def slope(self, x):
if self.option == 0:
return self.gradient(x)
if self.option == 1:
# implement AD here
obj = AD.AutoDiff(x)
return self.curve(obj).dx
if self.option == 2:
# implement numerical method here
h = 1e-2
return (self.curve(x + h) - self.curve(x)) / h
def test_log_invalid_base():
with pytest.raises(ValueError):
AD.log(x1, base='a')
def test_cos_log10_rpow():
f = AD.cos(AD.log(2**x1, base=10))
assert tol > abs(f.x - 0.82417070595)
assert tol > abs(f.dx - -0.17048576675265)
def test_tan_exp_div_neg():
f = -AD.tan(x1) / AD.exp(x1)
assert tol > abs(f.x - 0.29571298878)
assert tol > abs(f.dx - -1.077192940578)
def test_sin_pow_log():
f = AD.sin(x1)**2 * AD.log(x1)
assert tol > abs(f.x - 0.573109206726)
assert tol > abs(f.dx - -0.111164610647518727)
def test_logistic():
f = AD.logistic(x1)
assert f.x == 1 / (1 + np.exp(-2))
assert f.dx == np.exp(-2) / (1 + np.exp(-2))**2
f = AD.logistic(2.0)
assert f == 1 / (1 + np.exp(-2.0))
def test_exp():
f = AD.exp(x1)
assert f.x == np.exp(2)
assert f.dx == np.exp(2)
f = AD.exp(2)
assert f == np.exp(2)
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import modules.rollingball as RB
import AutoDiff_CKMZ.modules.AutoDiff as AD
from time import time
function_list = [lambda x: AD.sin(x),
lambda x: AD.exp(x),
lambda x: x * AD.sin(x),
lambda x: - AD.log(x),
lambda x: AD.sinh(x),
lambda x: AD.exp(AD.cos(x)),
lambda x: 2 ** x,
lambda x: 1 / AD.tan(x),
lambda x: AD.sin(x) / x,
lambda x: x ** 2]
derivative_list = [lambda x: np.cos(x),
lambda x: np.exp(x),
lambda x: np.sin(x) + x * np.cos(x),
lambda x: -1 / x,
lambda x: np.cosh(x),
lambda x: - np.exp(np.cos(x)) * np.sin(x),
lambda x: 2 ** x * np.log(2),
lambda x: - 1 / np.sin(x) ** 2,
lambda x: (x * np.cos(x) - np.sin(x)) / x ** 2,
lambda x: 2 * x]
class function():
def test_arcsin():
f = AD.arcsin(AD.AutoDiff(0.5))
assert f.x == np.arcsin(0.5)
assert f.dx == 1 / np.sqrt(1 - 0.5**2)
f = AD.arcsin(0.5)
assert f == np.arcsin(0.5)
def test_arccos():
f = AD.arccos(AD.AutoDiff(0.5))
assert f.x == np.arccos(0.5)
assert f.dx == -1 / np.sqrt(1 - 0.5**2)
f = AD.arccos(0.5)
assert f == np.arccos(0.5)
def test_arctan():
f = AD.arctan(x1)
assert f.x == np.arctan(2)
assert f.dx == 1 / (1 + 2**2)
f = AD.arctan(0.5)
assert f == np.arctan(0.5)
def test_tan():
f = AD.tan(x1)
assert f.x == np.tan(2)
assert f.dx == 1 / np.cos(2)**2
f = AD.tan(0.5)
assert f == np.tan(0.5)
def test_cos():
f = AD.cos(x1)
assert f.x == np.cos(2)
assert f.dx == -np.sin(2)
f = AD.cos(0.2)
assert f == np.cos(0.2)
def test_sin():
f = AD.sin(x1)
assert f.x == np.sin(2)
assert f.dx == np.cos(2)
f = AD.sin(1)
assert f == np.sin(1)
def test_log():
f = AD.log(x1)
assert f.x == np.log(2)
assert f.dx == 1 / 2
f = AD.log(2)
assert f == np.log(2)
def test_multivariate():
f = x3[0] * AD.exp(3 * x3[1])
assert f.dx[0] == 1
assert f.dx[1] == 6
def test_eq():
assert x1 == AD.AutoDiff(2.0)
assert AD.AutoDiff(2.0, 0) == 2.0
def test_tanh():
f = AD.tanh(x1)
assert f.x == np.tanh(2)
assert f.dx == 1 / (np.cosh(2)**2)
f = AD.tanh(2)
assert f == np.tanh(2)
def test_sinh():
f = AD.sinh(x1)
assert f.x == np.sinh(2)
assert f.dx == np.cosh(2)
f = AD.sinh(0.5)
assert f == np.sinh(0.5)
import pytest
import numpy as np
#from AutoDiff_CKMZ.modules.AutoDiff import AutoDiff
import AutoDiff_CKMZ.modules.AutoDiff as AD
x1 = AD.AutoDiff(2.0)
x2 = AD.AutoDiff(3.0)
tol = 1e-8
def test_add():
f = x1 + 3
assert f.x == 5
assert f.dx == 1
def test_radd():
f = 1 + x1
assert f.x == 3
assert f.dx == 1
def test_sub():
f = x1 - 3
assert f.x == -1
assert f.dx == 1
def test_rsub():
f = 3 - x1