block stripped = strip_lineinfo(arg) append!(new_args, stripped.args) else push!(new_args, strip_lineinfo(arg)) end end Expr(expr.head, new_args...) end function strip_lineinfo(expr) expr end println("\n######################################################################\n") obs = get_assignment(simulate(obs_sub, (1.2,))) #println(strip_lineinfo( #Gen.codegen_generate(typeof(kernel), Tuple{Int,State,Params}, typeof(obs), Nothing))) import InteractiveUtils InteractiveUtils.code_warntype( generate, (typeof(kernel), Tuple{Int,State,Params}, typeof(obs), Nothing)) println("\n######################################################################\n") function initial_collapsed_trace(ys) T = length(ys) constraints = get_assignment(simulate(observer, (ys,))) (trace, weight) = generate(model_collapsed, (T,), constraints) trace end import Random Random.seed!(1) # generate synthetic dataset T = 100 # was 500 (xs_sim, ys_sim) = hmm(10., 1., T) # do inference function do_inference(n) trace = initial_collapsed_trace(ys_sim) for iter=1:n score = get_call_record(trace).score println("score: $score") trace = mh(model_collapsed, var_proposal, (), trace) choices = get_assignment(trace) println("var_x: $(choices[:var_x]), var_y: $(choices[:var_y])") end end import Profile @time do_inference(2) @time do_inference(100) #Profile.@profile do_inference(17) #Profile.print(format=:flat, sortedby=:count) #Profile.print(mincount=10)
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2.414213
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module TestDistance using ParallelKMeans: pairwise!, SingleThread, MultiThread using Test @testset "naive singlethread pairwise" begin X = [1.0 2.0; 3.0 5.0; 4.0 6.0] y = [1.0 2.0; ] r = Array{Float64, 2}(undef, 3, 1) pairwise!(r, X, y) @test all(r .≈ [0.0, 13.0, 25.0]) end @testset "multithread pairwise" begin X = [1.0 2.0; 3.0 5.0; 4.0 6.0] y = [1.0 2.0; ] r = Array{Float64, 2}(undef, 3, 1) pairwise!(r, X, y, MultiThread()) @test all(r .≈ [0.0, 13.0, 25.0]) end end # module
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1.973783
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# ------------------------------------------------------------------------------------------ # # Condicionales # # En Julia, la sintaxis # # ```julia # if *condición 1* # *opción 1* # elseif *condición 2* # *opción 2* # else # *opción 3* # end # ``` # # Nos permite eventualmente evaluar una de nuestras opciones. # <br><br> # Por ejemplo, tal vez queremos implementar la prueba de FizzBuzz: Dado un número N, imprime # "Fizz" si N es divisible entre 3, "Buzz" si N es divisible entre 5, y "FizzBuzz" si N es # divisible entre ambos 3 y 5. En cualquier otro caso, imprimo el número mismo. # ------------------------------------------------------------------------------------------ N = if (N % 3 == 0) & (N % 5 == 0) println("FizzBuzz") elseif N % 3 == 0 println("Fizz") elseif N % 5 == 0 println("Buzz") else println(N) end # ------------------------------------------------------------------------------------------ # Ahora digamos que queremos regresar el mayor número de ambos. Escoge tus propios x y y # ------------------------------------------------------------------------------------------ x = y = if x > y x else y end # ------------------------------------------------------------------------------------------ # Para el último bloque, podemos usar el operador ternario, con la sintaxis # # ```julia # a ? b : c # ``` # # que equivale a # # ```julia # if a # b # else # c # end # ``` # ------------------------------------------------------------------------------------------ (x > y) ? x : y # ------------------------------------------------------------------------------------------ # Un truco relacionado es la evaluación de corto-circuito # # ```julia # a && b # ``` # ------------------------------------------------------------------------------------------ (x > y) && println(x) (x < y) && println(y) # ------------------------------------------------------------------------------------------ # Cuando escribimos `a && b`, `b` se ejecuta sólo si `a` se evalúa a `true`. # <br> # Si `a` se evalúa a `false`, la expresión `a && b` regresa `false` # ------------------------------------------------------------------------------------------ # ------------------------------------------------------------------------------------------ # ### Ejercicios # # 5.1 Reescribe FizzBuzz sin usar `elseif`. # ------------------------------------------------------------------------------------------ # ------------------------------------------------------------------------------------------ # 5.2 Reescribe FizzBuzz usando el operador ternario. # ------------------------------------------------------------------------------------------
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module RandomVariates export # SEED, A, C, MOD, bernoulli_rng, beta_rng, binomial_rng, erlang_rng, expon_rng, gamma_rng, geometric_rng, neg_binomial_rng, conv_neg_binomial_rng, normal_rng, lognormal_rng, mv_normal_rng, poisson_rng, uniform_rng, weibull_rng, tausworthe_rng, triag_rng include("uniform.jl") include("exponential.jl") include("erlang.jl") include("weibull.jl") include("bernoulli.jl") include("geometric.jl") include("poisson.jl") include("binomial.jl") include("neg_binomial.jl") include("normal.jl") include("gamma.jl") include("beta.jl") include("tausworthe.jl") include("triangular.jl") using Dates global SEED = Dates.value(Dates.now()) # Use current epoch time as default seed # using POSIX params for LCG # https://en.wikipedia.org/wiki/Linear_congruential_generator#Parameters_in_common_use const A = 25214903917 const C = 11 const MOD = 2^48 """ set_seed(seed::Int) Set the global `SEED` variable. """ function set_seed(seed::Int) global SEED = seed end """ set_user_seed(seed::Int) Set a user-defined seed as global `SEED` variable. """ function set_user_seed(seed::Int) global SEED = seed * 7856209 end """ seed_setter(seed::Union{Int, Nothing}=nothing) Set a user defined seed, if given. """ function seed_setter(seed::Union{Int, Nothing}=nothing) if !isnothing(seed) set_user_seed(seed) # only set user seed once so we get new seed in subsequent calls end end """ get_seed() Get the global `SEED` variable. """ function get_seed() return SEED end """ check_p(p::Real) Check that parameter `p` falls between 0 and 1. """ function check_p(p::Real) if (p > 1) || (p < 0) throw(ArgumentError("Parameter `p` must fall between 0 and 1.")) end end # End of Module end
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# Don't modify this, it's just there to make the tests work. module MLJTutorials end
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3.269231
26
### Generic MUSE code abstract type AbstractMuseProblem end ## interface to be implemented by specific problem types function ∇θ_logLike end function logLike_and_∇z_logLike end function sample_x_z end logPriorθ(prob::AbstractMuseProblem, θ) = 0 standardizeθ(prob::AbstractMuseProblem, θ) = θ # this can also be overriden by specific problems # the default does LBFGS using the provided logLike_and_∇z_logLike function ẑ_at_θ(prob::AbstractMuseProblem, x, z₀, θ; ∇z_logLike_atol) soln = optimize(Optim.only_fg(z -> .-logLike_and_∇z_logLike(prob, x, z, θ)), z₀, Optim.LBFGS(), Optim.Options(g_tol=∇z_logLike_atol)) soln.minimizer, soln end ### MUSE result @doc doc""" Stores the result of a MUSE run. Can be constructed by-hand as `MuseResult()` and passed to any of the inplace `muse!`, `get_J!`, or `get_H!`. Fields: * `θ` — The estimate of the $\theta$ parameters. * `Σ, Σ⁻¹` — The approximate covariance of $\theta$ and its inverse. * `H, J` — The $H$ and $J$ matrices which form the covariance (see [Millea & Seljak, 2021](https://arxiv.org/abs/2112.09354)) * `gs` — The MAP gradient sims used to compute `J`. * `Hs` — The jacobian sims used to compute `H`. * `dist` — A `Normal` or `MvNormal` built from `θ` and `Σ`, for convenience. * `history` — Internal diagnostic info from the run. * `rng` — RNG used to generate sims for this run (so the same sims can be reused if resuming later). * `time` — Total `Millisecond` wall-time spent computing the result. """ Base.@kwdef mutable struct MuseResult θ = nothing H = nothing J = nothing Σ⁻¹ = nothing Σ = nothing dist = nothing history = [] gs = [] Hs = [] rng = nothing time = Millisecond(0) end ### MUSE solver @doc doc""" muse(prob::AbstractMuseProblem, θ₀; kwargs...) muse!(result::MuseResult, prob::AbstractMuseProblem, [θ₀=nothing]; kwargs...) Run the MUSE estimate. The `muse!` form resumes an existing result. If the `muse` form is used instead, `θ₀` must give a starting guess for $\theta$. See [`MuseResult`](@ref) for description of return value. Optional keyword arguments: * `rng` — Random number generator to use. Taken from `result.rng` or `Random.default_rng()` if not passed. * `z₀` — Starting guess for the latent space MAP. * `maxsteps = 50` — Maximum number of iterations. * `θ_rtol = 1e-1` — Error tolerance on $\theta$ relative to its standard deviation. * `∇z_logLike_atol = 1e-2` — Absolute tolerance on the $z$-gradient at the MAP solution. * `nsims = 100` — Number of simulations. * `α = 0.7` — Step size for root-finder. * `progress = false` — Show progress bar. * `pmap` — Parallel map function. * `regularize = identity` — Apply some regularization after each step. * `H⁻¹_like = nothing` — Initial guess for the inverse Jacobian of $s^{\rm MUSE}(\theta)$ * `H⁻¹_update` — How to update `H⁻¹_like`. Should be `:sims`, `:broyden`, or `:diagonal_broyden`. * `broyden_memory = Inf` — How many past steps to keep for Broyden updates. * `checkpoint_filename = nothing` — Save result to a file after each iteration. * `get_covariance = false` — Also call `get_H` and `get_J` to get the full covariance. """ muse(args...; kwargs...) = muse!(MuseResult(), args...; kwargs...) function muse!( result :: MuseResult, prob :: AbstractMuseProblem, θ₀ = nothing; rng = nothing, z₀ = nothing, maxsteps = 50, θ_rtol = 1e-1, ∇z_logLike_atol = 1e-2, nsims = 100, α = 0.7, progress = false, pmap = _map, batch_size = 1, regularize = identity, H⁻¹_like = nothing, H⁻¹_update = :sims, broyden_memory = Inf, checkpoint_filename = nothing, get_covariance = false ) rng = @something(rng, result.rng, copy(Random.default_rng())) θunreg = θ = θ₀ = standardizeθ(prob, @something(result.θ, θ₀)) z₀ = @something(z₀, sample_x_z(prob, copy(rng), θ₀).z) local H⁻¹_post, g_like_sims history = result.history result.rng = _rng = copy(rng) xz_sims = [sample_x_z(prob, _rng, θ) for i=1:nsims] xs = [[prob.x]; getindex.(xz_sims, :x)] ẑs = [[z₀]; getindex.(xz_sims, :z)] # set up progress bar pbar = progress ? RemoteProgress((maxsteps-length(result.history))*(nsims+1)÷batch_size, 0.1, "MUSE: ") : nothing try for i = (length(result.history)+1):maxsteps t₀ = now() if i > 1 _rng = copy(rng) xs = [[prob.x]; [sample_x_z(prob, _rng, θ).x for i=1:nsims]] end if i > 2 Δθ = history[end].θ - history[end-1].θ norm(Δθ ./ θ) < θ_rtol && break end # MUSE gradient gẑs = pmap(xs, ẑs, fill(θ,length(xs)); batch_size) do x, ẑ_prev, θ local ẑ, history = ẑ_at_θ(prob, x, ẑ_prev, θ; ∇z_logLike_atol) g = ∇θ_logLike(prob, x, ẑ, θ) progress && ProgressMeter.next!(pbar) (;g, ẑ, history) end ẑs = getindex.(gẑs, :ẑ) ẑ_history_dat, ẑ_history_sims = peel(getindex.(gẑs, :history)) g_like_dat, g_like_sims = peel(getindex.(gẑs, :g)) g_like = g_like_dat .- mean(g_like_sims) g_prior = AD.gradient(AD.ForwardDiffBackend(), θ -> logPriorθ(prob, θ), θ)[1] g_post = g_like .+ g_prior # Jacobian h⁻¹_like_sims = -1 ./ var(collect(g_like_sims)) H⁻¹_like_sims = h⁻¹_like_sims isa Number ? h⁻¹_like_sims : Diagonal(h⁻¹_like_sims) if (H⁻¹_like == nothing) || (H⁻¹_update == :sims) H⁻¹_like = H⁻¹_like_sims elseif i > 2 && (H⁻¹_update in [:broyden, :diagonal_broyden]) # on subsequent steps, do a Broyden's update using at # most the previous `broyden_memory` steps j₀ = Int(max(2, i - broyden_memory)) H⁻¹_like = history[j₀-1].H⁻¹_like_sims for j = j₀:i-1 Δθ = history[j].θ - history[j-1].θ Δg_like = history[j].g_like - history[j-1].g_like H⁻¹_like = H⁻¹_like + ((Δθ - H⁻¹_like * Δg_like) / (Δθ' * H⁻¹_like * Δg_like)) * Δθ' * H⁻¹_like if H⁻¹_update == :diagonal_broyden H⁻¹_like = Diagonal(H⁻¹_like) end end end H_prior = AD.hessian(AD.ForwardDiffBackend(), θ -> logPriorθ(prob, θ), θ)[1] H⁻¹_post = inv(inv(H⁻¹_like) + H_prior) t = now() - t₀ push!( history, (;θ, θunreg, g_like_dat, g_like_sims, g_like, g_prior, g_post, H⁻¹_post, H_prior, H⁻¹_like, H⁻¹_like_sims, ẑ_history_dat, ẑ_history_sims, t) ) # Newton-Rhapson step θunreg = θ .- α .* (H⁻¹_post * g_post) θ = regularize(θunreg) (checkpoint_filename != nothing) && save(checkpoint_filename, "result", result) end finally progress && ProgressMeter.finish!(pbar) end result.time += sum(getindex.(history,:t)) result.θ = θunreg result.gs = collect(g_like_sims) if get_covariance get_J!(result, prob) get_H!(result, prob) end result end function get_H!( result :: MuseResult, prob :: AbstractMuseProblem, θ₀ = result.θ; fdm :: FiniteDifferenceMethod = central_fdm(3,1), ∇z_logLike_atol = 1e-8, rng = Random.default_rng(), nsims = 10, step = nothing, pmap = _map, batch_size = 1, pmap_over = :auto, progress = false, skip_errors = false, ) θ₀ = standardizeθ(prob, @something(θ₀, result.