def fix_Psi(fixture_path):
"""Call Psi for a range of possible inputs and save result as fixture."""
function_name = 'Psi'
output_file = fixture_path + function_name + '.npz'
z_range = np.concatenate(
[-np.logspace(2, -5, 4), [0],
np.logspace(-5, 2, 4)])
a, b = np.meshgrid(z_range, z_range)
zs = a.flatten() + complex(0, 1) * b.flatten()
xs = np.linspace(-10, 10, 8)
zs, xs = np.meshgrid(zs, xs)
zs = zs.flatten()
xs = xs.flatten()
pcfu_outputs = []
for z, x in zip(zs, xs):
result = mpmath.pcfu(z, -x)
pcfu_outputs.append(complex(result.real, result.imag))
outputs = []
for z, x in zip(zs, xs):
outputs.append(Psi(z, x))
np.savez(output_file, zs=zs, xs=xs, pcfus=pcfu_outputs, outputs=outputs)
def normal_cdf_moment_ratio(n, x):
mpmath.mp.dps = 500
xmpf = x._to_mpmath(500)
nmpf = n._to_mpmath(500)
if x < 0:
return Float(mpmath.power(2, -0.5 - nmpf / 2) * mpmath.hyperu(nmpf / 2 + 0.5, 0.5, xmpf * xmpf / 2))
return Float(mpmath.exp(xmpf * xmpf / 4) * mpmath.pcfu(0.5 + nmpf, -xmpf))
def Phi_mpmath(z, x):
"""
Calculates Phi(a,x) = exp(x**2/4)*U(a,x), where U(a,x) is the
parabolic cylinder function. Implementation uses the mpmath
functions. This is slower than the Fortran implementation `Phi`
and not used in this package but added for completeness.
"""
value = np.exp(0.25 * x**2) * complex(mpmath.pcfu(z, -x))
return value
def Phi_mpmath(z, x):
"""
Calculates Phi(a,x) = exp(x**2/4)*U(a,x), where U(a,x) is the
parabolic cylinder function. Implementation uses the mpmath
functions. This is slower than the Fortran implementation `Phi`
and not used in this package but added for completeness.
"""
value = np.exp(0.25*x**2) * complex(mpmath.pcfu(z, -x))
return value
def Phi1_mpmath_pcfu(z, x):
'''mpmath implementation has revered sign in x'''
try:
value = np.exp(0.25 * x**2) * complex(mpmath.pcfu(z, -x))
# value_mpc = U_Kummer_fortran(z,x)
# value_mpc = U_Kummer_mpmath(z,x)
# value = complex(value_mpc.real,value_mpc.imag)
return value
except mpmath.libmp.libhyper.NoConvergence:
return np.NaN
def Psi(z, x):
"""
Calcs Psi(z,x)=exp(x**2/4)*U(z,x), with U(z,x) the parabolic cylinder func.
"""
return np.exp(0.25 * x**2) * complex(mpmath.pcfu(z, -x))