def test_derivative_sin():
# Evaluate the indicated (default = first)
# derivative at multiple points
for method in ['forward', 'reverse']:
dsin = nd.Derivative(np.sin, method=method)
x = np.linspace(0, 2. * np.pi, 13)
y = dsin(x)
assert_allclose(y, np.cos(x))
def test_derivative_on_sinh(self, x):
true_val = np.cosh(x)
for method in ['forward', 'backward']:
dsinh = nd.Derivative(np.sinh, method=method)
val = dsinh(x)
if np.isnan(true_val):
assert np.isnan(val) == np.isnan(true_val)
else:
assert_allclose(val, true_val)
def test_high_order_derivative_cos():
true_vals = (-1.0, 0.0, 1.0, 0.0) * 5
x = np.pi / 2 # np.linspace(0, np.pi/2, 15)
for method in ['forward', 'reverse']:
nmax = 15 if method in ['forward'] else 2
for n in range(1, nmax):
d3cos = nd.Derivative(np.cos, n=n, method=method)
y = d3cos(x)
assert_allclose(y, true_vals[n - 1], atol=1e-15)
def test_derivative_cube():
"""Test for Issue 7"""
def cube(x):
return x * x * x
shape = (3, 2)
x = np.ones(shape) * 2
for method in ['forward', 'reverse']:
dcube = nd.Derivative(cube, method=method)
dx = dcube(x)
assert_allclose(list(dx.shape),
list(shape),
err_msg='Shape mismatch')
txt = 'First differing element %d\n value = %g,\n true value = %g'
for i, (val, tval) in enumerate(zip(dx.ravel(),
(3 * x**2).ravel())):
assert_allclose(val, tval, err_msg=txt % (i, val, tval))
def test_derivative_on_log(x):
for method in ['forward', 'reverse']:
dlog = nd.Derivative(np.log, method=method)
assert_allclose(dlog(x), 1.0 / x)
def test_derivative_exp(x):
for method in ['forward', 'reverse']:
dexp = nd.Derivative(np.exp, method=method)
assert_allclose(dexp(x), np.exp(x))