# Path: pybobyqa/util.py
# def sumsq(x):
#     # There are several ways to calculate sum of squares of a vector:
#     #   np.dot(x,x)
#     #   np.sum(x**2)
#     #   np.sum(np.square(x))
#     #   etc.
#     # Using the timeit routine, it seems like dot(x,x) is ~3-4x faster than other methods
#     return np.dot(x, x)
# 
# def model_value(g, H, s):
#     # Calculate model value (s^T * g + 0.5* s^T * H * s) = s^T * (gopt + 0.5 * H*s)
#     assert g.shape == s.shape, "g and s have incompatible sizes"
#     Hs = H.dot(s)
#     return np.dot(s, g + 0.5*Hs)


from math import sqrt
from .util import sumsq, model_value
import numpy as np
import warnings
    import trustregion
            continue
        else:
            break  # end outer loop and quit

    # End while True (label 100)
    return d_within_bounds(d, xopt, sl, su, xbdi), gnew


def d_within_bounds(d, xopt, sl, su, xbdi):
    # Used in TRSBOX, force d to be within bounds
    # In Fortran code, is at label 190
    xnew = np.maximum(np.minimum(xopt + d, su), sl)
    xnew[xbdi == -1] = sl[xbdi == -1]
    xnew[xbdi == 1] = su[xbdi == 1]
    d = xnew - xopt
    return d


def trsbox_geometry(xbase, c, g, H, lower, upper, Delta, use_fortran=USE_FORTRAN):
    # Given a Lagrange polynomial defined by: L(x) = c + g' * (x - xbase) + 0.5*(x-xbase)*H*(x-xbase)
    # Maximise |L(x)| in a box + trust region - that is, solve:
    #   max_x  abs(c + g' * (x - xbase) + 0.5*(x-xbase)*H*(x-xbase))
    #    s.t.  lower <= x <= upper
    #          ||x-xbase|| <= Delta
    # Setting s = x-xbase (or x = xbase + s), this is equivalent to:
    #   max_s  abs(c + g' * s + 0.5*s*H*s)
    #   s.t.   lower <= xbase + s <= upper
    #          ||s|| <= Delta
    smin, gmin, crvmin = trsbox(xbase, g, H, lower, upper, Delta, use_fortran=use_fortran)  # minimise L(x)
    smax, gmax, crvmax = trsbox(xbase, -g, -H, lower, upper, Delta, use_fortran=use_fortran)  # maximise L(x)

# Path: pybobyqa/util.py
# def sumsq(x):
#     # There are several ways to calculate sum of squares of a vector:
#     #   np.dot(x,x)
#     #   np.sum(x**2)
#     #   np.sum(np.square(x))
#     #   etc.
#     # Using the timeit routine, it seems like dot(x,x) is ~3-4x faster than other methods
#     return np.dot(x, x)
# 
# def model_value(g, H, s):
#     # Calculate model value (s^T * g + 0.5* s^T * H * s) = s^T * (gopt + 0.5 * H*s)
#     assert g.shape == s.shape, "g and s have incompatible sizes"
#     Hs = H.dot(s)
#     return np.dot(s, g + 0.5*Hs)


# Path: pybobyqa/trust_region.py
from math import sqrt
from .util import sumsq, model_value
import numpy as np
import warnings
    import trustregion

            continue
        else:
            break  # end outer loop and quit

    # End while True (label 100)
    return d_within_bounds(d, xopt, sl, su, xbdi), gnew


def d_within_bounds(d, xopt, sl, su, xbdi):
    # Used in TRSBOX, force d to be within bounds
    # In Fortran code, is at label 190
    xnew = np.maximum(np.minimum(xopt + d, su), sl)
    xnew[xbdi == -1] = sl[xbdi == -1]
    xnew[xbdi == 1] = su[xbdi == 1]
    d = xnew - xopt
    return d


def trsbox_geometry(xbase, c, g, H, lower, upper, Delta, use_fortran=USE_FORTRAN):
    # Given a Lagrange polynomial defined by: L(x) = c + g' * (x - xbase) + 0.5*(x-xbase)*H*(x-xbase)
    # Maximise |L(x)| in a box + trust region - that is, solve:
    #   max_x  abs(c + g' * (x - xbase) + 0.5*(x-xbase)*H*(x-xbase))
    #    s.t.  lower <= x <= upper
    #          ||x-xbase|| <= Delta
    # Setting s = x-xbase (or x = xbase + s), this is equivalent to:
    #   max_s  abs(c + g' * s + 0.5*s*H*s)
    #   s.t.   lower <= xbase + s <= upper
    #          ||s|| <= Delta
    smin, gmin, crvmin = trsbox(xbase, g, H, lower, upper, Delta, use_fortran=use_fortran)  # minimise L(x)
    smax, gmax, crvmax = trsbox(xbase, -g, -H, lower, upper, Delta, use_fortran=use_fortran)  # maximise L(x)

    if abs(c + model_value(g, H, smin)) >= abs(c + model_value(g, H, smax)):  # take largest abs value