""" Tests related to the construction of integration tables.
.. autosummary::
:toctree: _generated/
:template: tests-formatting/base.rst
:nosignatures:
test_ImplicitRKDefaultDPSIsEnough
test_ImplicitSymplecticPairs
test_ImplicitSymmetricPairs
test_ImplicitSymmetricSymplecticPairs
"""
import pytest
from .test_config import *
import numpy as np
import scipy
import choreo
[docs]
@ParametrizeDocstrings
@pytest.mark.parametrize("method", ClassicalImplicitRKMethods)
@pytest.mark.parametrize("nsteps", Small_orders)
def test_ImplicitRKDefaultDPSIsEnough(float64_tols_strict, method, nsteps):
""" Tests whether the default precision is sufficient for computing implicit Runge-Kutta tables.
Tests whether the default value of the dps parameter of :func:`choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss` is large enough to ensure that that the Runge-Kutta tables are exact at least up to double precision.
"""
dps_overkill = 1000
rk = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method)
rk_overkill = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, dps=dps_overkill, method=method)
print(np.linalg.norm(rk.a_table - rk_overkill.a_table))
print(np.linalg.norm(rk.b_table - rk_overkill.b_table))
print(np.linalg.norm(rk.c_table - rk_overkill.c_table))
print(np.linalg.norm(rk.beta_table - rk_overkill.beta_table))
print(np.linalg.norm(rk.gamma_table - rk_overkill.gamma_table))
assert np.allclose(
rk.a_table ,
rk_overkill.a_table ,
atol = float64_tols_strict.atol ,
rtol = float64_tols_strict.rtol ,
)
assert np.allclose(
rk.b_table ,
rk_overkill.b_table ,
atol = float64_tols_strict.atol ,
rtol = float64_tols_strict.rtol ,
)
assert np.allclose(
rk.c_table ,
rk_overkill.c_table ,
atol = float64_tols_strict.atol ,
rtol = float64_tols_strict.rtol ,
)
assert np.allclose(
rk.beta_table ,
rk_overkill.beta_table ,
atol = float64_tols_strict.atol ,
rtol = float64_tols_strict.rtol ,
)
assert np.allclose(
rk.gamma_table ,
rk_overkill.gamma_table ,
atol = float64_tols_strict.atol ,
rtol = float64_tols_strict.rtol ,
)
rk_ad = rk.symplectic_adjoint()
print(rk.symplectic_default(rk_ad))
assert rk.is_symplectic_pair(rk_ad, tol = float64_tols_strict.atol)
rk_ad = rk.symmetric_adjoint()
print(rk.symmetry_default(rk_ad))
assert rk.is_symmetric_pair(rk_ad, tol = float64_tols_strict.atol)
[docs]
@ParametrizeDocstrings
@pytest.mark.parametrize("method_pair", SymplecticImplicitRKMethodPairs)
@pytest.mark.parametrize("nsteps", Small_orders)
def test_ImplicitSymplecticPairs(float64_tols_strict, method_pair, nsteps):
""" Tests whether symplectic pairs of implicit Runge-Kutta tables are indeed symplectic at least up to double precision accuracy.
"""
rk = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method_pair[0])
rk_ad = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method_pair[1])
print(rk.symplectic_default(rk_ad))
assert rk.is_symplectic_pair(rk_ad, tol = float64_tols_strict.atol)
[docs]
@ParametrizeDocstrings
@pytest.mark.parametrize("method_pair", SymmetricImplicitRKMethodPairs)
@pytest.mark.parametrize("nsteps", Small_orders)
def test_ImplicitSymmetricPairs(float64_tols_strict, method_pair, nsteps):
""" Tests whether symmetric pairs of implicit Runge-Kutta tables are indeed symmetric at least up to double precision accuracy.
"""
rk = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method_pair[0])
rk_ad = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method_pair[1])
print(rk.symmetry_default(rk_ad))
assert rk.is_symmetric_pair(rk_ad, tol = float64_tols_strict.atol)
[docs]
@ParametrizeDocstrings
@pytest.mark.parametrize("method_pair", SymmetricSymplecticImplicitRKMethodPairs)
@pytest.mark.parametrize("nsteps", Small_orders)
def test_ImplicitSymmetricSymplecticPairs(float64_tols_strict, method_pair, nsteps):
rk = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method_pair[0])
rk_ad = choreo.scipy_plus.multiprec_tables.ComputeImplicitRKTable_Gauss(nsteps, method=method_pair[1]).symmetric_adjoint()
print(rk.symplectic_default(rk_ad))
assert rk.is_symplectic_pair(rk_ad, tol = float64_tols_strict.atol)