θ)) nsims_remaining = nsims - length(result.Hs) (nsims_remaining <= 0) && return pbar = progress ? RemoteProgress(nsims_remaining*(1+length(θ₀))÷batch_size, 0.1, "get_H: ") : nothing t₀ = now() # generate simulation locally, advancing rng, and saving rng state to be reused remotely xs_zs_rngs = map(1:nsims_remaining) do i _rng = copy(rng) (x, z) = sample_x_z(prob, rng, θ₀) (x, z, _rng) end # initial fit at fiducial, used at starting points for finite difference below ẑ₀s_rngs = pmap(xs_zs_rngs; batch_size) do (x, z, rng) ẑ, = ẑ_at_θ(prob, x, z, θ₀; ∇z_logLike_atol) progress && ProgressMeter.next!(pbar) (ẑ, rng) end # finite difference Jacobian pmap_sims, pmap_jac = (pmap_over == :jac || (pmap_over == :auto && length(θ₀) > nsims_remaining)) ? (_map, pmap) : (pmap, _map) append!(result.Hs, skipmissing(pmap_sims(ẑ₀s_rngs; batch_size) do (ẑ₀, rng) try return first(pjacobian(fdm, θ₀, step; pmap=pmap_jac, batch_size, pbar) do θ x, = sample_x_z(prob, copy(rng), θ) ẑ, = ẑ_at_θ(prob, x, ẑ₀, θ₀; ∇z_logLike_atol) ∇θ_logLike(prob, x, ẑ, θ₀) end) catch err if skip_errors && !(err isa InterruptException) @warn err return missing else rethrow(err) end end end)) result.H = (θ₀ isa Number) ? mean(first.(result.Hs)) : mean(result.Hs) result.time += now() - t₀ finalize_result!(result, prob) end function get_J!( result :: MuseResult, prob :: AbstractMuseProblem, θ₀ = nothing; ∇z_logLike_atol = 1e-1, rng = Random.default_rng(), nsims = 100, pmap = _map, batch_size = 1, progress = false, skip_errors = false, covariance_method = LinearShrinkage(target=DiagonalCommonVariance(), shrinkage=:rblw), ) θ₀ = standardizeθ(prob, @something(θ₀, result.θ)) nsims_remaining = nsims - length(result.gs) if nsims_remaining > 0 pbar = progress ? RemoteProgress(nsims_remaining÷batch_size, 0.1, "get_J: ") : nothing (xs, zs) = map(Base.vect, map(1:nsims_remaining) do i sample_x_z(prob, rng, θ₀) end...) append!(result.gs, skipmissing(pmap(xs, zs, fill(θ₀,length(xs)); batch_size) do x, z, θ₀ try ẑ, = ẑ_at_θ(prob, x, z, θ₀; ∇z_logLike_atol) g = ∇θ_logLike(prob, x, ẑ, θ₀) progress && ProgressMeter.next!(pbar) return g catch err if skip_errors && !(err isa InterruptException) @warn err return missing else rethrow(err) end end end)) end result.J = (θ₀ isa Number) ? var(result.gs) : cov(covariance_method, identity.(result.gs)) finalize_result!(result, prob) end function finalize_result!(result::MuseResult, prob::AbstractMuseProblem) @unpack H, J = result if H != nothing && J != nothing H_prior = -AD.hessian(AD.ForwardDiffBackend(), θ -> logPriorθ(prob, θ), result.θ)[1] result.Σ⁻¹ = H' * inv(J) * H + H_prior result.Σ = inv(result.Σ⁻¹) if length(result.θ) == 1 result.dist = Normal(result.θ[1], sqrt(result.Σ[1])) else result.dist = MvNormal(result.θ, result.Σ) end end result end
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1.931469
5,866
using GeometricBase using Test dt = Float64 nt = 10 @testset "$(rpad("Dataseries 1d (scalar data)",80))" begin nd = 1 ni = 1 ds = DataSeries(rand(dt), nt) @test typeof(ds) == typeof(DataSeries{dt,1}(nt, ni)) @test typeof(ds) <: AbstractArray{dt,1} @test firstindex(ds) == 0 @test firstindex(ds,1) == firstindex(ds.d,1) - 1 @test firstindex(ds,2) == 1 @test lastindex(ds) == nt @test lastindex(ds,1) == lastindex(ds.d,1) - 1 @test lastindex(ds,2) == 1 @test strides(ds) == (1,) @test stride(ds,1) == 1 @test axes(ds) == (0:nt,) @test axes(ds,1) == 0:nt @test axes(ds,2) == 1:1 @test size(ds.d) == (nt+1,) @test size(ds.d) == size(ds) @test size(ds.d,1) == nt+1 @test ndims(ds) == 1 @test eltype(ds) == dt @test parent(ds) == ds.d @test eachindex(ds) == 0:nt @test eachindex(IndexLinear(), ds) == 0:nt @test eachindex(IndexCartesian(), ds) == CartesianIndices((0:nt,)) for i in 0:nt ds[i] = i end @test ds.d[1] == ds[0] @test ds.d[end] == ds[nt] @test ds.d[end] == ds[end] @test ds.d == collect(0:nt) @test parent(ds)[:] == parent(ds[:]) reset!(ds) @test ds[0] == ds[end] d = rand(nt+1) ds = DataSeries(d) @test ds.d == d @test similar(ds).d == zero(d) for i in 0:nt set_data!(ds, dt(i), i) end @test ds.d == collect(0:nt) end @testset "$(rpad("Dataseries 1d (vector-valued data)",80))" begin nd = 2 ni = 1 ds = DataSeries(rand(dt, nd), nt) @test typeof(ds) == typeof(DataSeries{Vector{dt},1}(nt, ni)) @test typeof(ds) <: AbstractArray{Vector{dt},1} @test firstindex(ds) == 0 @test firstindex(ds,1) == firstindex(ds.d,1) - 1 @test firstindex(ds,2) == 1 @test lastindex(ds) == nt @test lastindex(ds,1) == lastindex(ds.d,1) - 1 @test lastindex(ds,2) == 1 @test strides(ds) == (1,) @test stride(ds,1) == 1 @test axes(ds) == (0:nt,) @test axes(ds,1) == 0:nt @test axes(ds,2) == 1:1 @test size(ds.d) == (nt+1,) @test size(ds.d) == size(ds) @test size(ds.d,1) == nt+1 @test ndims(ds) == 1 @test eltype(ds) == Vector{dt} @test parent(ds) == ds.d @test eachindex(ds) == 0:nt @test eachindex(IndexLinear(), ds) == 0:nt @test eachindex(IndexCartesian(), ds) == CartesianIndices((0:nt,)) for i in 0:nt ds[i] = [i, i^2] end @test ds.d[1] == ds[0] @test ds.d[end] == ds[nt] @test ds.d[end] == ds[end] @test ds.d == [Vector{dt}([i, i^2]) for i in 0:nt] @test parent(ds)[:] == parent(ds[:]) reset!(ds) @test ds[0] == ds[end] d = rand(nt+1) ds = DataSeries(d) @test ds.d == d @test similar(ds).d == zero(d) for i in 0:nt set_data!(ds, dt(i), i) end @test ds.d == collect(0:nt) end @testset "$(rpad("Dataseries 2d (scalar data)",80))" begin ni = 2 ds = DataSeries(rand(dt, ni), nt, ni) @test typeof(ds) == typeof(DataSeries{dt,2}(nt, ni)) @test typeof(ds) <: AbstractArray{dt,2} @test firstindex(ds) == firstindex(ds.d) @test firstindex(ds,1) == firstindex(ds.d,1) - 1 @test firstindex(ds,2) == 1 @test lastindex(ds) == lastindex(ds.d) @test lastindex(ds,1) == lastindex(ds.d,1) - 1 @test lastindex(ds,2) == lastindex(ds.d,2) @test strides(ds) == (1,nt+1) @test stride(ds,1) == 1 @test stride(ds,2) == nt+1 @test axes(ds) == (0:nt, 1:ni) @test axes(ds,1) == 0:nt @test axes(ds,2) == 1:2 @test size(ds.d) == (nt+1, ni) @test size(ds.d) == size(ds) @test size(ds.d,1) == nt+1 @test size(ds.d,2) == ni @test ndims(ds) == 2 @test eltype(ds) == dt @test parent(ds) == ds.d for i in 0:nt set_data!(ds, dt(i), i, 1) set_data!(ds, dt(i)^2, i, 2) end @test ds.d[:,1] == collect(0:nt) @test ds.d[:,2] == collect(0:nt) .^ 2 @test ds.d[1,1] == ds[0,1] @test ds.d[1,1:ni] == ds[0,1:nsamples(ds)] @test ds[end,1] == ds.d[end,1] @test ds[end,1] == ds[nt,1] @test ds[end,1:nsamples(ds)] == ds[nt,1:ni] @test ds.d[1,:] == ds[0,:] @test ds.d[:,1] == parent(ds[:,1]) @test ds.d[:,:] == parent(ds[:,:]) reset!(ds) @test ds[0,1] == ds[end,1] # tx = rand(nd) # ds[:,0] .= tx # @test ds.d[:,1] == tx d = rand(nt+1,ni) ds = DataSeries(d) @test ds.d == d @test similar(ds).d == zero(d) end @testset "$(rpad("Dataseries 2d (vector-valued data)",80))" begin nd = 2 ni = 5 ds = DataSeries([rand(dt, nd) for i in 1:ni], nt) @test typeof(ds) == typeof(DataSeries{Vector{dt},2}(nt, ni)) @test typeof(ds) <: AbstractArray{Vector{dt},2} @test firstindex(ds) == firstindex(ds.d) @test firstindex(ds,1) == firstindex(ds.d,1) - 1 @test firstindex(ds,2) == 1 @test lastindex(ds) == lastindex(ds.d) @test lastindex(ds,1) == lastindex(ds.d,1) - 1 @test lastindex(ds,2) == lastindex(ds.d,2) @test strides(ds) == (1,nt+1) @test stride(ds,1) == 1 @test stride(ds,2) == nt+1 @test axes(ds) == (0:nt, 1:ni) @test axes(ds,1) == 0:nt @test axes(ds,2) == 1:ni @test size(ds.d) == (nt+1, ni) @test size(ds.d) == size(ds) @test size(ds.d,1) == nt+1 @test size(ds.d,2) == ni @test ndims(ds) == 2 @test eltype(ds) == Vector{dt} @test parent(ds) == ds.d for k in 1:ni for i in 0:nt ds[i,k][1] = k*i ds[i,k][2] = k*i^2 end end tx = zeros(dt, nd) for k in 1:ni for i in 0:nt get_data!(ds, tx, i, k) @test tx == Array{eltype(tx)}(k .* [i, i^2]) end end @test ds.d[1,1] == ds[0,1] @test ds.d[1,1:ni] == ds[0,1:nsamples(ds)] @test ds[end,1] == ds.d[end,1] @test ds[end,1] == ds[nt,1] @test ds[end,1:nsamples(ds)] == ds[nt,1:ni] @test ds.d[1,:] == ds[0,:] @test ds.d[:,1] == parent(ds[:,1]) @test ds.d[:,:] == parent(ds[:,:]) reset!(ds) @test ds[0,1] == ds[end,1] # tx = rand(nd) # ds[:,0] .= tx # @test ds.d[:,1] == tx d = rand(nt+1,ni) ds = DataSeries(d) @test ds.d == d @test similar(ds).d == zero(d) end # TODO: Add tests for array-valued data # @testset "$(rpad("Dataseries 3d",80))" begin # nd = 2 # ni = 2 # ds = DataSeries(dt, nd, nt, ni) # @test typeof(ds) <: AbstractArray{dt,3} # @test firstindex(ds) == firstindex(ds.d) # @test firstindex(ds,1) == firstindex(ds.d,1) # @test firstindex(ds,2) == firstindex(ds.d,2) - 1 # @test firstindex(ds,3) == firstindex(ds.d,3) # @test firstindex(ds,4) == 1 # @test lastindex(ds) == lastindex(ds.d) # @test lastindex(ds,1) == lastindex(ds.d,1) # @test lastindex(ds,2) == lastindex(ds.d,2) - 1 # @test lastindex(ds,3) == lastindex(ds.d,3) # @test lastindex(ds,4) == 1 # @test strides(ds) == (1,nd,nd*(nt+1)) # @test stride(ds,1) == 1 # @test stride(ds,2) == nd # @test axes(ds) == (1:nd, 0:nt, 1:ni) # @test axes(ds,1) == 1:nd # @test axes(ds,2) == 0:nt # @test axes(ds,3) == 1:ni # @test axes(ds,4) == 1:1 # @test size(ds.d) == (nd, nt+1, ni) # @test size(ds.d) == size(ds) # @test size(ds.d,1) == nd # @test size(ds.d,2) == nt+1 # @test size(ds.d,3) == ni # @test ndims(ds) == 3 # @test eltype(ds) == dt # @test parent(ds) == ds.d # for j in 1:ni # for i in 1:nt # ds[1,i,j] = j*i # ds[2,i,j] = j*i^2 # end # end # tx = zeros(nd) # ty = zeros(nd,ni) # tz = zeros(nd,ni) # for i in 1:nt # for j in 1:ni # get_data!(ds, tx, i, j) # @test tx == Array{eltype(tx)}([j*i, j*i^2]) # tz[1,j] = j*i # tz[2,j] = j*i^2 # end # get_data!(ds, ty, i) # @test ty == tz # end # @test ds.d[1,1,1] == ds[1,0,1] # @test ds.d[1:ds.nd,1,1] == ds[1:ds.nd,0,1] # @test ds[1,end,1] == ds.d[1,end,1] # @test ds[1,nt,1] == ds[1,end,1] # @test ds[1:ds.nd,nt,1] == ds[1:ds.nd,end,1] # @test ds.d[:,1,1] == ds[:,0,1] # @test ds.d[:,1,:] == ds[:,0,:] # reset!(ds) # @test ds[1,0,1] == ds[1,end,1] # tx = rand(nd) # ds[:,0,1] .= tx # @test ds.d[:,1,1] == tx # d = rand(nd,nt+1,ni) # ds = DataSeries(d) # @test ds.d == d # @test similar(ds).d == zero(d) # end
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220, 288, 82, 796, 6060, 27996, 26933, 25192, 7, 28664, 11, 299, 67, 8, 329, 1312, 287, 352, 25, 8461, 4357, 299, 83, 8, 198, 220, 220, 220, 2488, 9288, 2099, 1659, 7, 9310, 8, 6624, 2099, 1659, 7, 6601, 27996, 90, 38469, 90, 28664, 5512, 17, 92, 7, 429, 11, 37628, 4008, 198, 220, 220, 220, 2488, 9288, 2099, 1659, 7, 9310, 8, 1279, 25, 27741, 19182, 90, 38469, 90, 28664, 5512, 17, 92, 198, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 8, 220, 220, 6624, 717, 9630, 7, 9310, 13, 67, 8, 198, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 11, 16, 8, 6624, 717, 9630, 7, 9310, 13, 67, 11, 16, 8, 532, 352, 198, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 11, 17, 8, 6624, 352, 198, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 8, 220, 220, 220, 6624, 938, 9630, 7, 9310, 13, 67, 8, 198, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 11, 16, 8, 220, 6624, 938, 9630, 7, 9310, 13, 67, 11, 16, 8, 532, 352, 198, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 11, 17, 8, 220, 6624, 938, 9630, 7, 9310, 13, 67, 11, 17, 8, 198, 220, 220, 220, 2488, 9288, 35002, 7, 9310, 8, 220, 220, 220, 220, 220, 6624, 357, 16, 11, 429, 10, 16, 8, 198, 220, 220, 220, 2488, 9288, 33769, 7, 9310, 11, 16, 8, 220, 220, 220, 220, 6624, 352, 198, 220, 220, 220, 2488, 9288, 33769, 7, 9310, 11, 17, 8, 220, 220, 220, 220, 6624, 299, 83, 10, 16, 198, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 8, 220, 220, 6624, 357, 15, 25, 429, 11, 352, 25, 8461, 8, 198, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 11, 16, 8, 6624, 657, 25, 429, 198, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 11, 17, 8, 6624, 352, 25, 8461, 198, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 8, 6624, 357, 429, 10, 16, 11, 37628, 8, 198, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 8, 6624, 2546, 7, 9310, 8, 198, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 11, 16, 8, 6624, 299, 83, 10, 16, 198, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 11, 17, 8, 6624, 37628, 198, 220, 220, 220, 2488, 9288, 299, 67, 12078, 7, 9310, 8, 220, 6624, 362, 198, 220, 220, 220, 2488, 9288, 1288, 4906, 7, 9310, 8, 6624, 20650, 90, 28664, 92, 198, 220, 220, 220, 2488, 9288, 2560, 7, 9310, 8, 6624, 288, 82, 13, 67, 628, 220, 220, 220, 329, 479, 287, 352, 25, 8461, 198, 220, 220, 220, 220, 220, 220, 220, 329, 1312, 287, 657, 25, 429, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 288, 82, 58, 72, 11, 74, 7131, 16, 60, 796, 479, 9, 72, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 288, 82, 58, 72, 11, 74, 7131, 17, 60, 796, 479, 9, 72, 61, 17, 198, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 886, 628, 220, 220, 220, 27765, 796, 1976, 27498, 7, 28664, 11, 299, 67, 8, 198, 220, 220, 220, 329, 479, 287, 352, 25, 8461, 198, 220, 220, 220, 220, 220, 220, 220, 329, 1312, 287, 657, 25, 429, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 651, 62, 7890, 0, 7, 9310, 11, 27765, 11, 1312, 11, 479, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 9288, 27765, 6624, 15690, 90, 417, 4906, 7, 17602, 38165, 7, 74, 764, 9, 685, 72, 11, 1312, 61, 17, 12962, 198, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 886, 628, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 16, 11, 16, 60, 6624, 288, 82, 58, 15, 11, 16, 60, 198, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 16, 11, 16, 