# Path: pomp/spaces/biassets.py
# class TimeBiasSet(BoxSet):
#     """A set for an integration time variable that samples more-or-less
#     uniformly from the *outcome* state, given a maximum integration duration
#     and a space of controls uspace.
# 
#     It assumes the next state is obtained by the integral
#        int[0,T] f(x(t),u) dt
#     and the function f(x,u) is not degenerate.  With this assumption, the
#     the volume of the reachable set grows proportionally to T^d where d
#     is the control dimension.  Hence, the sampler samples T from the range
#     [0,tmax] according to the distribution U(0,1)^(1/d)*tmax.  In practice,
#     this places more samples toward the tail end of the integration region. 
#     """
#     def __init__(self,tmax,uspace):
#         BoxSet.__init__(self,[0],[tmax])
#         self.tmax = tmax
#         self.controlDimension = len(uspace.sample())
#         #if self.controlDimension == 1:
#         #    self.controlDimension = 2
#     def sample(self):
#         #plain time sampling
#         #return [random.uniform(0,self.tmax)]
#         #sampling from upper half
#         #return [random.uniform(self.tmax*0.5,self.tmax)]
#         #sampling with a power law bias
#         return [math.pow(random.random(),1.0/self.controlDimension)*self.tmax]


from .configurationspace import *
from .timespace import *
from .interpolators import *
from .sets import *
from .biassets import TimeBiasSet
from . import differences
import numpy as np
        pass
    def configurationSpace(self):
        """Returns the configuration space associated with this."""
        return None
    def controlSet(self,x):
        """Returns the set from which controls should be sampled"""
        raise NotImplementedError()
    def nextState(self,x,u):
        """Produce the next state after applying control u to state x"""
        raise NotImplementedError()
    def interpolator(self,x,u):
        """Returns the interpolator that goes from x to self.nextState(x,u)"""
        raise NotImplementedError()
    def connection(self,x,y):
        """Returns the sequence of controls that connects x to y, if
        applicable"""
        return None
        
    def nextState_jacobian(self,x,u):
        """If you want to use numerical optimization methods, implement
        this. It should return a pair of matrices dx_n/dx, dx_n/du.
        Subclasses can use nextState_jacobian_diff to approximate
        the Jacobian."""
        return self.nextState_jacobian_diff(x,u)
    
    def nextState_jacobian_diff(self,x,u,h=1e-4):
        Jx = differences.jacobian_forward_difference((lambda y:self.nextState(y,u)),x,h)
        Ju = differences.jacobian_forward_difference((lambda v:self.nextState(x,v)),u,h)
        return (Jx,Ju)


# Path: pomp/spaces/biassets.py
# class TimeBiasSet(BoxSet):
#     """A set for an integration time variable that samples more-or-less
#     uniformly from the *outcome* state, given a maximum integration duration
#     and a space of controls uspace.
# 
#     It assumes the next state is obtained by the integral
#        int[0,T] f(x(t),u) dt
#     and the function f(x,u) is not degenerate.  With this assumption, the
#     the volume of the reachable set grows proportionally to T^d where d
#     is the control dimension.  Hence, the sampler samples T from the range
#     [0,tmax] according to the distribution U(0,1)^(1/d)*tmax.  In practice,
#     this places more samples toward the tail end of the integration region. 
#     """
#     def __init__(self,tmax,uspace):
#         BoxSet.__init__(self,[0],[tmax])
#         self.tmax = tmax
#         self.controlDimension = len(uspace.sample())
#         #if self.controlDimension == 1:
#         #    self.controlDimension = 2
#     def sample(self):
#         #plain time sampling
#         #return [random.uniform(0,self.tmax)]
#         #sampling from upper half
#         #return [random.uniform(self.tmax*0.5,self.tmax)]
#         #sampling with a power law bias
#         return [math.pow(random.random(),1.0/self.controlDimension)*self.tmax]


# Path: pomp/spaces/controlspace.py
from .configurationspace import *
from .timespace import *
from .interpolators import *
from .sets import *
from .biassets import TimeBiasSet
from . import differences
import numpy as np

        pass
    def configurationSpace(self):
        """Returns the configuration space associated with this."""
        return None
    def controlSet(self,x):
        """Returns the set from which controls should be sampled"""
        raise NotImplementedError()
    def nextState(self,x,u):
        """Produce the next state after applying control u to state x"""
        raise NotImplementedError()
    def interpolator(self,x,u):
        """Returns the interpolator that goes from x to self.nextState(x,u)"""
        raise NotImplementedError()
    def connection(self,x,y):
        """Returns the sequence of controls that connects x to y, if
        applicable"""
        return None
        
    def nextState_jacobian(self,x,u):
        """If you want to use numerical optimization methods, implement
        this. It should return a pair of matrices dx_n/dx, dx_n/du.
        Subclasses can use nextState_jacobian_diff to approximate
        the Jacobian."""
        return self.nextState_jacobian_diff(x,u)
    
    def nextState_jacobian_diff(self,x,u,h=1e-4):
        Jx = differences.jacobian_forward_difference((lambda y:self.nextState(y,u)),x,h)
        Ju = differences.jacobian_forward_difference((lambda v:self.nextState(x,v)),u,h)
        return (Jx,Ju)


    def checkDerivatives(self,x,u,baseTol=1e-3):