def extend(self, new_left, new_right, order = 0, new_parameters = None):
"""Extends the solution to a new domain using polynomial extrapolation.
Parameters
----------
new_left : float
Location of the new left boundary point.
new_right : float
Location of the new right boundary point.
order : int
Order of the polynomial to use for extrapolation
new_parameters : castable to floating point ndarray
Value of new parameters to use.
Returns
-------
extended : Solution
Extended :class:`Solution`.
"""
new_parameters = tools.preparg(new_parameters)
if new_parameters is None:
new_parameters = self._parameters
npar = 0
if not (self._parameters is None):
npar = len(self._parameters)
bvp_solverf.bvp.bvp_extend_wrap(node_in = self._solution.shape[0],
npar_in = npar,
leftbc_in = 1, # this value doesn't matter
npts_in = len(self._mesh),
info_in = self._successIndicator,
mxnsub_in = 300, # nor does this
x_in = tools.farg(self._mesh),
y_in = tools.farg(self._solution),
parameters_in = tools.farg(self._parameters),
work_in = tools.farg(self._work),
iwork_in = tools.farg(self._iwork),
anew = new_left,
bnew = new_right,
order = order,
p = tools.farg(new_parameters),
max_num_subintervals = 300 # nor does this
)
result = self.from_arg_list(bvp_solverf.bvp)
result._extended = True
return result
def __call__(self, points, eval_derivative = False):
"""Evaluates the approximate solution and optionally the first derivative at an array of points.
Parameters
----------
points : castable to floating point ndarray, shape (N)
Array of points where the approximate solution and derivative should be evaluated.
eval_derivative : logical
Determines whether the first derivative should be returned.
Returns
-------
S : floating point ndarray, shape(num_ODE,N)
Vector containing the approximate solution evaluated at points. Variable index is first, point index is second.
D : floating point ndarray, shape(num_ODE,N)
Vector of the first derivative to the approximate solution evaluated at points. Variable index is first, point index is second (only returned if eval_derivative = True).
Raises
------
ValueError
If the approximate solution cannot be evaluated.
ValueError
If the Solution is the result of an :meth:`extend` operation.
"""
if self._successIndicator == -1:
raise ValueError("Solution is the result of a failed run, cannot evaluate")
if self._extended == True:
raise ValueError("""this solution is the result of extending a previous solution and cannot be evaluated.
If you really want to know what the solution looks like, look at .mesh and .solution""")
# if any of the points are more than a certain tolerance outside of the bounds, something has gone wrong
tol = 1e-12
dist = tol * (self._mesh[-1] - self._mesh[0])
if (points < self._mesh[0] - dist).any() or (points > self._mesh[-1] + dist).any():
raise ValueError("some points are outside the bounds of the solution")
npar = 0
if not (self._parameters is None):
npar = len(self._parameters)
bvp_solverf.bvp.bvp_eval_wrap(eval_derivative = eval_derivative,
points = tools.farg(points),
node_in = self._solution.shape[0],
npar_in = npar,
leftbc_in = 1, # this value doesn't matter
npts_in = len(self._mesh),
info_in = self._successIndicator,
mxnsub_in = 300, # nor does this
x_in = tools.farg(self._mesh),
y_in = tools.farg(self._solution),
parameters_in = tools.farg(self._parameters),
work_in = tools.farg(self._work),
iwork_in = tools.farg(self._iwork))
#would prefer not to copy arrays here
# but the results end up getting screwed up when this function is called again for some other purpose
# this is probably because the old arrays "deallocated" by Fortran
if eval_derivative:
return bvp_solverf.bvp.evaluated.copy(), bvp_solverf.bvp.evaluated_d.copy()
else:
return bvp_solverf.bvp.evaluated.copy()
def solve(bvp_problem,
solution_guess,
initial_mesh = None,
parameter_guess = None,
max_subintervals = 300,
singular_term = None,
tolerance = 1.0e-6,
method = 4,
trace = 0,
error_on_fail = True):
"""Attempts to solve the supplied boundary value problem starting from the user supplied guess for the solution using BVP_SOLVER.