25, 8461, 60, 6624, 288, 82, 58, 15, 11, 16, 25, 5907, 12629, 7, 9310, 15437, 628, 220, 220, 220, 2488, 9288, 288, 82, 58, 437, 11, 16, 60, 6624, 288, 82, 13, 67, 58, 437, 11, 16, 60, 198, 220, 220, 220, 2488, 9288, 288, 82, 58, 437, 11, 16, 60, 6624, 288, 82, 58, 429, 11, 16, 60, 198, 220, 220, 220, 2488, 9288, 288, 82, 58, 437, 11, 16, 25, 5907, 12629, 7, 9310, 15437, 6624, 288, 82, 58, 429, 11, 16, 25, 8461, 60, 628, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 16, 11, 47715, 6624, 288, 82, 58, 15, 11, 47715, 198, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 45299, 16, 60, 6624, 2560, 7, 9310, 58, 45299, 16, 12962, 198, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 45299, 47715, 6624, 2560, 7, 9310, 58, 45299, 25, 12962, 628, 220, 220, 220, 13259, 0, 7, 9310, 8, 198, 220, 220, 220, 2488, 9288, 288, 82, 58, 15, 11, 16, 60, 6624, 288, 82, 58, 437, 11, 16, 60, 628, 220, 220, 220, 1303, 27765, 796, 43720, 7, 358, 8, 198, 220, 220, 220, 1303, 288, 82, 58, 45299, 15, 60, 764, 28, 27765, 198, 220, 220, 220, 1303, 2488, 9288, 288, 82, 13, 67, 58, 45299, 16, 60, 6624, 27765, 628, 220, 220, 220, 288, 796, 43720, 7, 429, 10, 16, 11, 8461, 8, 198, 220, 220, 220, 288, 82, 796, 6060, 27996, 7, 67, 8, 198, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 6624, 288, 628, 220, 220, 220, 2488, 9288, 2092, 7, 9310, 737, 67, 6624, 6632, 7, 67, 8, 198, 437, 628, 198, 198, 2, 16926, 46, 25, 3060, 5254, 329, 7177, 12, 39728, 1366, 628, 198, 198, 2, 2488, 9288, 2617, 17971, 7, 81, 15636, 7203, 27354, 6005, 444, 513, 67, 1600, 1795, 4008, 1, 2221, 198, 2, 220, 220, 220, 220, 299, 67, 796, 362, 198, 2, 220, 220, 220, 220, 37628, 796, 362, 198, 198, 2, 220, 220, 220, 220, 288, 82, 796, 6060, 27996, 7, 28664, 11, 299, 67, 11, 299, 83, 11, 37628, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 2099, 1659, 7, 9310, 8, 1279, 25, 27741, 19182, 90, 28664, 11, 18, 92, 198, 2, 220, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 8, 220, 220, 6624, 717, 9630, 7, 9310, 13, 67, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 11, 16, 8, 6624, 717, 9630, 7, 9310, 13, 67, 11, 16, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 11, 17, 8, 6624, 717, 9630, 7, 9310, 13, 67, 11, 17, 8, 532, 352, 198, 2, 220, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 11, 18, 8, 6624, 717, 9630, 7, 9310, 13, 67, 11, 18, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 717, 9630, 7, 9310, 11, 19, 8, 6624, 352, 198, 2, 220, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 8, 220, 220, 220, 6624, 938, 9630, 7, 9310, 13, 67, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 11, 16, 8, 220, 6624, 938, 9630, 7, 9310, 13, 67, 11, 16, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 11, 17, 8, 220, 6624, 938, 9630, 7, 9310, 13, 67, 11, 17, 8, 532, 352, 198, 2, 220, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 11, 18, 8, 220, 6624, 938, 9630, 7, 9310, 13, 67, 11, 18, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 938, 9630, 7, 9310, 11, 19, 8, 220, 6624, 352, 198, 2, 220, 220, 220, 220, 2488, 9288, 35002, 7, 9310, 8, 220, 220, 220, 220, 220, 6624, 357, 16, 11, 358, 11, 358, 9, 7, 429, 10, 16, 4008, 198, 2, 220, 220, 220, 220, 2488, 9288, 33769, 7, 9310, 11, 16, 8, 220, 220, 220, 220, 6624, 352, 198, 2, 220, 220, 220, 220, 2488, 9288, 33769, 7, 9310, 11, 17, 8, 220, 220, 220, 220, 6624, 299, 67, 198, 2, 220, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 8, 220, 220, 6624, 357, 16, 25, 358, 11, 657, 25, 429, 11, 352, 25, 8461, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 11, 16, 8, 6624, 352, 25, 358, 198, 2, 220, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 11, 17, 8, 6624, 657, 25, 429, 198, 2, 220, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 11, 18, 8, 6624, 352, 25, 8461, 198, 2, 220, 220, 220, 220, 2488, 9288, 34197, 7, 9310, 11, 19, 8, 6624, 352, 25, 16, 198, 2, 220, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 8, 6624, 357, 358, 11, 299, 83, 10, 16, 11, 37628, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 8, 6624, 2546, 7, 9310, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 11, 16, 8, 6624, 299, 67, 198, 2, 220, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 11, 17, 8, 6624, 299, 83, 10, 16, 198, 2, 220, 220, 220, 220, 2488, 9288, 2546, 7, 9310, 13, 67, 11, 18, 8, 6624, 37628, 198, 2, 220, 220, 220, 220, 2488, 9288, 299, 67, 12078, 7, 9310, 8, 220, 6624, 513, 198, 2, 220, 220, 220, 220, 2488, 9288, 1288, 4906, 7, 9310, 8, 6624, 288, 83, 198, 2, 220, 220, 220, 220, 2488, 9288, 2560, 7, 9310, 8, 6624, 288, 82, 13, 67, 198, 198, 2, 220, 220, 220, 220, 329, 474, 287, 352, 25, 8461, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 329, 1312, 287, 352, 25, 429, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 288, 82, 58, 16, 11, 72, 11, 73, 60, 796, 474, 9, 72, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 288, 82, 58, 17, 11, 72, 11, 73, 60, 796, 474, 9, 72, 61, 17, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 2, 220, 220, 220, 220, 886, 198, 198, 2, 220, 220, 220, 220, 27765, 796, 1976, 27498, 7, 358, 8, 198, 2, 220, 220, 220, 220, 1259, 796, 1976, 27498, 7, 358, 11, 8461, 8, 198, 2, 220, 220, 220, 220, 256, 89, 796, 1976, 27498, 7, 358, 11, 8461, 8, 198, 2, 220, 220, 220, 220, 329, 1312, 287, 352, 25, 429, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 329, 474, 287, 352, 25, 8461, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 651, 62, 7890, 0, 7, 9310, 11, 27765, 11, 1312, 11, 474, 8, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 9288, 27765, 6624, 15690, 90, 417, 4906, 7, 17602, 38165, 26933, 73, 9, 72, 11, 474, 9, 72, 61, 17, 12962, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 256, 89, 58, 16, 11, 73, 60, 796, 474, 9, 72, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 256, 89, 58, 17, 11, 73, 60, 796, 474, 9, 72, 61, 17, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 651, 62, 7890, 0, 7, 9310, 11, 1259, 11, 1312, 8, 198, 2, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 9288, 1259, 6624, 256, 89, 198, 2, 220, 220, 220, 220, 886, 198, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 16, 11, 16, 11, 16, 60, 6624, 288, 82, 58, 16, 11, 15, 11, 16, 60, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 16, 25, 9310, 13, 358, 11, 16, 11, 16, 60, 6624, 288, 82, 58, 16, 25, 9310, 13, 358, 11, 15, 11, 16, 60, 198, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 58, 16, 11, 437, 11, 16, 60, 6624, 288, 82, 13, 67, 58, 16, 11, 437, 11, 16, 60, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 58, 16, 11, 429, 11, 16, 60, 6624, 288, 82, 58, 16, 11, 437, 11, 16, 60, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 58, 16, 25, 9310, 13, 358, 11, 429, 11, 16, 60, 6624, 288, 82, 58, 16, 25, 9310, 13, 358, 11, 437, 11, 16, 60, 198, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 45299, 16, 11, 16, 60, 6624, 288, 82, 58, 45299, 15, 11, 16, 60, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 45299, 16, 11, 47715, 6624, 288, 82, 58, 45299, 15, 11, 47715, 198, 198, 2, 220, 220, 220, 220, 13259, 0, 7, 9310, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 58, 16, 11, 15, 11, 16, 60, 6624, 288, 82, 58, 16, 11, 437, 11, 16, 60, 198, 198, 2, 220, 220, 220, 220, 27765, 796, 43720, 7, 358, 8, 198, 2, 220, 220, 220, 220, 288, 82, 58, 45299, 15, 11, 16, 60, 764, 28, 27765, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 58, 45299, 16, 11, 16, 60, 6624, 27765, 198, 198, 2, 220, 220, 220, 220, 288, 796, 43720, 7, 358, 11, 429, 10, 16, 11, 8461, 8, 198, 2, 220, 220, 220, 220, 288, 82, 796, 6060, 27996, 7, 67, 8, 198, 2, 220, 220, 220, 220, 2488, 9288, 288, 82, 13, 67, 6624, 288, 198, 198, 2, 220, 220, 220, 220, 2488, 9288, 2092, 7, 9310, 737, 67, 6624, 6632, 7, 67, 8, 198, 2, 886, 198 ]
1.788502
4,766
module COFF using StructIO # Bring in ObjectFile definitions using ObjectFile import ObjectFile: DynamicLink, DynamicLinks, RPath, ObjectHandle, Section, Sections, SectionRef, Segment, Segments, SegmentRef, StrTab, Symbols, SymtabEntry, SymbolRef, getindex, length, lastindex, iterate, keys, eltype, handle, header, path, rpaths, canonical_rpaths, find_library, readmeta, seek, seekstart, skip, iostream, position, read, readuntil, eof, endianness, is64bit, isrelocatable, isexecutable, islibrary, isdynamic, mangle_section_name, mangle_symbol_name, format_string, section_header_offset, section_header_size, section_header_type, segment_header_offset, segment_header_size, segment_header_type, startaddr, symtab_entry_offset, symtab_entry_size, symtab_entry_type, find_libraries, findfirst, deref, section_name, section_size, section_offset, section_address, section_number, segment_name, segment_offset, segment_file_size, segment_memory_size, segment_address, strtab_lookup, symbol_name, symbol_value, isundef, isglobal, islocal, isweak, symbol_number # Load in imported C #define constants include("constants.jl") # Start to bring in concrete types, in the order they're needed include("COFFHeader.jl") include("COFFOptionalHeader.jl") include("COFFHandle.jl") include("COFFSection.jl") include("COFFStrTab.jl") include("COFFSymbol.jl") include("COFFDynamicLink.jl") end # module COFF
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2.490015
651
# Test Interpolation @testset "lagrange order 1" begin order = 1 ip = Lagrange{1,RefLine,order}() bf = getnbasefunctions(ip) nv = CGMethod1D.nvertexdofs(ip) @test isapprox(bf, order+1, atol=1e-8) @test isapprox(nv, 1, atol=1e-8) end @testset "lagrange order 2" begin order = 2 ip = Lagrange{1,RefLine,order}() bf = getnbasefunctions(ip) nv = CGMethod1D.nvertexdofs(ip) @test isapprox(bf, order+1, atol=1e-8) @test isapprox(nv, 1, atol=1e-8) end @testset "value order 1" begin order = 1 ip = Lagrange{1,RefLine,order}() i1 = 1 i2 = 2 ξ = Vec{1}((-1.0,)) N1 = value(ip, i1, ξ) N2 = value(ip, i2, ξ) println("N1:$N1; N2:$N2") @test isapprox(N1+N2, 1, atol=1e-8) end @testset "value order 2" begin order = 2 ip = Lagrange{1,RefLine,order}() i1 = 1 i2 = 2 i3 = 3 ξ = Vec{1}((-1.0,)) N1 = value(ip, i1, ξ) N2 = value(ip, i2, ξ) N3 = value(ip, i3, ξ) println("N1:$N1; N2:$N2; N3:$N3") @test isapprox(N1+N2+N3, 1, atol=1e-8) end @testset "reference_coordinates order 1" begin order = 1; n = order+1; ip = Lagrange{1,RefLine,order}() coords = reference_coordinates(ip) println(coords) ξ_vec = collect(range(-1, stop=1, length=n)) for (idx,val) in enumerate(ξ_vec) @test coords[idx][1] in ξ_vec end @test coords[1][1] == -1.0 @test coords[2][1] == 1.0 @test issorted(coords[3:end-1]) end @testset "reference_coordinates order 2" begin order = 20; n = order+1; ip = Lagrange{1,RefLine,order}() coords = reference_coordinates(ip) println(coords) ξ_vec = collect(range(-1, stop=1, length=n)) for (idx,val) in enumerate(ξ_vec) @test coords[idx][1] in ξ_vec end @test coords[1][1] == -1.0 @test coords[2][1] == 1.0 @test issorted(coords[3:end-1]) end @testset "Ferrite 1D order 1" begin order = 1 i1 = 1 i2 = 2 ξ = Vec{1}((0.25,)) ip_F = Lagrange{1,RefCube,order}() bf_F = getnbasefunctions(ip_F) ip_C = Lagrange{1,RefLine,order}() bf_C = getnbasefunctions(ip_C) N1_F = value(ip_F, i1, ξ) N2_F = value(ip_F, i2, ξ) N1_C = value(ip_C, i1, ξ) N2_C = value(ip_C, i2, ξ) @test isapprox(bf_F, bf_C, atol=1e-8) @test isapprox(N1_F, N1_C, atol=1e-8) @test isapprox(N2_F, N2_C, atol=1e-8) end @testset "Ferrite 1D order 2" begin order = 2 i1 = 1 i2 = 2 i3 = 3 ξ = Vec{1}((0.25,)) ip_F = Lagrange{1,RefCube,order}() bf_F = getnbasefunctions(ip_F) ip_C = Lagrange{1,RefLine,order}() bf_C = getnbasefunctions(ip_C) N1_F = value(ip_F, i1, ξ) N2_F = value(ip_F, i2, ξ) N3_F = value(ip_F, i3, ξ) N1_C = value(ip_C, i1, ξ) N2_C = value(ip_C, i2, ξ) N3_C = value(ip_C, i3, ξ) @test isapprox(bf_F, bf_C, atol=1e-8) @test isapprox(N1_F, N1_C, atol=1e-8) @test isapprox(N2_F, N2_C, atol=1e-8) @test isapprox(N3_F, N3_C, atol=1e-8) end
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1.803021
1,655
