Coverage for pySDC/implementations/problem_classes/polynomial_test_problem.py: 100%
36 statements
« prev ^ index » next coverage.py v7.17.0, created at 2026-11-02 12:30 +0000
1import numpy as np
3from pySDC.core.problem import Problem
4from pySDC.implementations.datatype_classes.mesh import mesh, imex_mesh
7class polynomial_testequation(Problem):
8 """
9 Scalar ODE whose exact solution is a random polynomial in time, to test operations exact on polynomials.
11 Dummy problem for tests only! In particular, the `solve_system` function just returns the exact solution instead of
12 solving an appropriate system. This class is indented to be used for tests of operations that are exact on polynomials.
14 Parameters
15 ----------
16 degree : int, optional
17 Number of coefficients of the polynomial, i.e., the polynomial has degree ``degree - 1``.
18 seed : int, optional
19 Seed for ``np.random.RandomState``, which draws the coefficients uniformly from :math:`[0, 1)`.
20 useGPU : bool, optional
21 Use ``CuPy`` for the solution. This switches the data types of the class, not only of this instance.
22 """
24 dtype_u = mesh
25 dtype_f = mesh
26 xp = np
28 def __init__(self, degree=1, seed=26266, useGPU=False):
29 """Initialization routine"""
31 if useGPU:
32 import cupy as cp
33 from pySDC.implementations.datatype_classes.cupy_mesh import cupy_mesh, imex_cupy_mesh
35 # on the instance, since setting them on the class would switch every later instance to the GPU
36 self.xp = cp
37 self.dtype_u = cupy_mesh
38 self.dtype_f = imex_cupy_mesh if self.dtype_f is imex_mesh else cupy_mesh
40 # invoke super init, passing number of dofs, dtype_u and dtype_f
41 super().__init__(init=(1, None, np.dtype('float64')))
43 self.rng = np.random.RandomState(seed=seed)
44 self.poly = np.polynomial.Polynomial(self.rng.rand(degree))
45 self._makeAttributeAndRegister('degree', 'seed', localVars=locals(), readOnly=True)
47 def eval_f(self, u, t):
48 """
49 Derivative of the polynomial.
51 Parameters
52 ----------
53 u : dtype_u
54 Current values of the numerical solution.
55 t : float
56 Current time of the numerical solution is computed.
58 Returns
59 -------
60 f : dtype_f
61 The right-hand side of the problem.
62 """
64 f = self.dtype_f(self.init)
65 f[:] = self.xp.array(self.poly.deriv(m=1)(t))
66 return f
68 def solve_system(self, rhs, factor, u0, t):
69 """
70 Just return the exact solution...
72 Parameters
73 ----------
74 rhs : dtype_f
75 Right-hand side for the linear system.
76 factor : float
77 Abbrev. for the local stepsize (or any other factor required).
78 u0 : dtype_u
79 Initial guess for the iterative solver.
80 t : float
81 Current time (e.g. for time-dependent BCs).
83 Returns
84 -------
85 me : dtype_u
86 The solution as mesh.
87 """
89 return self.u_exact(t)
91 def u_exact(self, t, **kwargs):
92 """
93 Evaluate the polynomial.
95 Parameters
96 ----------
97 t : float
98 Time of the exact solution.
99 **kwargs
100 Takes ``u_init`` and ``t_init`` of the generic interface, which are ignored since the polynomial is known
101 everywhere.
103 Returns
104 -------
105 me : dtype_u
106 The exact solution.
107 """
108 me = self.dtype_u(self.init)
109 me[:] = self.xp.array(self.poly(t))
110 return me
113class polynomial_testequation_IMEX(polynomial_testequation):
114 """
115 IMEX version of the polynomial test problem that assigns half the derivative to the implicit part and the other half to the explicit part.
116 Keep in mind that you still cannot Really perform any solves.
117 """
119 dtype_f = imex_mesh
121 def eval_f(self, u, t):
122 """
123 Derivative of the polynomial.
125 Parameters
126 ----------
127 u : dtype_u
128 Current values of the numerical solution.
129 t : float
130 Current time of the numerical solution is computed.
132 Returns
133 -------
134 f : dtype_f
135 The right-hand side of the problem.
136 """
138 f = self.dtype_f(self.init)
139 derivative = self.xp.array(self.poly.deriv(m=1)(t))
140 f.impl[:] = derivative / 2
141 f.expl[:] = derivative / 2
142 return f