Parameters
----------
bvp_problem : :class:`ProblemDefinition`
Defines the boundary value problem to be solved.
solution_guess : :class:`Solution`, constant, array of values or function
A guess for the solution.
initial_mesh : castable to floating point ndarray
Points on the x-axis to use for the supplied solution guess, default is 10 evenly spaced points. Must not be supplied if solution_guess is a :class:`Solution` object.
parameter_guess : castable to floating point ndarray, shape (num_parameters)
Guesses for the unknown parameters. Must not be supplied if solution_guess is a :class:`Solution` object.
max_subintervals : int
Maximum number of points on the mesh before an error is returned.
singular_term : castable to floating point ndarray, shape(num_ODE, num_ODE)
Matrix that defines the singular term for the problem if one exist.
tolerance : positive float
Tolerance for size of defect of approximate solution.
method : {2, 4, 6}
Order of Runge-Kutta to use.
trace : {0, 1, 2}
Indicates verbosity of output. 0 for no output, 1 for some output, 2 for full output.
error_on_fail : logical
Indicates whether an exception should be raised if solving fails.
Returns
-------
sol : :class:`Solution`
Approximate problem solution.
Raises
------
ValueError
If bvp_problem failed validation in some way.
ValueError
If solving fails.
"""
init_solution = 0
if isinstance(solution_guess, Solution):
if not (initial_mesh == None and
parameter_guess == None):
raise ValueError("values for initial mesh and parameter_guess must not be given if solution_guess is a Solution object")
init_solution = solution_guess
else:
if initial_mesh == None:
initial_mesh = numpy.linspace(bvp_problem.boundary_points[0],bvp_problem.boundary_points[1] , 10)
# here we call one of the BVP_GUESS_i routines that make up BVP_INIT to set up the solution
if ( not callable(solution_guess)): # in this case the initial solution passed was not a function
#try to cast the solution to an array
solution_guess = numpy.array(solution_guess)
# if the solution_guess is just an array the size of ODE
if solution_guess.shape == (bvp_problem.num_ODE,) or (solution_guess.shape == () and bvp_problem.num_ODE == 1):
bvp_solverf.bvp.guess_1_wrap(nparam_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
x_in = tools.farg(initial_mesh),
y_in = tools.farg(solution_guess),
parameters_in = tools.farg(parameter_guess),
mxnsub_in = max_subintervals,
node_in = bvp_problem.num_ODE)
init_solution = Solution.from_arg_list(bvp_solverf.bvp)
else:
tools.argShapeTest(solution_guess, (bvp_problem.num_ODE,initial_mesh.shape[0]), "solution guess")
bvp_solverf.bvp.guess_2_wrap(nparam_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
x_in = tools.farg(initial_mesh),
y_in = tools.farg(solution_guess),
parameters_in = tools.farg(parameter_guess),
mxnsub_in = max_subintervals,
node_in = bvp_problem.num_ODE)
init_solution = Solution.from_arg_list(bvp_solverf.bvp)
else:
bvp_solverf.bvp.guess_3_wrap(node_in = bvp_problem.num_ODE,
nparam_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
x_in= tools.farg(initial_mesh),
fcn = solution_guess,
parameters_in = tools.farg(parameter_guess),
mxnsub_in = max_subintervals)
init_solution = Solution.from_arg_list(bvp_solverf.bvp)
if not (method == 2 or method == 4 or method == 6 ):
raise ValueError ("method must be either 2, 4 or 6 but got " + str(method) )
if (tolerance < 0):
raise ValueError("tolerance must be nonnegative")
singular = not (singular_term is None)