using MicroCoverage using Test module MicroCoverageTestSuite using MicroCoverage using Test function get_test_directory()::String return dirname(@__FILE__) end function get_filename(parts...)::String return joinpath(get_test_directory(), parts...) end function readstring_filename(parts...)::String _filename = get_filename(parts...) return read(_filename, String) end @testset "MicroCoverage.jl" begin @testset "assert.jl" begin @test MicroCoverage.always_assert(true, "") == nothing @test_throws MicroCoverage.AlwaysAssertionError MicroCoverage.always_assert(false, "") end @testset "instrument.jl" begin MicroCoverage.instrument("", Expr(:block), Val(:block)) == Expr(:block) end @testset "public_interface.jl" begin MicroCoverage.with_temp_dir() do tmp_depot MicroCoverage.with_temp_dir() do tmp_src_directory nonexistent_filename = joinpath(tmp_src_directory, "nonexistent.jl") foo_jl_filename = joinpath(tmp_src_directory, "foo.jl") test_foo_jl_filename = joinpath(tmp_src_directory, "test_foo.jl") foo_jl_microcov_filename = joinpath(tmp_src_directory, "foo.jl.microcov") bar_jl_filename = joinpath(tmp_src_directory, "bar.jl") test_bar_jl_filename = joinpath(tmp_src_directory, "test_bar.jl") bar_jl_microcov_filename = joinpath(tmp_src_directory, "bar.jl.microcov") open(foo_jl_filename, "w") do io print(io, readstring_filename("inputs", "foo.jl")) end open(test_foo_jl_filename, "w") do io print(io, readstring_filename("inputs", "test_foo.jl")) end open(bar_jl_filename, "w") do io print(io, readstring_filename("inputs", "bar.jl")) end open(test_bar_jl_filename, "w") do io print(io, readstring_filename("inputs", "test_bar.jl")) end @test_throws ArgumentError MicroCoverage.start(nonexistent_filename) @test_throws ArgumentError MicroCoverage.clean(nonexistent_filename) MicroCoverage.start(strip(foo_jl_filename)) MicroCoverage.start(bar_jl_filename) MicroCoverage.preview_coverage(; dump_coverage_io = devnull) include(foo_jl_filename) MicroCoverage.preview_coverage(; dump_coverage_io = devnull) include(bar_jl_filename) MicroCoverage.preview_coverage(; dump_coverage_io = devnull) include(test_foo_jl_filename) MicroCoverage.preview_coverage(; dump_coverage_io = devnull) include(test_bar_jl_filename) MicroCoverage.preview_coverage(; dump_coverage_io = devnull) @test !isfile(foo_jl_microcov_filename) @test !ispath(foo_jl_microcov_filename) @test !isfile(bar_jl_microcov_filename) @test !ispath(bar_jl_microcov_filename) MicroCoverage.stop(; dump_coverage = true, dump_coverage_io = devnull) @test isfile(foo_jl_microcov_filename) @test ispath(foo_jl_microcov_filename) @test isfile(bar_jl_microcov_filename) @test ispath(bar_jl_microcov_filename) if Sys.iswindows() @test chomp(read(foo_jl_microcov_filename, String)) == chomp(readstring_filename("expected_outputs", "foo.jl.microcov.expected")) @test chomp(read(bar_jl_microcov_filename, String)) == chomp(readstring_filename("expected_outputs", "bar.jl.microcov.expected")) else @test read(foo_jl_microcov_filename, String) == readstring_filename("expected_outputs", "foo.jl.microcov.expected") @test read(bar_jl_microcov_filename, String) == readstring_filename("expected_outputs", "bar.jl.microcov.expected") end touch(foo_jl_microcov_filename) MicroCoverage.clean(foo_jl_filename) touch(foo_jl_microcov_filename) MicroCoverage.clean(tmp_src_directory) end end end end end # end module MicroCoverageTestSuite
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@testset "wiener" begin k_1 = WienerKernel(i=-1) @test typeof(k_1) <: WhiteKernel k0 = WienerKernel() @test typeof(k0) <: WienerKernel{0} k1 = WienerKernel(i=1) @test typeof(k1) <: WienerKernel{1} k2 = WienerKernel(i=2) @test typeof(k2) <: WienerKernel{2} k3 = WienerKernel(i=3) @test typeof(k3) <: WienerKernel{3} @test_throws AssertionError WienerKernel(i=4) @test_throws AssertionError WienerKernel(i=-2) v1 = rand(4) v2 = rand(4) X = sqrt(sum(abs2, v1)) Y = sqrt(sum(abs2, v2)) minXY = min(X, Y) @test k0(v1, v2) ≈ minXY @test k1(v1, v2) ≈ 1 / 3 * minXY^3 + 1 / 2 * minXY^2 * euclidean(v1, v2) @test k2(v1, v2) ≈ 1 / 20 * minXY^5 + 1 / 12 * minXY^3 * euclidean(v1, v2) * ( X + Y - 1 / 2 * minXY ) @test k3(v1, v2) ≈ 1 / 252 * minXY^7 + 1 / 720 * minXY^4 * euclidean(v1, v2) * ( 5 * max(X, Y)^2 + 2 * X * Y + 3 * minXY^2 ) # kernelmatrix tests m1 = rand(3,4) m2 = rand(3,4) @test kernelmatrix(k0, m1, m1) ≈ kernelmatrix(k0, m1) atol=1e-5 K = zeros(4,4) kernelmatrix!(K,k0,m1,m2) @test K ≈ kernelmatrix(k0, m1, m2) atol=1e-5 V = zeros(4) kerneldiagmatrix!(V,k0,m1) @test V ≈ kerneldiagmatrix(k0,m1) atol=1e-5 x1 = rand() x2 = rand() @test kernelmatrix(k0, x1*ones(1,1), x2*ones(1,1))[1] ≈ k0(x1, x2) atol=1e-5 @test kernelmatrix(k1, x1*ones(1,1), x2*ones(1,1))[1] ≈ k1(x1, x2) atol=1e-5 @test kernelmatrix(k2, x1*ones(1,1), x2*ones(1,1))[1] ≈ k2(x1, x2) atol=1e-5 @test kernelmatrix(k3, x1*ones(1,1), x2*ones(1,1))[1] ≈ k3(x1, x2) atol=1e-5 # test_ADs(()->WienerKernel(i=1)) @test_broken "No tests passing" end
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module Data export List, Fun include("TypedFn.jl") @info TypedFn using MLStyle.Data.TypedFn include("List.jl") end
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#***************************************************************************** # Written by Ritchie Lee, [email protected] # ***************************************************************************** # Copyright ã 2015, United States Government, as represented by the # Administrator of the National Aeronautics and Space Administration. All # rights reserved. The Reinforcement Learning Encounter Simulator (RLES) # platform is licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. You # may obtain a copy of the License at # http://www.apache.org/licenses/LICENSE-2.0. Unless required by applicable # law or agreed to in writing, software distributed under the License is # distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY # KIND, either express or implied. See the License for the specific language # governing permissions and limitations under the License. # _____________________________________________________________________________ # Reinforcement Learning Encounter Simulator (RLES) includes the following # third party software. The SISLES.jl package is licensed under the MIT Expat # License: Copyright (c) 2014: Youngjun Kim. # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to # deal in the Software without restriction, including without limitation the # rights to use, copy, modify, merge, publish, distribute, sublicense, and/or # sell copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # The above copyright notice and this permission notice shall be included in # all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED # "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT # NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR # PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT # HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN # ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN # CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # ***************************************************************************** using TensorFlow import TensorFlow.API: shape, gather, concat, expand_dims, div_ type Normalizer{T<:AbstractFloat} ndim::Int64 maxes::Array{T} mins::Array{T} end function Normalizer(data::TFDataset; converttype::Union{Type,Void}=nothing) N = ndims(data.X) rmdims = collect(1:N-1) #find max/mins per column over entire dataset maxes = maximum(data.X, rmdims) mins = minimum(data.X, rmdims) if converttype != nothing maxes = convert(Array{converttype}, maxes) mins = convert(Array{converttype}, mins) end norm = Normalizer(N, maxes, mins) norm end #""" #""" function normalize01(norm::Normalizer, Xin::Tensor) N = norm.ndim maxes = constant(norm.maxes) mins = constant(norm.mins) tileshape = concat(Tensor(0), Tensor([gather(shape(Xin), Tensor(collect(0:N-2))); Tensor([1])])) tiledmaxes = tile(maxes, tileshape) tiledmins = tile(mins, tileshape) Xout = div_((Xin - tiledmins), (tiledmaxes - tiledmins)) Xout end function normalize(norm::Normalizer, Xin::Tensor, minval::AbstractFloat=-1.0, maxval::AbstractFloat=1.0) X01 = normalize(Xin) max = constant(maxval) min = constant(minval) shape = get_shape(Xin) tiledmax = tile(max, Tensor(shape)) tiledmin = tile(min, Tensor(shape)) Xout = X01 * (tiledmax - tiledmin) + tiledmin Xout end
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""" Contains some functions for calculating cross-correlations, autocorrelations, and Pearson correlations among rate units in a rate network """ using Statistics import DSP.xcorr """ xcorr_unbiased(x::Vector, y::Vector, maxlag::Int64) Returns the cross-correlation of two signals normalized by the length of the available convolution window. Written by Rainer Engelken ([email protected]). """ function xcorr_unbiased(x, y, maxlag) l = length(x) # we assume same length for x and y lags = -maxlag:maxlag scale = l .- abs.(lags) scale[scale .<= 0] .= 1 # avoid zero division xcorr(x, y)[l .+ lags] ./ scale end """ avg_autocorrs(A::Matrix{T}, maxlag::Int64, wait::Int64=0) where T <: AbstractFloat Returns the average autocorrelation for the activity of each unit described in the `N x NT` matrix `A`. Note the autocorrelations are not mean-subtracted. The `maxlag` parameter gives the maximum shift of the signal, and the `wait` parameter gives the number of timesteps in the beginning to disregard. """ function avg_autocorrs(A::Matrix{T}, maxlag::Int64, wait::Int64=0) where T <: AbstractFloat (N, NT) = size(A) unit_autocorrs = mapslices(view(A, :, (wait + 1):NT), dims=2) do x return xcorr_unbiased(x, x, maxlag) end return vec(mean(unit_autocorrs, dims=1)) end
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function mnistgrid(images, nrow, filename=nothing) yy = reshape(images, 28, 28, size(images)[end]) yy = permutedims(yy, (2,1,3)) yy = Images.imresize(yy, 40, 40) yy = Gray.(mosaicview(yy, 0.5f0, nrow=nrow, npad=1, rowmajor=true)) if filename == nothing display(yy) else save(filename, yy) end end
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using Random, LightGraphs, SimpleWeightedGraphs @testset "Testing local_search.jl" begin @testset "Testing pearson_correlation" begin # Check equal b1 = [i/6 for i in 1:6] b2 = [i/6 for i in 1:6] @test AbrkgaObop.pearson_correlation(b1,b2,6) == 1.0 # Check reverse b3 = reverse(b1) @test AbrkgaObop.pearson_correlation(b1,b3,6) ≈ -1.0 end; @testset "Testing weighted_label_propagation" begin Random.seed!(0) keys = [0.16666666666666666 0.159 0.84; 0.3333333333333333 0.32 0.82; 0.5 0.49 0.65; 0.6666666666666666 0.65 0.49; 0.8333333333333334 0.82 0.32; 1.0 0.84 0.159] # Create weighted graph sigma = 0.7 # Used to make graph sparse n_itens = size(keys,1) n_voters = size(keys,2) graph = SimpleWeightedGraph(n_voters) for i in 1:n_voters-1 for j in i+1:n_voters weight = AbrkgaObop.pearson_correlation(keys[:,i],keys[:,j],n_itens) if weight >= sigma add_edge!(graph, i, j, weight) end end end # Return the index of the chromosomes that the LS will be applied index_local_search = AbrkgaObop.weighted_label_propagation(graph) @test index_local_search == [1,3] end @testset "Testing objective_partial" begin instance = read_dataset("datasets/movie.toi") bucket = [0 0; 0 0; 0 0; 0 0; 0 0; 0 0] keys = [0.16666666666666666 0.159; 0.3333333333333333 0.32; 0.5 0.49; 0.6666666666666666 0.65; 0.8333333333333334 0.82; 1.0 0.84] fitness = [0,0] AbrkgaObop.decoder!(1,bucket,keys) AbrkgaObop.objective!(1,bucket,fitness,instance) # Check i -> j fitness_from_i_j = AbrkgaObop.objective_partial(bucket[:,1], fitness[1], 1, 1, 6, instance) @test fitness_from_i_j == 32 # Check j -> i fitness_from_j_i = AbrkgaObop.objective_partial(bucket[:,1], fitness_from_i_j, 1, 6, 1, instance) @test fitness_from_j_i == fitness[1] # Compare with another bucket with same bucket order AbrkgaObop.decoder!(2,bucket,keys) AbrkgaObop.objective!(2,bucket,fitness,instance) @test fitness_from_i_j == AbrkgaObop.objective_partial(bucket[:,2], fitness[2], 1, 1, 6, instance) end @testset "Testing local_search" begin Random.seed!(0) instance = read_dataset("datasets/movie.toi") bucket = [0 0; 0 0; 0 0; 0 0; 0 0; 0 0] keys = [0.16666666666666666 0.159; 0.3333333333333333 0.32; 0.5 0.49; 0.6666666666666666 0.65; 0.8333333333333334 0.82; 1.0 0.84] fitness = [0,0] statistics = AbrkgaObop.OBOPStatistics([],[],[],[],[],[],0.0,0.0,0,0) AbrkgaObop.decoder!(1,bucket,keys) AbrkgaObop.objective!(1,bucket,fitness,instance) best_solution = AbrkgaObop.OBOPSolution(instance.total_itens,time()) AbrkgaObop.local_search!(1,keys,bucket,fitness,instance,best_solution,1,statistics) @test best_solution.objective == 72 @test best_solution.bucket == [1,1,1,2,2,3] end @testset "Testing local_search_parallel" begin Random.seed!(0) instance = read_dataset("datasets/movie.toi") bucket = [0 0; 0 0; 0 0; 0 0; 0 0; 0 0] keys = [0.16666666666666666 0.159; 0.3333333333333333 0.32; 0.5 0.49; 0.6666666666666666 0.65; 0.8333333333333334 0.82; 1.0 0.84] fitness = [0,0] statistics = AbrkgaObop.OBOPStatistics([],[],[],[],[],[],0.0,0.0,0,0) AbrkgaObop.decoder!(1,bucket,keys) AbrkgaObop.objective!(1,bucket,fitness,instance) best_solution = AbrkgaObop.OBOPSolution(instance.total_itens,time()) AbrkgaObop.local_search_parallel!(1,keys,bucket,fitness,instance,best_solution,1,statistics) @test best_solution.objective == 72 @test best_solution.bucket == [1,1,1,2,2,3] end #= @testset "Testing clustering_search" begin Random.seed!(0) instance = read_dataset("datasets/movie.toi") bucket = [0 0; 0 0; 0 0; 0 0; 0 0; 0 0] keys = [0.16666666666666666 0.159; 0.3333333333333333 0.32; 0.5 0.49; 0.6666666666666666 0.65; 0.8333333333333334 0.82; 1.0 0.84] fitness = [0,0] AbrkgaObop.decoder!(1,bucket,keys) AbrkgaObop.objective!(1,bucket,fitness,instance) AbrkgaObop.decoder!(2,bucket,keys) AbrkgaObop.objective!(2,bucket,fitness,instance) best_solution = AbrkgaObop.OBOPSolution(instance.total_itens,time()) statistics = AbrkgaObop.OBOPStatistics([],[],[],[],[],[],0.0,0.0,0,0) AbrkgaObop.clustering_search(2, [1,2], keys, bucket, fitness, instance, best_solution, 1, statistics) @test best_solution.objective == 72 @test best_solution.bucket == [1,1,1,2,2,3] end =# end
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@testset "utilities.jl" begin f_test(x, a, b) = a .* x .+ b @test EasyPhys.number_of_arguments(f_test) == 3 @test EasyPhys.argument_names(f_test) == [:x, :a, :b] EasyPhys.@partially_applicable g_test(x, a, b; kwargs...) = (a * x + b) for x in 1:5, a in 6:10, b in 1:10 @test g_test(x, a, b; test=true) == x |> g_test(a, b; test=false) == a * x + b end EasyPhys.@partially_applicable g_test(x; kwargs...) = (println(kwargs); 5*x) @test g_test(2; test=:somearg) == (2::Int) |> g_test(test=:someotherarg) == 10 end
