def test_al_mohy_higham_2012_experiment_1(self):
# Fractional powers of a tricky upper triangular matrix.
A = _get_al_mohy_higham_2012_experiment_1()
# Test remainder matrix power.
A_funm_sqrt, info = funm(A, np.sqrt, disp=False)
A_sqrtm, info = sqrtm(A, disp=False)
A_rem_power = _matfuncs_inv_ssq._remainder_matrix_power(A, 0.5)
A_power = fractional_matrix_power(A, 0.5)
assert_array_equal(A_rem_power, A_power)
assert_allclose(A_sqrtm, A_power)
assert_allclose(A_sqrtm, A_funm_sqrt)
# Test more fractional powers.
for p in (1/2, 5/3):
A_power = fractional_matrix_power(A, p)
A_round_trip = fractional_matrix_power(A_power, 1/p)
assert_allclose(A_round_trip, A, rtol=1e-2)
assert_allclose(np.tril(A_round_trip, 1), np.tril(A, 1))
def test_al_mohy_higham_2012_experiment_1(self):
# Fractional powers of a tricky upper triangular matrix.
A = _get_al_mohy_higham_2012_experiment_1()
# Test remainder matrix power.
A_funm_sqrt, info = funm(A, np.sqrt, disp=False)
A_sqrtm, info = sqrtm(A, disp=False)
A_rem_power = _matfuncs_inv_ssq._remainder_matrix_power(A, 0.5)
A_power = fractional_matrix_power(A, 0.5)
assert_array_equal(A_rem_power, A_power)
assert_allclose(A_sqrtm, A_power)
assert_allclose(A_sqrtm, A_funm_sqrt)
# Test more fractional powers.
for p in (1/2, 5/3):
A_power = fractional_matrix_power(A, p)
A_round_trip = fractional_matrix_power(A_power, 1/p)
assert_allclose(A_round_trip, A, rtol=1e-2)
assert_allclose(np.tril(A_round_trip, 1), np.tril(A, 1))
