Source code for sfepy.linalg.check_derivatives

"""
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