'''
Created on 22. apr. 2015
@author: pab
'''
import unittest
# from functools import partial
from numdifftools.multicomplex import bicomplex
from numdifftools.test_functions import get_function
import numpy as np
EPS = np.MachAr().eps
def _default_base_step(x, scale, epsilon=None):
h = (10 * EPS) ** (1. / scale) * np.maximum(np.log1p(np.abs(x)), 0.1)
return h
[docs]class BicomplexTester(unittest.TestCase):
def test_init(self):
z = bicomplex(1, 2)
np.testing.assert_array_equal(z.z1, 1)
np.testing.assert_array_equal(z.z2, 2)
def test_neg(self):
z = bicomplex(1, 2)
z2 = -z
self.assertEqual(z2.z1, -z.z1)
self.assertEqual(z2.z2, -z.z2)
def test_subsref(self):
shape = (3, 3)
t = np.arange(9).reshape(shape)
z = bicomplex(t, 2 * t)
z0 = z[0]
np.testing.assert_array_equal(z0.z1, z.z1[0])
np.testing.assert_array_equal(z0.z2, z.z2[0])
z1 = z[:]
np.testing.assert_array_equal(z1.z1, z.z1[:])
np.testing.assert_array_equal(z1.z2, z.z2[:])
z1 = z[1:3, 1:3]
np.testing.assert_array_equal(z1.z1, z.z1[1:3, 1:3])
np.testing.assert_array_equal(z1.z2, z.z2[1:3, 1:3])
def test_assign(self):
shape = (3, 3)
z = bicomplex(np.ones(shape), 2 * np.ones(shape))
z0 = z[0]
np.testing.assert_array_equal(z0.z1, z.z1[0])
np.testing.assert_array_equal(z0.z2, z.z2[0])
z1 = z[:]
np.testing.assert_array_equal(z1.z1, z.z1[:])
np.testing.assert_array_equal(z1.z2, z.z2[:])
def test_add(self):
shape = (3, 3)
z0 = bicomplex(np.ones(shape), 2 * np.ones(shape))
z1 = bicomplex(3 * np.ones(shape), 4 * np.ones(shape))
z2 = z0 + z1
np.testing.assert_array_equal(z2.z1, z0.z1 + z1.z1)
np.testing.assert_array_equal(z2.z2, z0.z2 + z1.z2)
z3 = z0 + 1
np.testing.assert_array_equal(z3.z1, z0.z1 + 1)
np.testing.assert_array_equal(z3.z2, z0.z2)
def test_sub(self):
shape = (3, 3)
z0 = bicomplex(np.ones(shape), 2 * np.ones(shape))
z1 = bicomplex(3 * np.ones(shape), 4 * np.ones(shape))
z2 = z0 - z1
np.testing.assert_array_equal(z2.z1, z0.z1 - z1.z1)
np.testing.assert_array_equal(z2.z2, z0.z2 - z1.z2)
def test_rsub(self):
z1 = bicomplex(2, 1)
a = 1 + 1j
z2 = a - z1
np.testing.assert_array_equal(z2.z1, a - z1.z1)
np.testing.assert_array_equal(z2.z2, -z1.z2)
def test_repr(self):
z = bicomplex(1, 2)
txt = repr(z)
self.assertEqual(txt, "bicomplex(z1=(1+0j), z2=(2+0j))")
def test_multiplication(self):
z1 = bicomplex(1, 2)
z2 = bicomplex(3, 4)
z3 = z1 * z2
np.testing.assert_array_equal(z3.z1, z1.z1 * z2.z1 - z1.z2 * z2.z2)
np.testing.assert_array_equal(z3.z2, z1.z1 * z2.z2 + z1.z2 * z2.z1)
def test_pow(self):
z1 = bicomplex(1, 2)
z2 = z1 ** 2
z3 = z1 * z1
np.testing.assert_allclose(z2.z1, z1.z1 * z1.z1 - z1.z2 * z1.z2)
np.testing.assert_allclose(z2.z2, z1.z1 * z1.z2 + z1.z2 * z1.z1)
np.testing.assert_allclose(z3.z1, z1.z1 * z1.z1 - z1.z2 * z1.z2)
np.testing.assert_allclose(z3.z2, z1.z1 * z1.z2 + z1.z2 * z1.z1)
z1 = bicomplex(z1=(-1j), z2=(-1-0j))
z2 = z1 * z1
z3 = z1 ** 2
np.testing.assert_allclose(z2.z1, z1.z1 * z1.z1 - z1.z2 * z1.z2)
np.testing.assert_allclose(z2.z2, z1.z1 * z1.z2 + z1.z2 * z1.z1)