# check to see if the singular term is of the right size
singular_term = tools.preparg(singular_term)
if singular and not (singular_term.shape == (bvp_problem.num_ODE, bvp_problem.num_ODE)):
raise ValueError("singular_term has the wrong shape/size. Expected: " +
(bvp_problem.num_ODE, bvp_problem.num_ODE)+
" but got :" +
singular_term.shape)
# test the problem specifications with the initial solution
bvp_problem.test(init_solution)
bvp_solverf.bvp.bvp_solver_wrap(node_in = bvp_problem.num_ODE,
npar_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
npts_in = len(init_solution.mesh),
info_in = init_solution.successIndicator,
mxnsub_in = max_subintervals,
x_in = tools.farg(init_solution.mesh),
y_in = tools.farg(init_solution.solution),
parameters_in = tools.farg(init_solution.parameters),
work_in = tools.farg(init_solution.work),
iwork_in = tools.farg(init_solution.iwork),
fsub = bvp_problem._function,
fsubp = bvp_problem._functionp,
bcsub = bvp_problem._boundary_conditions,
bcsubp = bvp_problem._boundary_conditionsp,
singular = singular,
hasdfdy = bvp_problem.has_function_derivative,
dfdy = bvp_problem._function_derivative,
dfdyp = bvp_problem._function_derivativep,
hasdbcdy = bvp_problem.has_boundary_conditions_derivative,
dbcdy = bvp_problem._boundary_conditions_derivative,
dbcdyp = bvp_problem._boundary_conditions_derivativep,
#optional arguments
method = method,
tol = tolerance,
trace = trace,
# we never want the actual program to shut down from the fortran side, we should throw an error
stop_on_fail = False,
singularterm = tools.farg(singular_term))
calculatedSolution = Solution.from_arg_list(bvp_solverf.bvp)
# check to see if there was a problem with the solution
if error_on_fail and calculatedSolution._successIndicator == -1:
raise ValueError("Boundary value problem solving failed. Run with trace = 1 or 2 for more information.")
return calculatedSolution
def solve(bvp_problem,
solution_guess,
initial_mesh = None,
parameter_guess = None,
max_subintervals = 300,
singular_term = None,
tolerance = 1.0e-6,
method = 4,
trace = 0,
error_on_fail = True):
"""Attempts to solve the supplied boundary value problem starting from the user supplied guess for the solution using BVP_SOLVER.
Parameters
----------
bvp_problem : :class:`ProblemDefinition`
Defines the boundary value problem to be solved.
solution_guess : :class:`Solution`, constant, array of values or function
A guess for the solution.
initial_mesh : castable to floating point ndarray
Points on the x-axis to use for the supplied solution guess, default is 10 evenly spaced points. Must not be supplied if solution_guess is a :class:`Solution` object.
parameter_guess : castable to floating point ndarray, shape (num_parameters)
Guesses for the unknown parameters. Must not be supplied if solution_guess is a :class:`Solution` object.
max_subintervals : int
Maximum number of points on the mesh before an error is returned.
singular_term : castable to floating point ndarray, shape(num_ODE, num_ODE)
Matrix that defines the singular term for the problem if one exist.
tolerance : positive float
Tolerance for size of defect of approximate solution.
method : {2, 4, 6}
Order of Runge-Kutta to use.
trace : {0, 1, 2}
Indicates verbosity of output. 0 for no output, 1 for some output, 2 for full output.
error_on_fail : logical
Indicates whether an exception should be raised if solving fails.
Returns
-------
sol : :class:`Solution`
Approximate problem solution.
Raises
------
ValueError
If bvp_problem failed validation in some way.
ValueError
If solving fails.