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abstract AbstractNoiseModel noise(s::Symbol,args...) = _noise(Val{s},args...) noisemodelname(::AbstractNoiseModel) = "AbstractNoiseModel" function show(io::IO,n::AbstractNoiseModel) println(io,noisemodelname(n)) for f in fieldnames(n) print(io," ",f,": ",typeof(getfield(n,f))) println(io) end nothing end
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# License for this file: MIT (expat) # Copyright 2017-2018, DLR Institute of System Dynamics and Control # # This file is part of module # ModiaMath.SimulationEngine(ModiaMath/SimulationEngine/_module.jl) # # Methods that involve IDA UserData #= "KLU sparse matrix type" type SlsMat M::Cint # number of rows N::Cint # number of columns NNZ::Cint # maximum number of nonzero entries in the matrix data::Ptr{Sundials.realtype} # data[NNZ] - value of nonzero entries rowvals::Ptr{Cint} # rowvals[NNZ] - row indices of data (index starts at zero) colptrs::Ptr{Cint} # colptrs[N+1] - index of the first column entry into the # data and rowvals arrays (index starts at zero) # The last entry contains the total number of nonzero values # in the matrix and hence points one past the end # of the active data in the data and rowvals arrays. end const SlsMat_Ptr = Ptr{SlsMat} """ CSCtoSlsMat!(mat, matKLU) Copy SparseMatrixCSC mat to SlsMat data structure matKLU (storage for both objects are provided in the calling program) """ function CSCtoSlsMat!(mat::SparseMatrixCSC{Float64,Cint}, matKLU::SlsMat) for i = 1:length(mat.nzval) unsafe_store!(matKLU.data , mat.nzval[i], i) unsafe_store!(matKLU.rowvals, mat.rowval[i]-1, i) end for i = 1:length(mat.colptr) unsafe_store!(matKLU.colptrs, mat.colptr[i]-1, i) end end =# ################################################################## # # Wrappers to IDA code # ################################################################## function sol_f!(simModel::IntegratorData, sim, t::Float64, _y::Vector{Float64}, _yp::Vector{Float64}, r::Vector{Float64}, hcur) stat = simModel.statistics stat.hMin = min(stat.hMin, simModel.hcur[1]) stat.hMax = max(stat.hMax, simModel.hcur[1]) stat.orderMax = max(stat.orderMax, simModel.order[1]) stat.nResidues += 1 sim = simModel.simulationState sim.time = t simModel.last_t = t simModel.last_norm_y = norm(simModel.y, Inf) ModiaMath.DAE.getResidues!(simModel.model, sim, t, _y, _yp, r, hcur) #println(_y, _yp, t, r, hcur ) return nothing end #------- full jacobian function sol_fulljac(t::Float64, cj::Float64, _y::Vector{Float64}, _yp::Vector{Float64}, _r::Vector{Float64}, _fulljac::Array{Float64}, simModel::IntegratorData, tmp1::Vector{Float64}, tmp2::Vector{Float64}, tmp3::Vector{Float64}) # Compute full Jacobian sim = simModel.simulationState sim.time = t simModel.hcur[1] = simModel.sol_data.hcur simModel.eweight = simModel.sol_data.weights simModel.y = _y simModel.yp = _yp r = _r ModiaMath.DAE.computeJacobian!(simModel.model, sim, t, y, yp, r, simModel.fulljac, simModel.hcur[1], cj, simModel.eweight) simModel.statistics += sim.nx return 0 # indicates normal return end function find_roots(t::Array{Float64, 1}, ys::Array{Array{Float64, 1}, 1}, yps::Array{Array{Float64,1},1}, simModel::IntegratorData, resprob!, abstol::Float64, reltol::Array{Float64,1}) #solve again with better precision to be sure FTOL=eps(Float64)^(1 / 3) sim = simModel.simulationState nsol_f!(r, y) = ModiaMath.DAE.getResidues!(simModel.model, sim, t[1], ys[1], yps[1], r, simModel.hcur[1]) nsol = nlsolve(nsol_f!, ys[1], ftol=FTOL) y = nsol.zero prob = DAEProblem{true}(resprob!, yps[1], y, (t[1], t[end]), differential_vars=[true,true,false]) sol = solve(prob, dassl(), reltol = reltol, abstol = abstol/100) return sol.t[end], sol.u[end], sol.du[end] end
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2.226426
1,771
using Dash using DashCoreComponents using DashHtmlComponents using PlotlyJS include("IntegralUtils.jl") include("GraphingUtils.jl") using .IntegralUtils using .GraphingUtils mathjax = "https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_CHTML" app = dash(external_stylesheets=["https://codepen.io/chriddyp/pen/bWLwgP.css"], assets_folder="assets", external_scripts=[mathjax]) options_ = ["S: r(u, v)", "S: z = f(x, y), y = g(x)"] app.layout = html_div() do html_div(children = [ html_h1("\$\$\\text{Surface integrals calculator}\$\$", style=Dict("textAlign" => "center", "margin" => "3%")), html_div(id="header", children=[ html_h3(id="header_h3", "\$\$ \\text{Hello, let the fun begin!}\$\$") ] ), html_hr(style=Dict("borderTop" => "1px dashed #d69c2f")), html_div(id="surface", children=[ html_label(id="surface_label", "\$\$\\text{Choose the way of defining the surface:}\$\$"), dcc_dropdown( id = "dropdown", options = [(label = i, value = i) for i in options_], value = options_[1], ), ]), html_hr(style=Dict("borderTop" => "1px dashed #d69c2f")), html_div(id="main", children=[ html_div(id="inputs", children=[ html_label(id="vector_field_l", "\$\$\\text{Enter your vector field formula}\$\$"), html_div(id="field", children=[ html_label(id="mFx", "\$\$\\vec{F}\\cdot\\hat{i}\$\$"), dcc_input(id="Fx", type="text", value="x"), html_label(id="mFy", "\$\$\\vec{F}\\cdot\\hat{j}\$\$"), dcc_input(id="Fy", type="text", value="y"), html_label(id="mFz", "\$\$\\vec{F}\\cdot\\hat{k}\$\$"), dcc_input(id="Fz", type="text", value="z"), ] ), html_label(id="method_dropdown", "\$\$\\text{Choose method of numeric integration:}\$\$"), dcc_dropdown( id = "method", options = [(label = i, value = i) for i in ("Simpson", "Monte Carlo")], value = "Simpson" ), html_label(id="accurary", "\$\$\\text{Choose the accuracy of numeric integration:}\$\$"), dcc_slider( id = "integral_accuracy", min = 10, max = 100, marks = Dict([Symbol(v) => Symbol(v) for v in 10:10:100]), value = 10, step = 10, ), html_div(id="parametric_bounds", children=[ html_label(id="r1lab", "\$\$\\vec{r}(u, v)\\cdot\\hat{i} =\$\$"), dcc_input(id="r1", type="text", value="sqrt(1/4 + u^2) * cos(v)"), html_label(id="r2lab", "\$\$\\vec{r}(u, v)\\cdot\\hat{j} =\$\$"), dcc_input(id="r2", type="text", value="sqrt(1/4 + u^2) * sin(v)"), html_label(id="r3lab", "\$\$\\vec{r}(u, v)\\cdot\\hat{k} =\$\$"), dcc_input(id="r3", type="text", value="u"), html_label(id="u_range1", "\$\$u_{min} =\$\$"), dcc_input(id="u_range1i", type="text", value="-1"), html_label(id="u_range2", "\$\$u_{max} =\$\$"), dcc_input(id="u_range2i", type="text", value="1"), html_label(id="v_range1", "\$\$\\phi(u) =\$\$"), dcc_input(id="v_range1i", type="text", value="0"), html_label(id="v_range2", "\$\$\\theta(u) =\$\$"), dcc_input(id="v_range2i", type="text", value="2pi") ], style=Dict("display" => "grid") ), html_div(id="fxy_bounds", children=[ html_label(id="x_range1", "\$\$x_{\\text{min}} =\$\$"), dcc_input(id="x_range1i", type="text", value="-2"), html_label(id="x_range2", "\$\$ x_{\\text{max}} =\$\$"), dcc_input(id="x_range2i", type="text", value="3"), html_label(id="y_range1", "\$\$ \\zeta(x) =\$\$"), dcc_input(id="y_range1i", type="text", value="-2"), html_label(id="y_range2", "\$\$ \\eta(x) =\$\$"), dcc_input(id="y_range2i", type="text", value="2"), html_label(id="z_range1", "\$\$ f(x, y) =\$\$"), dcc_input(id="z_range1i", type="text", value="-(x^2 + y^2)"), html_label(id="z_range2", "\$\$ g(x, y) =\$\$"), dcc_input(id="z_range2i", type="text", value="x^2+y^2"), ], style=Dict("display" => "none") ), html_button(id = "submit-button-state", children = "submit", n_clicks = 0), html_div(id="output_") ]), html_div(id="graphing", children=[ dcc_graph( id = "surface_plot", figure = ( data = [ (x = [0], y = [0], z = [[0], [0]], type = "surface") ], layout = ( autosize=false, width=600, height=600 ) ) ), ] ), ]), html_div(id="plot_attributes", children=[ html_label(id="field_density_lab", "\$\$\\text{Choose the density of the vector field.}\$\$"), dcc_slider( id = "field_density", min = 0, max = ,10 marks = Dict([Symbol(v) => Symbol(v) for v in 0:1:10]), value = 5, step = 1, ), html_label(id="graph_accuracy_lab", "\$\$\\text{Choose the accuracy of plotting.}\$\$"), dcc_slider( id = "graph_accuracy", min = 10, max = 100, marks = Dict([Symbol(v) => Symbol(v) for v in 10:10:100]), value = 20, step = 10, ) ] ), html_footer("\$\$\\text{MIT License}. \\ \\text{MM, ML, MK.}\$\$", style=Dict("marginTop" => "3em", "textAlign" => "center")) ]) end callback!(app, Output("parametric_bounds", "style"), Output("fxy_bounds", "style"), Input("dropdown", "value") ) do user_choice if user_choice == options_[1] return Dict("display" => "grid"), Dict("display" => "none") else return Dict("display" => "none"), Dict("display" => "grid") end end callback!(app, Output("output_", "children"), Input("submit-button-state", "n_clicks"), State("dropdown", "value"), State("r1", "value"), State("r2", "value"), State("r3", "value"), State("Fx", "value"), State("Fy", "value"), State("Fz", "value"), State("method", "value"), State("integral_accuracy", "value"), State("u_range1i", "value"), State("u_range2i", "value"), State("v_range1i", "value"), State("v_range2i", "value"), State("x_range1i", "value"), State("x_range2i", "value"), State("y_range1i", "value"), State("y_range2i", "value"), State("z_range1i", "value"), State("z_range2i", "value") ) do n_clicks, dropdown_value, r1, r2, r3, Fx, Fy, Fz, technique, n, u_min, u_max, v_min, v_max, x_min, x_max, y_min, y_max, z_min, z_max if dropdown_value == options_[1] try u_min, u_max = parse_num.([u_min, u_max]) p = parse_function(join(["[" * r1, r2, r3 *"]" ], ", "), :u, :v) q = parse_function(join(["[" * Fx, Fy, Fz * "]"], ", "), :x, :y, :z) ϕ = parse_function(v_min, :u) ψ = parse_function(v_max, :u) value(f, g, a, b) = round_float(Φ(f, g, (u_min, u_max), a, b; N = Int(n ÷ 2), technique = technique), 1e-3) value_ = @eval abs(($value($q, $p, $ϕ, $ψ))) return html_h5("|Φ| = $(value_).", style=Dict("textAlign" => "center")) catch e return html_h5("\$\$\\text{Wrong input. Try again.}\$\$", style=Dict("textAlign" => "center")) end else try x_min, x_max = parse_num.([x_min, x_max]) q = parse_function(join(["[" * Fx, Fy, Fz * "]"], ", "), :x, :y, :z) ϕ = parse_function(y_min, :x) ψ = parse_function(y_max, :x) ρ = parse_function(z_min, :x, :y) η = parse_function(z_max, :x, :y) value(f, a, b, c, d) = round_float(Φ(f, (x_min, x_max), a, b, c, d; N = Int(n ÷ 2), technique = technique), 1e-3) value_ = @eval abs(($value($q, $ρ, $η, $ϕ, $ψ))) return html_h5("|Φ| = $(value_).", style=Dict("textAlign" => "center")) catch e return html_h5("\$\$ \\text{Wrong input. Try again.} \$\$", style=Dict("textAlign" => "center")) end end end callback!(app, Output("surface_plot", "figure"), Input("submit-button-state", "n_clicks"), State("r1", "value"), State("r2", "value"), State("r3", "value"), State("dropdown", "value"), State("graph_accuracy", "value"), State("u_range1i", "value"), State("u_range2i", "value"), State("v_range1i", "value"), State("v_range2i", "value"), State("x_range1i", "value"), State("x_range2i", "value"), State("y_range1i", "value"), State("y_range2i", "value"), State("z_range1i", "value"), State("z_range2i", "value"), State("Fx", "value"), State("Fy", "value"), State("Fz","value"), State("field_density", "value") ) do n_clicks, r1, r2, r3, dropdown_value, N, u_min, u_max, v_min, v_max, x_min, x_max, y_min, y_max, z_min, z_max, F1, F2, F3, density if dropdown_value == options_[1] # _______________parametric try u_min = parse_num(u_min) u_max = parse_num(u_max) v_min = parse_function(v_min, :u) v_max = parse_function(v_max, :u) catch e u_min = -1 u_max = 1 v_min = parse_function("0", :u) v_max = parse_function("2pi", :u) end if false return Plot(surface(; x = [0], y = [0], z = [[0], [0]])) else Fx = Fy = Fz = "_" X(u, v) = 0 Y(u, v) = 0 Z(u, v) = 0 try X = parse_function(r1, :u, :v) Y = parse_function(r2, :u, :v) Z = parse_function(r3, :u, :v) Fx = parse_function(F1, :x, :y, :z) Fy = parse_function(F2, :x, :y, :z) Fz = parse_function(F3, :x, :y, :z) @eval ($X(-2, 3), $Y(-2, 3), $Z(-2, 3)) @eval (isa($X(-2, 3), Array{Float64, 1})) @eval (isa($Y(-2, 3), Array{Float64, 1})) @eval (isa($Z(-2, 3), Array{Float64, 1})) @eval (isa($Fx(-2, -2, -2), Number)) @eval (isa($Fy(-2, -2, -2), Number)) @eval (isa($Fz(-2, -2, -2), Number)) catch e X = parse_function("0", :u, :v) Y = parse_function("0", :u, :v) Z = parse_function("0", :u, :v) Fx = parse_function("0", :x, :y, :z) Fy = parse_function("0", :x, :y, :z) Fz = parse_function("0", :x, :y, :z) end us = LinRange(u_min, u_max, N) value_(g, u::LinRange) = g.(u) value_(g, u::Number) = g(u) vs = @eval (LinRange(minimum($value_($v_min, $us)), maximum($value_($v_max, $us)), $N)) check(u, v, f) = @eval($value_($v_min, $u) <= $v && $value_($v_max, $u) >= $v ? $f($u, $v) : NaN) value(g) = check.(us', vs, g) x1 = @eval ($value($X)) y1 = @eval ($value($Y)) z1 = @eval ($value($Z)) return @eval($graph_all($x1, $y1, $z1, $Fx, $Fy, $Fz, minimum(filter(!isnan, $x1)), maximum(filter(!isnan, $x1)), minimum(filter(!isnan, $y1)), maximum(filter(!isnan, $y1)), minimum(filter(!isnan, $z1)), maximum(filter(!isnan, $z1)), $density)) end else # ______________________________________________f(x,y) Fx = Fy = Fz = "_" try x_min = parse_num(x_min) x_max = parse_num(x_max) y_min = parse_function(y_min, :x) y_max = parse_function(y_max, :x) z_min = parse_function(z_min, :x, :y) z_max = parse_function(z_max, :x, :y) Fx = parse_function(F1, :x, :y, :z) Fy = parse_function(F2, :x, :y, :z) Fz = parse_function(F3, :x, :y, :z) @eval (isa($Fx(-2, -2, -2), Number)) @eval (isa($Fy(-2, -2, -2), Number)) @eval (isa($Fz(-2, -2, -2), Number)) catch e x_min = -2 y_min = parse_function("-2", :x) z_min = parse_function("-2", :x, :y) x_max = 2 y_max = parse_function("2", :x) z_max = parse_function("2", :x, :y) Fx = parse_function("0", :x, :y, :z) Fy = parse_function("0", :x, :y, :z) Fz = parse_function("0", :x, :y, :z) end if false #(x_min > x_max) | (y_min > y_max) | (z_min > z_max) return Plot(surface(; x = [0], y = [0], z = [[0], [0]])) else xs = LinRange(x_min, x_max, N) value2_(g::Function, x::LinRange{Float64}) = g.(x) value2_(g::Function, x::Number) = g(x) ys = @eval (LinRange(minimum($value2_($y_min, $xs)), maximum($value2_($y_max, $xs)), $N)) check2(x::Number, y::Number, h::Function)::Float64 = @eval($value2_($y_min, $x) <= $y && $value2_($y_max, $x) >= $y ? $h($x, $y) : NaN) value2(g) = check2.(xs', ys, g) zs = @eval($value2($z_max)) z₀ = @eval($value2($z_min)) temp = deepcopy(zs) zs[zs .< z₀] .= NaN z₀[z₀ .> temp] .= NaN return @eval($graph_all($xs, $ys, $zs, $Fx, $Fy, $Fz, minimum($xs), maximum($xs), minimum(filter(!isnan, $ys)), maximum(filter(!isnan, $ys)), minimum(filter(!isnan, $z₀)), maximum(filter(!isnan, $zs)), $density, $z₀)) end end end run_server(app, "0.0.0.0")
