def test_issue_25():
def g_fun(x):
out = np.zeros((2, 2))
out[0] = x
out[1] = x
return out
dg_dx = nd.Jacobian(g_fun)
x = np.array([1., 2.])
v0 = nd.approx_fprime(x, g_fun)
assert_allclose(v0, [[[1., 0.],
[0., 1.]],
[[1., 0.],
[0., 1.]]])
dg = dg_dx(x)
assert_allclose(dg, [[[1., 0.],
[0., 1.]],
[[1., 0.],
[0., 1.]]])
fun3 = lambda x : np.vstack((x[0]*x[1]*x[2]**2, x[0]*x[1]*x[2]))
jfun3 = nd.Jacobian(fun3)
x = np.array([[1.,2.,3.], [4., 5., 6.]]).T
tv = [[[18., 180.],
[9., 144.],
[12., 240.]],
[[6., 30.],
[3., 24.],
[2., 20.]]]
assert_allclose(jfun3(x), tv)
assert_allclose(nd.approx_fprime(x, fun3), tv)
def test_on_matrix_valued_function():
def fun(x):
x = np.atleast_1d(x)
f0 = x[0] ** 2 + x[1] ** 2
f1 = x[0] ** 3 + x[1] ** 3
return np.array([f0, f1])
def dfun(x):
x = np.atleast_1d(x)
f0_d0 = np.atleast_1d(x[0] * 2)
f0_d1 = np.atleast_1d(x[1] * 2)
f1_d0 = np.atleast_1d(3 * x[0] ** 2)
f1_d1 = np.atleast_1d(3 * x[1] ** 2)
# algopy way:
# df0 = np.hstack([np.diag(f0_d0), np.diag(f0_d1)])
# df1 = np.hstack([np.diag(f1_d0), np.diag(f1_d1)])
# numdifftools way:
df0 = np.vstack([f0_d0, f0_d1])
df1 = np.vstack([f1_d0, f1_d1])
return np.array([df0, df1]).squeeze()
jaca = nd.Jacobian(fun)
assert_allclose(jaca([1, 2]), [[2., 4.],
[3., 12.]])
assert_allclose(jaca([3, 4]), [[6., 8.],
[27., 48.]])
assert_allclose(jaca([1, 2]), dfun([1, 2]))
assert_allclose(jaca([3, 4]), dfun([3, 4]))
v0 = jaca([[1, 2], [3, 4]])
print(v0)
assert_allclose(v0,
dfun([[1, 2],
[3, 4]]))
x = np.array([(1, 2, 3, 4),
(5, 6, 7, 8)], dtype=float)
y = fun(x)
assert_allclose(y, [[26., 40., 58., 80.],
[126., 224., 370., 576.]])
tval = dfun(x)
assert_allclose(tval, [[[2., 4., 6., 8.],
[10., 12., 14., 16.]],
[[3., 12., 27., 48.],
[75., 108., 147., 192.]]])
v0 = nd.approx_fprime(x, fun)
val = jaca(x)
assert_allclose(v0, tval)
assert_allclose(val, tval)
def test_on_vector_valued_function():
xdata = np.arange(0, 1, 0.1) #.reshape((-1, 1))
ydata = 1 + 2 * np.exp(0.75 * xdata)
def fun(c):
return (c[0] + c[1] * np.exp(c[2] * xdata) - ydata) ** 2
_j_0 = nd.approx_fprime([1, 2, 0.75], fun)
for method in ['complex', 'central', 'forward', 'backward']:
for order in [2, 4]:
j_fun = nd.Jacobian(fun, method=method, order=order)
j_val = j_fun([1, 2, 0.75]) # should be numerically zero
assert_allclose(j_val, np.zeros((ydata.size, 3)), atol=1e-12)
