def test_dawsn(self):
for shape in (
(2, 3),
(4, 3, 2, 5),
):
# sample some random numbers
x = UTPM(numpy.random.randn(*shape))
# construct the u and v arrays
u_data = x.data.copy()
v_data = numpy.empty_like(u_data)
v_data[0, ...] = scipy.special.dawsn(u_data[0])
# construct values like in Table (13.2) of "Evaluating Derivatives"
a_data = -2 * u_data.copy()
b_data = _plus_const(numpy.zeros_like(u_data), 1)
c_data = _plus_const(numpy.zeros_like(u_data), 1)
# fill the rest of the v_data
_taylor_polynomials_of_ode_solutions(
a_data, b_data, c_data,
u_data, v_data)
# compare the v_data array to the UTPM dawsn data
assert_allclose(v_data, UTPM.dawsn(x).data)
def test_dawsn(self):
for shape in (
(2, 3),
(4, 3, 2, 5),
):
# sample some random numbers
x = UTPM(numpy.random.randn(*shape))
# construct the u and v arrays
u_data = x.data.copy()
v_data = numpy.empty_like(u_data)
v_data[0, ...] = scipy.special.dawsn(u_data[0])
# construct values like in Table (13.2) of "Evaluating Derivatives"
a_data = -2 * u_data.copy()
b_data = _plus_const(numpy.zeros_like(u_data), 1)
c_data = _plus_const(numpy.zeros_like(u_data), 1)
# fill the rest of the v_data
_taylor_polynomials_of_ode_solutions(
a_data, b_data, c_data,
u_data, v_data)
# compare the v_data array to the UTPM dawsn data
assert_allclose(v_data, UTPM.dawsn(x).data)
def test_power(self):
# define a constant real exponent
r = 1.23
for shape in (
(2, 3),
(4, 3, 2, 5),
):
# sample some positive numbers for taking fractional real powers
x = UTPM(numpy.exp(numpy.random.randn(*shape)))
# construct the u and v arrays
u_data = x.data.copy()
v_data = numpy.empty_like(u_data)
v_data[0, ...] = numpy.power(u_data[0], r)
# construct values like in Table (13.2) of "Evaluating Derivatives"
a_data = _plus_const(numpy.zeros_like(u_data), r)
b_data = u_data.copy()
c_data = numpy.zeros_like(u_data)
# fill the rest of the v_data
_taylor_polynomials_of_ode_solutions(
a_data, b_data, c_data,
u_data, v_data)
# compare the v_data array to the UTPM power data
assert_allclose(v_data, (x ** r).data)
def test_power(self):
# define a constant real exponent
r = 1.23
for shape in (
(2, 3),
(4, 3, 2, 5),
):
# sample some positive numbers for taking fractional real powers
x = UTPM(numpy.exp(numpy.random.randn(*shape)))
# construct the u and v arrays
u_data = x.data.copy()
v_data = numpy.empty_like(u_data)
v_data[0, ...] = numpy.power(u_data[0], r)
# construct values like in Table (13.2) of "Evaluating Derivatives"
a_data = _plus_const(numpy.zeros_like(u_data), r)
b_data = u_data.copy()
c_data = numpy.zeros_like(u_data)
# fill the rest of the v_data
_taylor_polynomials_of_ode_solutions(
a_data, b_data, c_data,
u_data, v_data)
# compare the v_data array to the UTPM power data
assert_allclose(v_data, (x ** r).data)