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220, 220, 331, 796, 685, 15, 4357, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 796, 16410, 15, 4357, 685, 15, 11907, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2073, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 87, 796, 376, 88, 796, 376, 89, 796, 45434, 1, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1395, 7, 84, 11, 410, 8, 796, 657, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 575, 7, 84, 11, 410, 8, 796, 657, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1168, 7, 84, 11, 410, 8, 796, 657, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1949, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1395, 796, 21136, 62, 8818, 7, 81, 16, 11, 1058, 84, 11, 1058, 85, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 575, 796, 21136, 62, 8818, 7, 81, 17, 11, 1058, 84, 11, 1058, 85, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1168, 796, 21136, 62, 8818, 7, 81, 18, 11, 1058, 84, 11, 1058, 85, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 87, 796, 21136, 62, 8818, 7, 37, 16, 11, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 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220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 56, 32590, 17, 11, 513, 828, 15690, 90, 43879, 2414, 11, 352, 92, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 57, 32590, 17, 11, 513, 828, 15690, 90, 43879, 2414, 11, 352, 92, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 37, 87, 32590, 17, 11, 532, 17, 11, 532, 17, 828, 7913, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 37, 88, 32590, 17, 11, 532, 17, 11, 532, 17, 828, 7913, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 37, 89, 32590, 17, 11, 532, 17, 11, 532, 17, 828, 7913, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 4929, 304, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1395, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 84, 11, 1058, 85, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 575, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 84, 11, 1058, 85, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1168, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 84, 11, 1058, 85, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 87, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 88, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 89, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 628, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 514, 796, 5164, 17257, 7, 84, 62, 1084, 11, 334, 62, 9806, 11, 399, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1988, 41052, 70, 11, 334, 3712, 14993, 17257, 8, 796, 308, 12195, 84, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1988, 41052, 70, 11, 334, 3712, 15057, 8, 796, 308, 7, 84, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 3691, 796, 2488, 18206, 357, 14993, 17257, 7, 39504, 16763, 8367, 62, 16763, 85, 62, 1084, 11, 720, 385, 36911, 5415, 16763, 8367, 62, 16763, 85, 62, 9806, 11, 720, 385, 36911, 720, 45, 4008, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2198, 7, 84, 11, 410, 11, 277, 8, 796, 2488, 18206, 16763, 8367, 62, 16763, 85, 62, 1084, 11, 720, 84, 8, 19841, 720, 85, 11405, 720, 8367, 62, 16763, 85, 62, 9806, 11, 720, 84, 8, 18189, 720, 85, 5633, 720, 69, 16763, 84, 11, 720, 85, 8, 1058, 11013, 45, 8, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1988, 7, 70, 8, 796, 2198, 12195, 385, 3256, 3691, 11, 308, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 16, 796, 2488, 18206, 7198, 8367, 16763, 55, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 16, 796, 2488, 18206, 7198, 8367, 16763, 56, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 16, 796, 2488, 18206, 7198, 8367, 16763, 57, 4008, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1441, 2488, 18206, 16763, 34960, 62, 439, 16763, 87, 16, 11, 720, 88, 16, 11, 720, 89, 16, 11, 720, 37, 87, 11, 720, 37, 88, 11, 720, 37, 89, 11, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 5288, 7, 24455, 7, 0, 271, 12647, 11, 720, 87, 16, 36911, 5415, 7, 24455, 7, 0, 271, 12647, 11, 720, 87, 16, 36911, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 5288, 7, 24455, 7, 0, 271, 12647, 11, 720, 88, 16, 36911, 5415, 7, 24455, 7, 0, 271, 12647, 11, 720, 88, 16, 36911, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 5288, 7, 24455, 7, 0, 271, 12647, 11, 720, 89, 16, 36911, 5415, 7, 24455, 7, 0, 271, 12647, 11, 720, 89, 16, 36911, 720, 43337, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2073, 220, 1303, 220, 10221, 2602, 25947, 69, 7, 87, 11, 88, 8, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 87, 796, 376, 88, 796, 376, 89, 796, 45434, 1, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1949, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 62, 1084, 796, 21136, 62, 22510, 7, 87, 62, 1084, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 62, 9806, 796, 21136, 62, 22510, 7, 87, 62, 9806, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 62, 1084, 796, 21136, 62, 8818, 7, 88, 62, 1084, 11, 1058, 87, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 62, 9806, 796, 21136, 62, 8818, 7, 88, 62, 9806, 11, 1058, 87, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 62, 1084, 796, 21136, 62, 8818, 7, 89, 62, 1084, 11, 1058, 87, 11, 1058, 88, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 62, 9806, 796, 21136, 62, 8818, 7, 89, 62, 9806, 11, 1058, 87, 11, 1058, 88, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 87, 796, 21136, 62, 8818, 7, 37, 16, 11, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 88, 796, 21136, 62, 8818, 7, 37, 17, 11, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 89, 796, 21136, 62, 8818, 7, 37, 18, 11, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 37, 87, 32590, 17, 11, 532, 17, 11, 532, 17, 828, 7913, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 37, 88, 32590, 17, 11, 532, 17, 11, 532, 17, 828, 7913, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2488, 18206, 357, 9160, 16763, 37, 89, 32590, 17, 11, 532, 17, 11, 532, 17, 828, 7913, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 4929, 304, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 62, 1084, 796, 532, 17, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 62, 1084, 796, 21136, 62, 8818, 7203, 12, 17, 1600, 1058, 87, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 62, 1084, 796, 21136, 62, 8818, 7203, 12, 17, 1600, 1058, 87, 11, 1058, 88, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 62, 9806, 796, 362, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 62, 9806, 796, 21136, 62, 8818, 7203, 17, 1600, 1058, 87, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 62, 9806, 796, 21136, 62, 8818, 7203, 17, 1600, 1058, 87, 11, 1058, 88, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 87, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 88, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 376, 89, 796, 21136, 62, 8818, 7203, 15, 1600, 1058, 87, 11, 1058, 88, 11, 1058, 89, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 886, 628, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 611, 3991, 220, 1303, 7, 87, 62, 1084, 1875, 2124, 62, 9806, 8, 930, 357, 88, 62, 1084, 1875, 331, 62, 9806, 8, 930, 357, 89, 62, 1084, 1875, 1976, 62, 9806, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1441, 28114, 7, 42029, 7, 26, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 796, 685, 15, 4357, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 796, 685, 15, 4357, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1976, 796, 16410, 15, 4357, 685, 15, 11907, 4008, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2073, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 2124, 82, 796, 5164, 17257, 7, 87, 62, 1084, 11, 2124, 62, 9806, 11, 399, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1988, 17, 41052, 70, 3712, 22203, 11, 2124, 3712, 14993, 17257, 90, 43879, 2414, 30072, 796, 308, 12195, 87, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 1988, 17, 41052, 70, 3712, 22203, 11, 2124, 3712, 15057, 8, 796, 308, 7, 87, 8, 198, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 220, 331, 82, 796, 2488, 18206, 357, 14993, 17257, 7, 39504, 16763, 8367, 17, 62, 16763, 88, 62, 1084, 11, 720, 34223, 36911, 5415, 16763, 8367, 17, 62, 16763, 88, 62, 9806, 11, 720, 34223, 36911, 720, 45, 4008, 628, 220, 220, 220, 220, 220, 220, 220, 220, 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1.663592
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using SigmaRidgeRegression using Test using Random import StatsBase ar1_design = BlockCovarianceDesign([ AR1Design(;ρ=0.8), AR1Design(;ρ=0.5)]) id_design = BlockCovarianceDesign([ IdentityCovarianceDesign(), IdentityCovarianceDesign()]) grp1 = GroupedFeatures([2000,4000]) grp2 = GroupedFeatures([800,500]) for grp in [grp1; grp2] for _design in [ar1_design; id_design] _design = set_groups(_design, grp) _n = 2000 _γs = grp.ps ./ _n _λs = [2.0; 0.4] _αs = [1.0; 7.0] theory_risk = @show SigmaRidgeRegression.risk_formula(spectrum.(_design.blocks), _γs, _αs, _λs) _ridge_sim = GroupRidgeSimulationSettings(; groups=grp, ntrain=_n, ntest=20_000, Σ=_design, response_model=RandomLinearResponseModel(; αs=_αs, grp=grp), ) Random.seed!(1) _sim_res = simulate(_ridge_sim) _X_train = _sim_res.X[_sim_res.resampling_idx[1][1],:] _Y_train = _sim_res.Y[_sim_res.resampling_idx[1][1]] _X_test = _sim_res.X[_sim_res.resampling_idx[1][2],:] _Y_test = _sim_res.Y[_sim_res.resampling_idx[1][2]] ridge_risk = mse_ridge( StatsBase.fit( MultiGroupRidgeRegressor(; groups=grp, λs=_λs, center=false, scale=false), _X_train, _Y_train, grp, ), _X_test, _Y_test, ) @test ridge_risk ≈ theory_risk atol =1.0 end end
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1.789354
883
""" AbstractLattice Contains information about a crystal lattice. """ abstract type AbstractLattice end """ RealLattice{N} Describes an N-dimensional real space crystal lattice, with an associated primitive and conventional lattice. These lattices may be the same depending on the lattice type. """ struct RealLattice{N} <: AbstractLattice # Primitive and conventional lattice vectors are stored together prim::SVector{N,SVector{N,Float64}} conv::SVector{N,SVector{N,Float64}} end # TODO: Implement lattice checking and conversion # Some of this functionality might already be present in Crystalline.jl # However, we need to be able to recognize primitive lattices with their own unique conditions """ nuniqlen(basis::AbstractVector{<:AbstractVector{<:Real}}) -> Int Returns the number of vectors that are the same length. """ function nuniqlen(basis::AbstractVector{<:AbstractVector{<:Real}}) # unique!() does better than unique() here (per @btime) return length(unique!(norm.(basis))) end # Same thing for matrices nuniqlen(basis::AbstractMatrix{<:Real}) = nuniqlen(_tovectors(basis)) """ northog(basis::AbstractVector{<:AbstractVector{<:Real}}) -> Int Returns the number of pairs of orthogonal vectors. """ function northog(basis::AbstractVector{<:AbstractVector{<:Real}}) # FIXME: This doesn't work for arbitrary dimensions # It needs to use the upper portion of the dot product matrix return count(iszero, dot.(basis, basis[circshift(1:length(basis), 1)])) end northog(basis::AbstractMatrix{<:Real}) = northog(_tovectors(basis)) # TODO: Write a number of tests for checking if lattices meet certain criteria #= Criteria for primitive unit cells in 3 dimensions: aP: 6 parameters (a, b, c, α, β, γ) mP: 4 parameters (a, b, c, β), α = γ = 90° mS: 4 parameters (a, c, α, γ), a = b, α = β oP: 3 parameters (a, b, c), α = β = γ = 90° oS: 3 parameters (a, c, γ), a = b, α = β = 90° oI: 3 parameters (a, α, γ), a = b = c, |cos(α)| + |cos(β)| + |cos(γ)| = 1 oF: 3 parameters (a, b, c), sin(α)/a = sin(β)/b = sin(γ)/c, α + β + γ = 180° 3 parameters (a, c, γ), [forgot the rest of this alternate test] tP: 2 parameters (a, c), a = b, α = β = γ = 90° tI: 2 parameters (a, α), a = b = c, |cos(α)| + |cos(β)| + |cos(γ)| = 1 hP: 2 parameters (a, c), a = b, α = β = 90°, γ = 120° hR: 2 parameters (a, α), a = b = c, α = β = γ cP: 1 parameter (a), a = b = c, α = β = γ = 90° cI: 1 parameter (a), a = b = c, α = β = γ = arccos(-1/3)° cF: 1 parameter (a), a = b = c, α = β = γ = 60° Rules that need to be checked: Number of unique lengths Number of orthogonal vectors Number of unique angles Cosine rule: |cos(α)| + |cos(β)| + |cos(γ)| = 1 Sine rule: sin(α)/a = sin(β)/b = sin(γ)/c, α + β + γ = 180° The last three are probably going to be trickier to implement, or at the very least there might be some unintuitive linear algebra tricks to make those checks happen faster. =# # TODO: what are the crtieria for a "good" lattice basis? # Potentially worth looking at the Niggli reduction algorithm to do this # TODO: Tools for working with reciprocal space lattices