"""
init_solution = 0
if isinstance(solution_guess, Solution):
if not (initial_mesh == None and
parameter_guess == None):
raise ValueError("values for initial mesh and parameter_guess must not be given if solution_guess is a Solution object")
init_solution = solution_guess
else:
if initial_mesh == None:
initial_mesh = numpy.linspace(bvp_problem.boundary_points[0],bvp_problem.boundary_points[1] , 10)
# here we call one of the BVP_GUESS_i routines that make up BVP_INIT to set up the solution
if ( not callable(solution_guess)): # in this case the initial solution passed was not a function
#try to cast the solution to an array
solution_guess = numpy.array(solution_guess)
# if the solution_guess is just an array the size of ODE
if solution_guess.shape == (bvp_problem.num_ODE,) or (solution_guess.shape == () and bvp_problem.num_ODE == 1):
bvp_solverf.bvp.guess_1_wrap(nparam_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
x_in = tools.farg(initial_mesh),
y_in = tools.farg(solution_guess),
parameters_in = tools.farg(parameter_guess),
mxnsub_in = max_subintervals,
node_in = bvp_problem.num_ODE)
init_solution = Solution.from_arg_list(bvp_solverf.bvp)
else:
tools.argShapeTest(solution_guess, (bvp_problem.num_ODE,initial_mesh.shape[0]), "solution guess")
bvp_solverf.bvp.guess_2_wrap(nparam_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
x_in = tools.farg(initial_mesh),
y_in = tools.farg(solution_guess),
parameters_in = tools.farg(parameter_guess),
mxnsub_in = max_subintervals,
node_in = bvp_problem.num_ODE)
init_solution = Solution.from_arg_list(bvp_solverf.bvp)
else:
y_in = numpy.zeros((bvp_problem.num_ODE,1))
bvp_solverf.bvp.guess_1_wrap(nparam_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
x_in = tools.farg(initial_mesh),
y_in = y_in,
parameters_in = tools.farg(parameter_guess),
mxnsub_in = max_subintervals,
node_in = bvp_problem.num_ODE)
init_solution = Solution.from_arg_list(bvp_solverf.bvp)
for i,v in enumerate(init_solution._mesh):
init_solution._solution[:, i] = solution_guess(v)
if not (method == 2 or method == 4 or method == 6 ):
raise ValueError ("method must be either 2, 4 or 6 but got " + str(method) )
if (tolerance < 0):
raise ValueError("tolerance must be nonnegative")
singular = not (singular_term is None)
# check to see if the singular term is of the right size
singular_term = tools.preparg(singular_term)
if singular and not (singular_term.shape == (bvp_problem.num_ODE, bvp_problem.num_ODE)):
raise ValueError("singular_term has the wrong shape/size. Expected: " +
(bvp_problem.num_ODE, bvp_problem.num_ODE)+
" but got :" +
singular_term.shape)
# test the problem specifications with the initial solution
bvp_problem.test(init_solution)
bvp_solverf.bvp.bvp_solver_wrap(node_in = bvp_problem.num_ODE,
npar_in = bvp_problem.num_parameters,
leftbc_in = bvp_problem.num_left_boundary_conditions,
npts_in = len(init_solution.mesh),
info_in = init_solution.successIndicator,
mxnsub_in = max_subintervals,
x_in = tools.farg(init_solution.mesh),
y_in = tools.farg(init_solution.solution),
parameters_in = tools.farg(init_solution.parameters),
work_in = tools.farg(init_solution.work),
iwork_in = tools.farg(init_solution.iwork),
fsub = bvp_problem._function,
fsubp = bvp_problem._functionp,
bcsub = bvp_problem._boundary_conditions,
bcsubp = bvp_problem._boundary_conditionsp,
singular = singular,
hasdfdy = bvp_problem.has_function_derivative,
dfdy = bvp_problem._function_derivative,
dfdyp = bvp_problem._function_derivativep,
hasdbcdy = bvp_problem.has_boundary_conditions_derivative,
dbcdy = bvp_problem._boundary_conditions_derivative,
dbcdyp = bvp_problem._boundary_conditions_derivativep,
#optional arguments
method = method,
tol = tolerance,
trace = trace,
# we never want the actual program to shut down from the fortran side, we should throw an error
stop_on_fail = False,
singularterm = tools.farg(singular_term))
calculatedSolution = Solution.from_arg_list(bvp_solverf.bvp)
# check to see if there was a problem with the solution
if error_on_fail and calculatedSolution._successIndicator == -1:
raise ValueError("Boundary value problem solving failed. Run with trace = 1 or 2 for more information.")
return calculatedSolution