"""
Utilities for checking derivatives of functions.
"""
from __future__ import print_function
from __future__ import absolute_import
import numpy as nm
from six.moves import range
[docs]def check_fx(x0, fx, fx_args, dfx, dfx_args=None, delta=1e-5):
"""
Check derivatives of a (vectorized) scalar function of a scalar variable.
"""
if dfx_args is None:
dfx_args = fx_args
dfx_a = dfx(x0, *dfx_args)
x = x0 + delta
f1 = fx(x, *fx_args)
x = x0 - delta
f2 = fx(x, *fx_args)
dfx_d = 0.5 * (f1 - f2) / delta
error = nm.linalg.norm(dfx_a - dfx_d, nm.inf)
print('analytical:', dfx_a)
print('difference:', dfx_d)
print('error:', error)
return dfx_a, dfx_d, error
[docs]def check_vfvx(x0, fx, fx_args, dfx, dfx_args=None, delta=1e-5):
"""
Check derivatives of a (vectorized) vector or scalar function of a vector
variable.
"""
if x0.ndim != 2:
raise ValueError('The variable must have two dimensions!')
if dfx_args is None:
dfx_args = fx_args
dfx_a = dfx(x0, *dfx_args)
dfx_d = nm.zeros_like(dfx_a)
for ic in range(x0.shape[1]):
x = x0.copy()
x[:, ic] += delta
f1 = fx(x, *fx_args)
x = x0.copy()
x[:, ic] -= delta
f2 = fx(x, *fx_args)
dfx_d[:, ic] = 0.5 * (f1 - f2) / delta
error = nm.linalg.norm((dfx_a - dfx_d).ravel(), nm.inf)
print('analytical:', dfx_a)
print('difference:', dfx_d)
print('error:', error)
return dfx_a, dfx_d, error