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2.726039
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# # Singular Integrals # This example shows how to use the `Integration` module for computing # quadrature rules for functions with point singularities (such as those # appearing in the numerical discretization of boundary integral equations). # ## Change of variables # The first set of *tricks* revolve a round a simple change of variables. We # focus first on the one-dimensional case, where we wish to integrate ```math \int_0^1 f(x) dx, ``` # and where the function ``f`` can have an integrable singularity at using WaveProp.Geometry using WaveProp.Integration using WaveProp.Integration using QuadGK f = (x) -> x==0 ? 0.0 : log(abs(x))*cos(x) I,_ = quadgk(f,0,1,rtol=1e-16) rows = GaussLegendre.([5,10,20,40,80]) cols = [identity,IMT{1,2}(),Kress{8}(), Window{1,1,7}()] ee = [] for qstd in rows for shandler in cols q = SingularQuadratureRule(qstd,shandler) Is = integrate(f,q) er = abs(I-Is) push!(ee,er) end end using NamedArrays ee = reshape(ee,length(cols),length(rows)) |> transpose |> NamedArray setnames!(ee,string.(rows),1) setnames!(ee,string.(cols),2) setdimnames!(ee,["Base quadrature","Singularity handler"]) show(ee) # ## # using Plots # qstd = GaussLegendre(10) # x̂,ŵ = qstd() # cols = [IMT{1,2}(),Kress{8}(), Window{0.5,1,7}()] # fig = plot() # for shandler in cols # phi = shandler.(x̂) # phip = [jacobian(shandler,x)[1] for x in x̂] # plot!(fig,x̂,f.(phi) .* phip,label=string(shandler),m=:x) # end # display(fig)
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struct Acronym word::String components::Vector{Union{String, Nothing}} nvals::Vector{Int} end struct AcronymFamily word::String n_max::Int components::Matrix{Vector{String}} end Base.show(io::IO, af::AcronymFamily) = print(io, typeof(af), "(\"", af.word, "\", ", af.n_max, ", ...)") function _family_traces(af::AcronymFamily) max_n, l = size(af.components) a = [Vector{Tuple{Int, Int}}[] for _ in af.components] for i in l:-1:1, n in 1:max_n n > 1 && isempty(af.components[n, i]) && continue # No components ind = (i, n) next = i + n if next == l + 1 # Last push!(a[n, i], [ind]) elseif next <= l for nexttraces in a[:, next] for nexttrace in nexttraces push!(a[n, i], vcat(ind, nexttrace)) end end end end return vcat(a[:, 1]...) end function acronyms(af::AcronymFamily, trace::AbstractVector{NTuple{2, Int}}) comp_lists = [af.components[n, i] for (i, n) in trace] nvals = last.(trace) comps_iter = Iterators.product((isempty(c) ? [nothing] : c for c in comp_lists)...) return (Acronym(af.word, collect(comp), nvals) for comp in comps_iter) end acronyms(af::AcronymFamily) = Iterators.flatten(acronyms(af, trace) for trace in _family_traces(af)) function generate_acronyms(word::String, max_n::Int, prefix_map::Dict) word = lowercase(word) l = length(word) components = Matrix{Vector{String}}(undef, max_n, l) for i in 1:l for j in 1:max_n if i + j - 1 > l components[j, i] = String[] else prefix = word[i:(i + j - 1)] components[j, i] = get(prefix_map, prefix, String[]) end end end return AcronymFamily(word, max_n, components) end
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2.015528
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module VoronoiCells # We do not compile # 1. VoronoiDelaunay is not compiled. # 2. VoronoiCells itself loads in about 100ms include("voronoi_cells.jl") include("store_cells.jl") end # module
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# breadth first search function bfs(goal, start) reset_timer!(to::TimerOutput) node = createtree(start) if node.state == goal return node end frontier = [node] reached = [node.state] while !isempty(frontier) @timeit to "Moves" acts = moves(node.state) @timeit to "Pop" node = popfirst!(frontier) @timeit to "Expand" states = expansion(node.state) for (currentstate, currentaction) in zip(states, acts) if currentstate == goal sovle = addnode(currentaction, node, currentstate) displaysolution(sovle) return sovle end if !in(currentstate, reached) @timeit to "Node Creation" currentnode = addnode(currentaction, node, currentstate) @timeit to "Push" push!(frontier, currentnode) end end end println("No solutions found!"^10) return nothing end
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push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch2.dat") include("../../Basin.jl") pop!(ARGS) #= push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch3.dat") include("../../Basin.jl") pop!(ARGS) push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch3.dat") include("../../Basin.jl") pop!(ARGS) push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch4.dat") include("../../Basin.jl") pop!(ARGS) push!(ARGS, "../../input_files/dynamic/basin_switching/8GPa/switch5.dat") include("../../Basin.jl") pop!(ARGS) =#
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using Base: Broadcast.DefaultArrayStyle, AbstractUnitRange _broadcasted(style, f, x, r::AbstractRange) = invoke(Base.Broadcast.broadcasted, Tuple{typeof(style),typeof(f),Any,typeof(r)}, style, f, x, r) _broadcasted(style, f, r::AbstractRange, x) = invoke(Base.Broadcast.broadcasted, Tuple{typeof(style),typeof(f),typeof(r),Any}, style, f, r, x) for f in (+, -, *, /, \), R in (AbstractRange, AbstractUnitRange, StepRangeLen) @eval begin Base.Broadcast.broadcasted(style::DefaultArrayStyle{1}, ::typeof($f), x::Measurement, r::$R) = _broadcasted(style, $f, x, r) Base.Broadcast.broadcasted(style::DefaultArrayStyle{1}, ::typeof($f), r::$R, x::Measurement) = _broadcasted(style, $f, r, x) end end
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# Testing the Small Demo # Copyright (c) 2015 Harold Soh # based on MATLAB code by Mark Schmidt # For more details, see: http://www.cs.ubc.ca/~schmidtm/Software/UGM/small.html include("../src/UGM.jl") using UGM using Base.Test include("testUtils.jl") # ====================================== # Simple Independent Node Test # ====================================== srand(0) nodepot = [ 1 3; 9 1; 1 3; 9 1 ] nsamples = 100; samples = zeros(4, nsamples) for i = 1:4 for s = 1:nsamples samples[i,s] = sampleDiscrete(nodepot[i,:]/sum(nodepot[i,:])); end end sum_samples = sum(samples,2) println("Sum Samples: ", sum_samples') gold_result = [172; 107; 168; 110] # at seed 0 @test all(sum_samples .== gold_result) print("Independent Nodes Test: ") printPassed() # ====================================== # Set up Dependent Nodes # ====================================== nnodes = 4 nstates = 2 edgelist = [ 1 2; 2 1; 2 3; 3 2; 3 4; 4 3] # Make Edge Structure es = EdgeStruct(edgelist = edgelist, nstates = nstates, maxiter = 25) # edgestruct tests @test es.edgeends == [1 2; 2 3; 3 4] @test es.edgedict[1] == Set([2]) @test es.edgedict[2] == Set([1,3]) @test es.edgedict[3] == Set([2,4]) @test es.edgedict[4] == Set([3]) @test es.nnodes == 4 @test es.nedges == 3 @test all(es.nstates .== [2.0; 2.0; 2.0; 2.0]) @test es.maxiter == 25 print("Edge Structure Test: ") printPassed() # Node potentials nodepot = [1 3; 9 1; 1 3; 9 1] # Edge potentials maxstate = maximum(es.nstates); edgepot = zeros( int(maxstate), int(maxstate), int(es.nedges)); for e = 1:es.nedges edgepot[:,:,e] = [2 1 ; 1 2]; end # ====================================== # Decoding # ====================================== optdecoding = decodeExact(nodepot,edgepot,es) println("Optimal Decoding: ", optdecoding') @test all(optdecoding .== [2.0; 1.0; 1.0; 1.0]) print("Exact Decoding Test: ") printPassed() # ====================================== # Inference # ====================================== nodebel,edgebel,logZ,Z = inferExact(nodepot,edgepot,es) @test nodebel == [0.3596306068601583 0.6403693931398416 0.8430079155672823 0.15699208443271767 0.4862796833773087 0.5137203166226912 0.8810026385224274 0.11899736147757256] @test edgebel[:,:,1] == [0.33720316622691293 0.022427440633245383 0.5058047493403693 0.1345646437994723] @test edgebel[:,:,2] == [0.45118733509234826 0.391820580474934 0.03509234828496042 0.12189973614775726] @test edgebel[:,:,3] == [0.46068601583113455 0.02559366754617414 0.4203166226912929 0.09340369393139841] @test_approx_eq_eps(logZ, 8.240121298, 1e-8) print("Exact Inference Test: ") printPassed() # ====================================== # Sampling Test # ====================================== es.maxiter = 100 samples = sampleExact(nodepot,edgepot,es) @test all(samples[1,:] .== [2.0 1.0 2.0 2.0]) @test all(samples[4,:] .== [2.0 2.0 2.0 1.0]) @test all(samples[100,:] .== [2.0 1.0 2.0 1.0]) print("Exact Sampling Test: ") printPassed() # println(samples) # using Gadfly # spy(samples)
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using DelimitedFiles function solve(input) raw = vcat(readdlm(input,Int16)...) p1 = process(copy(raw),aggregate) @show p1 p2 = process(copy(raw),findRootValue) @show p2 end function process(list, f) numChildren = popfirst!(list) numMeta = popfirst!(list) return f(ntimes(numChildren,list,f), splice!(list,1:numMeta)) end function ntimes(n,list, f) result = Int16[] for i in 1:n push!(result,process(list,f)) end return result end function aggregate(child,metadata) return sum(child) + sum(metadata) end function childValue((child,value),index) if length(child)>index value+=child[index+1] else value+= 0 end return (child,value) end function findRootValue(child,metadata) pushfirst!(child,0) if length(child) == 1 return sum(metadata) else return reduce(childValue,metadata,init=(child,0))[2] end end solve("input.txt")
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2.367246
403
function runSimulation(p::precipParam) doInitialPrinting(p) if p.runID == 1 mainDriver(p::precipParam) elseif p.runID == 2 pureDiffusionOneChemicalTestDriver(p) elseif p.runID == 3 pureAdvectionOneChemicalTestDriver(p) elseif p.runID == 4 AdvectionDiffusionOneChemicalTestDriver(p) elseif p.runID == 5 MultiphaseBrinkmanTestDriver(p) elseif p.runID == 6 DiffusionAndReactionTwoChemicalTestDriver(p) elseif p.runID == 7 pureReactionTestDriver(p) else println("runID of ",p.runID," not recognized.") println("runID 1-7 required") end nothing end function mainDriver(p::precipParam) timer, mesh, soln, tsoln, prob = initializeData(p) # initial brinkman mpbparam = BrinkmanMPParam(1.0,mpbFriction(soln.θf.u),soln.θf.u) sol = solve(prob.fluid,mesh.fMesh,mpbparam) tsoln.fluid.u = sol.u tsoln.fluid.v = sol.v tsoln.fluid.p = sol.p intializeTimeSteppingTimer!(timer) doPrinting!(timer,p,mesh,tsoln) while timer.simulationTime < timer.finalTime #Ninterp = 80 #interpVals = zeros(Ninterp,6) #surf = mySurface([0.5,0.37],[0.5,-0.37]) # reaction computeReaction!(p,tsoln) soln.θs.u = tsoln.θs.u soln.θf.u = tsoln.θf.u θfn = normalize_thetaf(tsoln.θf.u) peAnormalized = p.PeA./(θfn .+ 0.0 .*(1 .- θfn)) # 0.0 -> 0.5 peBnormalized = p.PeB./(θfn .+ 0.0 .*(1 .- θfn)) # 0.0 -> 0.25 ψAParam = AdvDiffParam(tsoln.fluid.u,tsoln.fluid.v,peAnormalized) ψBParam = AdvDiffParam(tsoln.fluid.u,tsoln.fluid.v,peBnormalized) ψCParam = AdvDiffParam(tsoln.fluid.u,tsoln.fluid.v,p.PeC./θfn) # advection-diffusion M = generateMassMatrixWScalar(mesh.sMesh,θfn) StiffA = GenerateSystem(mesh.sMesh,prob.ψA,ψAParam) ApplyBC!(StiffA,mesh.sMesh,prob.ψA,ψAParam,prob.ψA.OperatorType) StiffB = GenerateSystem(mesh.sMesh,prob.ψB,ψBParam) ApplyBC!(StiffB,mesh.sMesh,prob.ψB,ψBParam,prob.ψB.OperatorType) StiffC = GenerateSystem(mesh.sMesh,prob.ψC,ψCParam) ApplyBC!(StiffC,mesh.sMesh,prob.ψC,ψCParam,prob.ψC.OperatorType) if timer.stepIndex < 5 soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=:backwardeuler) soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=:backwardeuler) soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=:backwardeuler) else soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=p.integrator) soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=p.integrator) soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=p.integrator) end # scrub scalars so they don't go below zero. for i=1:length(soln.ψA.u) if soln.ψA.u[i] < 0 soln.ψA.u[i] = 0.0 end if soln.ψB.u[i] < 0 soln.ψB.u[i] = 0.0 end if soln.ψC.u[i] < 0 soln.ψC.u[i] = 0.0 end end # brinkman # normalize thetaf mpbparam = BrinkmanMPParam(1.0,mpbFriction(θfn),θfn) sol = solve(prob.fluid,mesh.fMesh,mpbparam) soln.fluid.u = sol.u soln.fluid.v = sol.v soln.fluid.p = sol.p # inteprolate values #xvals = zeros(length(mesh.sMesh.xy)) #yvals = zeros(length(mesh.sMesh.xy)) #for i=1:length(mesh.sMesh.xy) # xvals[i] = mesh.sMesh.xy[i].x # yvals[i] = mesh.sMesh.xy[i].y #end #vmag = sqrt.(soln.fluid.u.^2 + soln.fluid.v.