from __future__ import absolute_import, print_function
import numpy as np
from hypothesis import given, note, settings # , reproduce_failure
from hypothesis import strategies as st
from numpy.testing import assert_allclose # @UnresolvedImport
from numdifftools.example_functions import function_names, get_function
from numdifftools.fornberg import (
CENTRAL_WEIGHTS_AND_POINTS,
derivative,
fd_derivative,
fd_weights,
fd_weights_all,
)
# @reproduce_failure('5.36.1', b'AAJRcYUpZHQ=')
# @reproduce_failure('4.32.2', b'AAJRcYUpZHQ=')
[docs]
@settings(deadline=800.0)
@given(st.floats(min_value=1e-1, max_value=0.98))
def test_high_order_derivative(x):
# small_radius = ['sqrt', 'log', 'log2', 'log10', 'arccos', 'log1p',
# 'arcsin', 'arctan', 'arcsinh', 'tan', 'tanh',
# 'arctanh', 'arccosh']
r = 0.0059
n_max = 20
y = x
for name in function_names + ["arccosh", "arctanh"]:
f, true_df = get_function(name, n=1)
if name == "arccosh":
y = y + 1
vals, info = derivative(f, y, r=r, n=n_max, full_output=True, step_ratio=1.6)
for n in range(1, n_max):
f, true_df = get_function(name, n=n)
if true_df is None:
continue
tval = true_df(y)
aerr0 = info.error_estimate[n] + 1e-15
aerr = min(aerr0, max(np.abs(tval) * 1e-6, 1e-8))
try:
assert_allclose(np.real(vals[n]), tval, rtol=1e-6, atol=aerr)
except AssertionError as error:
print(n, name, y, vals[n], tval, info.iterations, aerr0, aerr)
note(
"{}, {}, {}, {}, {}, {}, {}, {}".format(
n, name, y, vals[n], tval, info.iterations, aerr0, aerr
)
)
raise error
[docs]
def test_all_weights():
w = fd_weights_all(range(-2, 3), n=4)
print(w)
true_w = [
[0.0, 0.0, 1.0, 0.0, 0.0],
[0.0833333333333, -0.6666666666667, 0.0, 0.6666666666667, -0.0833333333333],
[-0.0833333333333, 1.333333333333, -2.5, 1.333333333333, -0.083333333333],
[-0.5, 1.0, 0.0, -1.0, 0.5],
[1.0, -4.0, 6.0, -4.0, 1.0],
]
assert_allclose(w, true_w, atol=1e-12)
[docs]
def test_weights():
for name in CENTRAL_WEIGHTS_AND_POINTS:
# print(name)
n, m = name
w, x = CENTRAL_WEIGHTS_AND_POINTS[name]
assert len(w) == m
weights = fd_weights(np.array(x, dtype=float), 0.0, n=n)
assert_allclose(weights, w, atol=1e-15)
[docs]
def test_fd_derivative():
x = np.linspace(-1, 1, 25)
fx = np.exp(x)
for n in range(1, 7):
df = fd_derivative(fx, x, n=n)
m = n // 2 + 2
assert_allclose(df[m:-m], fx[m:-m], atol=1e-5)
assert_allclose(df[-m:], fx[-m:], atol=1e-4)
assert_allclose(df[:m], fx[:m], atol=1e-4)
[docs]
class ExampleFunctions(object):
[docs]
@staticmethod
def fun0(z):
return np.exp(z)
[docs]
@staticmethod
def fun1(z):
return np.exp(z) / (np.sin(z) ** 3 + np.cos(z) ** 3)
[docs]
@staticmethod
def fun2(z):
return np.exp(1.0j * z)
[docs]
@staticmethod
def fun3(z):
return z**6
[docs]
@staticmethod
def fun4(z):
return z * (0.5 + 1.0 / np.expm1(z))
[docs]
@staticmethod
def fun5(z):
return np.tan(z)
[docs]
@staticmethod
def fun6(z):
return 1.0j + z + 1.0j * z**2
[docs]
@staticmethod
def fun7(z):
return 1.0 / (1.0 - z)
[docs]
@staticmethod
def fun8(z):
return (1 + z) ** 10 * np.log1p(z)
[docs]
@staticmethod
def fun9(z):
return 10 * 5 + 1.0 / (1 - z)
[docs]
@staticmethod
def fun10(z):
return 1.0 / (1 - z)
[docs]
@staticmethod
def fun11(z):
return np.sqrt(z)
[docs]
@staticmethod
def fun12(z):
return np.arcsinh(z)
[docs]
@staticmethod
def fun13(z):
return np.cos(z)
[docs]
@staticmethod
def fun14(z):
return np.log1p(z)
[docs]
def test_low_order_derivative_on_example_functions():
for j in range(15):
fun = getattr(ExampleFunctions, "fun{}".format(j))
der, info = derivative(fun, z0=0.0, r=0.06, n=10, max_iter=30, full_output=True, step_ratio=1.6)
print(info)
print("answer:")
msg = "{0:3d}: {1:24.18f} + {2:24.18f}j ({3:g})"
print(info.function_count)
for i, der_i in enumerate(der):
err = info.error_estimate[i]
print(msg.format(i, der_i.real, der_i.imag, err))