# -*- coding:utf-8 -*-
""""""
from __future__ import absolute_import, division
import numpy as np
import pytest
from hypothesis import given
from hypothesis import strategies as st
from numpy.testing import assert_allclose # @UnresolvedImport
try:
import scipy
except ImportError:
scipy = None
else:
import numdifftools.nd_scipy as nd
pytestmark = pytest.mark.skipif(scipy is None, reason="scipy is not installed!")
[docs]
class TestJacobian(object):
[docs]
@staticmethod
@given(st.floats(min_value=-1e53, max_value=1e53))
def test_scalar_to_vector(val):
def fun(x):
return np.array([x, x**2, x**3]).ravel()
for method in ["backward", "forward", "central", "complex"]:
j0 = nd.Jacobian(fun, method=method)(val).T
assert_allclose(j0, [[1.0, 2 * val, 3 * val**2]], atol=1e-6)
[docs]
@staticmethod
def test_on_scalar_function():
def fun(x):
return x[0] * x[1] * x[2] + np.exp(x[0]) * x[1]
for method in ["forward", "backward", "central", "complex"]:
j_fun = nd.Jacobian(fun, method=method)
x = j_fun([3.0, 5.0, 7.0])
assert_allclose(x, [135.42768462, 41.08553692, 15.0])
[docs]
def test_on_vector_valued_function(self):
xdata = np.arange(0, 1, 0.1)
ydata = 1 + 2 * np.exp(0.75 * xdata)
def fun(c):
return (c[0] + c[1] * np.exp(c[2] * xdata) - ydata) ** 2
for method in ["forward", "backward", "central", "complex"]:
j_fun = nd.Jacobian(fun, method=method)
J = j_fun([1, 2, 0.75]) # should be numerically zero
assert_allclose(J, np.zeros((ydata.size, 3)), atol=1e-6)
[docs]
@pytest.mark.skip("Not implemented for matrix valued functions")
def test_on_matrix_valued_function(self):
def fun(x):
f0 = x[0] ** 2 + x[1] ** 2
f1 = x[0] ** 3 + x[1] ** 3
s0 = f0.size
s1 = f1.size
out = np.zeros((2, (s0 + s1) // 2), dtype=float)
out[0, :] = f0
out[1, :] = f1
return out
x = np.array([(1, 2, 3, 4), (5, 6, 7, 8)], dtype=float)
y = fun(x)
assert_allclose(y, [[26.0, 40.0, 58.0, 80.0], [126.0, 224.0, 370.0, 576.0]])
for method in [
"forward",
]: # TODO: 'reverse' fails
jaca = nd.Jacobian(fun, method=method)
assert_allclose(jaca([1, 2]), [[[2.0, 4.0]], [[3.0, 12.0]]])
assert_allclose(jaca([3, 4]), [[[6.0, 8.0]], [[27.0, 48.0]]])
assert_allclose(
jaca([[1, 2], [3, 4]]),
[
[[2.0, 0.0, 6.0, 0.0], [0.0, 4.0, 0.0, 8.0]],
[[3.0, 0.0, 27.0, 0.0], [0.0, 12.0, 0.0, 48.0]],
],
)
val = jaca(x)
assert_allclose(
val,
[
[
[2.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0],
[0.0, 4.0, 0.0, 0.0, 0.0, 12.0, 0.0, 0.0],
[0.0, 0.0, 6.0, 0.0, 0.0, 0.0, 14.0, 0.0],
[0.0, 0.0, 0.0, 8.0, 0.0, 0.0, 0.0, 16.0],
],
[
[3.0, 0.0, 0.0, 0.0, 75.0, 0.0, 0.0, 0.0],
[0.0, 12.0, 0.0, 0.0, 0.0, 108.0, 0.0, 0.0],
[0.0, 0.0, 27.0, 0.0, 0.0, 0.0, 147.0, 0.0],
[0.0, 0.0, 0.0, 48.0, 0.0, 0.0, 0.0, 192.0],
],
],
)
[docs]
@pytest.mark.skip("Does not work on matrix valued functions.")
def test_issue_25(self):
def g_fun(x):
out = np.zeros((2, 2), dtype=float)
out[0, 0] = x[0]
out[0, 1] = x[1]
out[1, 0] = x[0]
out[1, 1] = x[1]
return out
dg_dx = nd.Jacobian(g_fun)
x = np.array([1, 2])
tv = [[[1.0, 0.0], [0.0, 1.0]], [[1.0, 0.0], [0.0, 1.0]]]
# _EPS = np.MachAr().eps
# epsilon = _EPS**(1./4)
# assert_allclose(nd.approx_fprime(x, g_fun, epsilon), tv)
dg = dg_dx(x)
assert_allclose(dg, tv)
[docs]
class TestGradient(object):
[docs]
@staticmethod
def test_on_scalar_function():
def fun(x):
return np.sum(x**2)
dtrue = [2.0, 4.0, 6.0]
for method in ["forward", "backward", "central", "complex"]:
dfun = nd.Gradient(fun, method=method)
d = dfun([1, 2, 3])
assert_allclose(d, dtrue)