^2) #interpVals[:,1] = SurfaceInterp(mesh.sMesh,xvals,surf,Ninterp-1) #interpVals[:,2] = SurfaceInterp(mesh.sMesh,yvals,surf,Ninterp-1) #interpVals[:,3] = SurfaceInterp(mesh.sMesh,soln.ψA.u,surf,Ninterp-1) #interpVals[:,4] = SurfaceInterp(mesh.sMesh,soln.ψB.u,surf,Ninterp-1) #interpVals[:,5] = SurfaceInterp(mesh.sMesh,soln.θs.u,surf,Ninterp-1) #interpVals[:,6] = SurfaceInterp(mesh.fMesh,vmag,surf,Ninterp-1) tsoln = deepcopy(soln) if isPrintIndex(timer) # save interpolated values #savefile = string(p.SaveFolder,"/interpVals_",timer.printIndex,".jld2") #save(savefile, "time", timer.simulationTime, "interpVals", interpVals) # ordinary printing doPrinting!(timer,p,mesh,soln) end updateSimulationTime!(timer) updateStepIndex!(timer) end printSimulationFinishedMessage(timer) nothing end function normalize_thetaf(θf::Vector{T}) where T<:Real N=length(θf) θf_normalized = zeros(T,N) TOL = 0.1 for i=1:N if θf[i] < TOL θf_normalized[i] = TOL else θf_normalized[i] = θf[i] end end return θf_normalized end function pureDiffusionOneChemicalTestDriver(p::precipParam) timer, mesh, soln, tsoln, prob = initializeData(p) ψAParam = PoissonParam(p.κA) for i=1:length(soln.θf.u) soln.θf.u[i] = 0.1 end M = generateMassMatrixWScalar(mesh.sMesh,soln.θf.u) StiffA = GenerateSystem(mesh.sMesh,prob.ψA,ψAParam) ApplyBC!(StiffA,mesh.sMesh,prob.ψA,ψAParam,prob.ψA.OperatorType) intializeTimeSteppingTimer!(timer) doPrinting!(timer,p,mesh,soln) while timer.simulationTime < timer.finalTime if timer.stepIndex < 5 soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=:backwardeuler) else soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=p.integrator) end tsoln = deepcopy(soln) if isPrintIndex(timer) doPrinting!(timer,p,mesh,soln) end updateSimulationTime!(timer) updateStepIndex!(timer) end printSimulationFinishedMessage(timer) nothing end function pureAdvectionOneChemicalTestDriver(p::precipParam) println("pure advection test driver isn't programmed yet") nothing end function AdvectionDiffusionOneChemicalTestDriver(p::precipParam) println("advection-diffusion test driver isn't programmed yet") nothing end function MultiphaseBrinkmanTestDriver(p::precipParam) function computeNorms(N) start = time() # load mesh mesh = squareMeshFluid([-2,2,-1,1],N) α1(x,y) = 1.0 α2(x,y) = 0.5+0.4*cos(3*x*y) α3(x,y) = 0.5+0.4*sin(7*x*y) xm = [i.x for i in mesh.xy] ym = [i.y for i in mesh.xy] α1arr = [α1(xm[i],ym[i]) for i=1:length(mesh.xy)] α2arr = [α2(xm[i],ym[i]) for i=1:length(mesh.xy)] α3arr = [α3(xm[i],ym[i]) for i=1:length(mesh.xy)] param = BrinkmanMPParam(α1arr,α2arr,α3arr) OperatorType = :BrinkmanMP2D dNodes = Dirichlet(:left,:top,:bottom,:right) Nodes = [dNodes] u(x,y) = -x^4*y^2 v(x,y) = 4x^3*y^3/3 dUBCf = Dirichlet( (x,y) -> u(x,y) ) dVBCf = Dirichlet( (x,y) -> v(x,y) ) d2dudx(x,y) = -12*x^2*y^2; d2dudy(x,y) = -2*x^4 d2dvdx(x,y) = 8*x*y^3; d2dvdy(x,y) = 8*x^3*y lapu(x,y) = d2dudx(x,y) + d2dudy(x,y) lapv(x,y) = d2dvdx(x,y) + d2dvdy(x,y) dpdx(x,y) = 3*x^2*y^3; dpdy(x,y) = 3*x^3*y^2 Fx(x,y) = -α1(x,y)*lapu(x,y) + α2(x,y)*u(x,y) + α3(x,y)*dpdx(x,y) Fy(x,y) = -α1(x,y)*lapv(x,y) + α2(x,y)*v(x,y) + α3(x,y)*dpdy(x,y) ffx = Forcing(Fx) ffy = Forcing(Fy) bcfun = [dUBCf,dVBCf,ffx,ffy] prob = Problem(mesh,Nodes,bcfun,OperatorType) sol = solve(prob,mesh,param) elapsed = time()-start # compute condition number of operator matrix #LinOp = GenerateSystem(mesh,prob,param) #ApplyBC!(LinOp,mesh,prob,param,OperatorType) #κ = cond(Array(LinOp.Op),2) κ = 0.5 # compute mesh h h = hCalc(mesh) # generate exact solution Uexact(x,y) = dUBCf.f(x,y) Vexact(x,y) = dVBCf.f(x,y) Pexact(x,y) = x^3*y^3 UexactArr = [Uexact.(mesh.xy[i].x,mesh.xy[i].y) for i=1:length(mesh.xy)] VexactArr = [Vexact.(mesh.xy[i].x,mesh.xy[i].y) for i=1:length(mesh.xy)] PexactArr = [Pexact.(mesh.xyp[i].x,mesh.xyp[i].y) for i=1:length(mesh.xyp)] # compute difference velErr = sqrt.((sol.u - UexactArr).^2 + (sol.v -VexactArr).^2) presErr = sol.p - PexactArr # compute Li norm L1v = DomainNorm(mesh.xy,mesh.cm,velErr;normID="1") L2v = DomainNorm(mesh.xy,mesh.cm,velErr;normID="2") Linfv = DomainNorm(mesh.xy,mesh.cm,velErr;normID="Inf") L1p = DomainNorm(mesh.xyp,mesh.cmp,presErr;normID="1") L2p = DomainNorm(mesh.xyp,mesh.cmp,presErr;normID="2") Linfp = DomainNorm(mesh.xyp,mesh.cmp,presErr;normID="Inf") # plot solution sD = ScalarData(sol.p,α1arr,α2arr,α3arr) sN = ScalarNames("pressure","alpha_1","alpha_2","alpha_3") vD = VectorData([sol.u,sol.v]) vN = VectorNames("velocity") fn = Path("solution_var") vtksave(mesh,sD,sN,vD,vN,fn) # plot solution sD = ScalarData(PexactArr) sN = ScalarNames("pressure") vD = VectorData([UexactArr,VexactArr]) vN = VectorNames("velocity") fn = Path("exact_var") vtksave(mesh,sD,sN,vD,vN,fn) return κ,h,L1v,L2v,Linfv,L1p,L2p,Linfp,elapsed end Narr = [4,4,8,16,32,64]#,96] N = length(Narr) harr = zeros(N) L1arrV = zeros(N) L2arrV = zeros(N) LInfarrV = zeros(N) L1arrP = zeros(N) L2arrP = zeros(N) LInfarrP = zeros(N) timearr = zeros(N) κarr = zeros(N) for i=1:N n = Narr[i] κarr[i],harr[i],L1arrV[i],L2arrV[i],LInfarrV[i], L1arrP[i],L2arrP[i],LInfarrP[i],timearr[i] = computeNorms(n) println("completed N=$(n)") end κarr = κarr[2:end] harr = harr[2:end] L1arrV = L1arrV[2:end] L2arrV = L2arrV[2:end] LInfarrV = LInfarrV[2:end] L1arrP = L1arrP[2:end] L2arrP = L2arrP[2:end] LInfarrP = LInfarrP[2:end] timearr = timearr[2:end] # export output to *.jld file run(`mkdir -p data`) save("data/TEMP_mpb2D_validation.jld", "harr",harr, "VL1arr", L1arrV, "VL2arr", L2arrV, "VLInfarr",LInfarrV, "PL1arr", L1arrP, "PL2arr", L2arrP, "PLInfarr",LInfarrP, "timearr",timearr, "κarr",κarr) nothing end function DiffusionAndReactionTwoChemicalTestDriver(p::precipParam) timer, mesh, soln, tsoln, prob = initializeData(p) ψAParam = PoissonParam(p.κA) ψBParam = PoissonParam(p.κB) ψCParam = PoissonParam(p.κC) M = generateMassMatrix(mesh.sMesh) StiffA = GenerateSystem(mesh.sMesh,prob.ψA,ψAParam) ApplyBC!(StiffA,mesh.sMesh,prob.ψA,ψAParam,prob.ψA.OperatorType) StiffB = GenerateSystem(mesh.sMesh,prob.ψB,ψBParam) ApplyBC!(StiffB,mesh.sMesh,prob.ψB,ψBParam,prob.ψB.OperatorType) StiffC = GenerateSystem(mesh.sMesh,prob.ψC,ψCParam) ApplyBC!(StiffC,mesh.sMesh,prob.ψC,ψCParam,prob.ψC.OperatorType) intializeTimeSteppingTimer!(timer) doPrinting!(timer,p,mesh,soln) while timer.simulationTime < timer.finalTime println("i1=",timer.stepIndex," ",computeTotalMass(p,mesh.sMesh,soln)) if timer.stepIndex < 5 soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=:backwardeuler) soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=:backwardeuler) soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=:backwardeuler) else soln.ψA.u = updateChemical(M,StiffA,tsoln.ψA.u,p;solver=p.integrator) soln.ψB.u = updateChemical(M,StiffB,tsoln.ψB.u,p;solver=p.integrator) soln.ψC.u = updateChemical(M,StiffC,tsoln.ψC.u,p;solver=p.integrator) end println("i2=",timer.stepIndex," ",computeTotalMass(p,mesh.sMesh,soln)) computeReaction!(p,soln) println("i3=",timer.stepIndex," ",computeTotalMass(p,mesh.sMesh,soln)) println() tsoln = deepcopy(soln) if isPrintIndex(timer) doPrinting!(timer,p,mesh,soln) end updateSimulationTime!(timer) updateStepIndex!(timer) end printSimulationFinishedMessage(timer) nothing end function pureReactionTestDriver(p::precipParam) timer, mesh, soln, tsoln, prob = initializeData(p) randomizeScalarSolutions!(soln) intializeTimeSteppingTimer!(timer) doPrinting!(timer,p,mesh,soln) while timer.simulationTime < timer.finalTime computeReaction!(p,soln) if isPrintIndex(timer) doPrinting!(timer,p,mesh,soln) end tsoln = deepcopy(soln) # step time updateSimulationTime!(timer) updateStepIndex!(timer) end printSimulationFinishedMessage(timer) nothing end function initializeData(p::precipParam) timer = initializeTimer(p) mesh = initializeMeshes(p) soln = initializeSolution(p) tsoln = initializeSolution(p) prob = defineProblems(p,mesh) return timer, mesh, soln, tsoln, prob end function mpbFriction(θf::Vector{T}) where T<:Real N = length(θf) friction = zeros(N) K=0.5 n=2 ξstar = 30.0 θstar = 0.5 h = 1000.0#computeH(ξstar,θstar,K,n) for i=1:N friction[i] = h*frictionKernel(θf[i],K,n) end return friction end function frictionKernel(θf,K,n) θs = (1.0-θf) return θs^n/(K^n + θs^n) end function computeH(ξstar,θstar,K,n) return ξstar/frictionKernel(θstar,K,n) end
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1.887396
6,847
using Maker using Base.Test using Glob x = [ 3.14159 6.28319 9.42478 12.5664 15.708 18.8496 21.9911 25.1327 28.2743 ] writecsv("in1.csv", x) writecsv("in2.csv", 3x) inputs = glob("in*.csv") outputs = ["$(splitext(f)[1])-out.csv" for f in inputs] for i in eachindex(inputs) inp = inputs[i] Maker.file(inp) dest = outputs[i] Maker.file(dest, inp) do out = 2 * readcsv(inp, skipstart = 1) writecsv(dest, out) end end Maker.task("default", outputs) Maker.clean(outputs) Maker.task("clean2") do # another way to clean println("CLEAN2") for fn in glob("in*-out.csv") Maker.rm(fn) end end Maker.task("cleanall") do # another way to clean for fn in glob("in*.csv") Maker.rm(fn) end end make() @test isfile(outputs[1]) @test isfile(outputs[2]) make("clean") @test !isfile(outputs[1]) @test !isfile(outputs[2]) make([]) # the [] are to test this call method @test isfile(outputs[1]) @test isfile(outputs[2]) make("clean2") @test !isfile(outputs[1]) @test !isfile(outputs[2]) make("cleanall")
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2.136015
522
@safetestset gray_code_symmetry = "Gray code symmetry" begin using BijectiveHilbert # for i in 0:10 # println(lpad(i, 3, " "), " ", lpad(string(BijectiveHilbert.brgc(i), base = 2), 8, "0")) # end # Here's a test of the gray code. n = 5 for i in 0x0:(0x1 << n - 0x1) # println(BijectiveHilbert.brgc(1<<n - 1 - i), " ", BijectiveHilbert.brgc(i) ⊻ (1 << (n-1))) @test(BijectiveHilbert.brgc(1<<n - 1 - i) == BijectiveHilbert.brgc(i) ⊻ (1 << (n - 1))) end end @safetestset gray_code_single = "Gray code changes one bit" begin using BijectiveHilbert: brgc, is_power_of_two for i in 0x1:0x1000 @test is_power_of_two(brgc(i) ⊻ brgc(i + 1)) end end @safetestset brgc_own_inverse = "Gray code is own inverse" begin using BijectiveHilbert for i in 0x0:0x1000 @test(BijectiveHilbert.brgc_inv(BijectiveHilbert.brgc(i)) == i) end end @safetestset brgc_equals_naive = "Gray code matches paper description" begin using BijectiveHilbert: brgc_inv using Random rng = MersenneTwister(9719742) for T in [UInt8, UInt16, UInt32, UInt64] for trial in 1:10000 v = rand(rng, T) n = brgc_inv(Int128(v)) # The paper version is used for integers. i = brgc_inv(v) @test n == i end end end @safetestset brgc_ranks_equal = "the rank calculation is the same as the paper" begin using BijectiveHilbert: brgc_rank, brgc_rank2 using Random rng = MersenneTwister(974073242) for trial in 1:1000 n = rand(rng, 2:7) w = UInt8(rand(rng, 0:(1<<n - 1))) mask = UInt8(rand(rng, 0:(1<<n - 1))) a = brgc_rank(mask, w, n) b = brgc_rank2(mask, w, n) @test a == b end end
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# TemplateName isNull(x::TemplateName) = clang_TemplateName_isNull(x) getKind(x::TemplateName) = clang_TemplateName_getKind(x) getUnderlying(x::TemplateName) = TemplateName(clang_TemplateName_getUnderlying(x)) getNameToSubstitute(x::TemplateName) = TemplateName(clang_TemplateName_getNameToSubstitute(x)) isDependent(x::TemplateName) = clang_TemplateName_isDependent(x) isInstantiationDependent(x::TemplateName) = clang_TemplateName_isInstantiationDependent(x) containsUnexpandedParameterPack(x::TemplateName) = clang_TemplateName_containsUnexpandedParameterPack(x) dump(x::TemplateName) = clang_TemplateName_dump(x) function getTemplateName(x::TemplateSpecializationType) return TemplateName(clang_TemplateSpecializationType_getTemplateName(get_type_ptr(x))) end
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import ..UncertainValues.TheoreticalDistributionScalarValue import ..UncertainValues.UncertainScalarBinomialDistributed import ..UncertainValues.UncertainScalarBetaBinomialDistributed import ..UncertainValues: AbstractUncertainValue import Distributions.pdf import ..SamplingConstraints: SamplingConstraint, constrain function get_density(uv::AbstractUncertainValue) some_sample = resample(uv, 10000) xmin = minimum(some_sample) * 0.97 xmax = maximum(some_sample) * 1.03 step = (xmax-xmin)/300 xvals = xmin:step:xmax+step density = pdf.(uv.distribution, xvals) xvals, density ./ sum(density) end function get_density(uv::UncertainScalarBinomialDistributed) some_sample = resample(uv, 10000) xmin = minimum(some_sample) xmax = maximum(some_sample) xvals = xmin:1:xmax density = pdf.(uv.distribution, xvals) xvals, density ./ sum(density) end function get_density(uv::UncertainScalarBetaBinomialDistributed) some_sample = resample(uv, 10000) xmin = minimum(some_sample) xmax = maximum(some_sample) xvals = xmin:1:xmax density = pdf.(uv.distribution, xvals) xvals, density ./ sum(density) end @recipe function plot_theoretical(uv::TheoreticalDistributionScalarValue, density = true, n_samples = 1000) if density @series begin get_density(uv) end else @series begin label --> "" resample(uv, n_samples) end end end @recipe function plot_theoretical(uv::TheoreticalDistributionScalarValue, constraint::SamplingConstraint, density = true, n_samples = 1000) cuv = constrain(uv, constraint) if density @series begin get_density(cuv) end else @series begin label --> "" resample(cuv, n_samples) end end end
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