np.testing.assert_allclose(z3.z1, z1.z1 * z1.z1 - z1.z2 * z1.z2)
np.testing.assert_allclose(z3.z2, z1.z1 * z1.z2 + z1.z2 * z1.z1)
def test_division(self):
z1 = bicomplex(1, 2)
z2 = bicomplex(3, 4)
z3 = z1 / z2
z4 = z1 * (z2**-1)
np.testing.assert_allclose(z3.z1, z4.z1)
np.testing.assert_allclose(z3.z2, z4.z2)
# TODO: test_rdivision crashes on python3.4 on travis
# def test_rdivision(self):
#
# z2 = bicomplex(3, 4)
# z3 = 1 / z2
# z4 = (z2**-1)
# np.testing.assert_array_equal(z3.z1, z4.z1)
# np.testing.assert_array_equal(z3.z2, z4.z2)
def test_rpow(self):
z2 = bicomplex(3, 4)
z3 = 2. ** z2
z4 = np.exp(z2*np.log(2))
np.testing.assert_allclose(z3.z1, z4.z1)
np.testing.assert_allclose(z3.z2, z4.z2)
def test_dot(self):
z1 = bicomplex(1, 2)
z2 = bicomplex(3, 4)
z3 = z1.dot(z2)
z4 = z1 * z2
np.testing.assert_array_equal(z3.z1, z4.z1)
np.testing.assert_array_equal(z3.z2, z4.z2)
def test_cos(self):
z1 = bicomplex(np.linspace(0, np.pi, 5), 0)
z2 = z1.cos() # np.cos(z1)
np.testing.assert_array_equal(z2.z1, np.cos(z1.z1))
def test_arg_c(self):
z1 = bicomplex(np.linspace(0, np.pi, 5), 0)
z2 = z1.arg_c()
np.testing.assert_array_equal(z2, np.arctan2(z1.z2.real, z1.z1.real))
z3 = bicomplex(0.1, np.linspace(0, np.pi, 5))
z4 = z3.arg_c()
np.testing.assert_allclose(z4.real, np.arctan2(z3.z2.real, z3.z1.real))
def test_arcsin(self):
z1 = bicomplex(np.linspace(-0.98, 0.98, 5), 0)
z2 = z1.arcsin()
np.testing.assert_allclose(z2.real, np.arcsin(z1.z1).real)
np.testing.assert_allclose(z2.imag1, np.arcsin(z1.z1).imag)
def test_arccos(self):
z1 = bicomplex(np.linspace(-0.98, 0.98, 5), 0)
z2 = z1.arccos()
np.testing.assert_allclose(z2.real, np.arccos(z1.z1).real)
np.testing.assert_allclose(z2.imag1, np.arccos(z1.z1).imag)
def test_der_cos(self):
x = np.linspace(-0.99, 0.99, 5)
h = 1e-9
der1 = np.cos(bicomplex(x + h * 1j, 0)).imag1 / h
np.testing.assert_allclose(der1, - np.sin(x))
h *= 100
der2 = np.cos(bicomplex(x + h * 1j, h)).imag12 / h**2
np.testing.assert_allclose(der2, -np.cos(x))
def test_der_log(self):
x = np.linspace(0.001, 5, 6)
h = 1e-15
der1 = np.log(bicomplex(x + h * 1j, 0)).imag1 / h
np.testing.assert_allclose(der1, 1./x)
der2 = np.log(bicomplex(x + h * 1j, h)).imag12 / h**2
np.testing.assert_allclose(der2, -1./x**2)
def test_der_arccos(self):
x = np.linspace(-0.98, 0.98, 5)
h = 1e-8
der1 = np.arccos(bicomplex(x + h * 1j, 0)).imag1 / h
np.testing.assert_allclose(der1, -1. / np.sqrt(1 - x**2))
h = (_default_base_step(x, scale=2.5) + 1) - 1
der2 = np.arccos(bicomplex(x + h * 1j, h)).imag12 / h**2
true_der2 = -x / (1 - x**2)**(3. / 2)
np.testing.assert_allclose(der2, true_der2, atol=1e-5)
def test_der_abs(self):
x = np.linspace(-0.98, 0.98, 5)
h = 1e-8
der1 = abs(bicomplex(x + h * 1j, 0)).imag1 / h
np.testing.assert_allclose(der1, np.where(x < 0, -1, 1))
der2 = abs(bicomplex(x + h * 1j, h)).imag12 / h**2
np.testing.assert_allclose(der2, 0, atol=1e-6)
def test_der_arctan(self):
x = np.linspace(0, 2, 5)
h = 1e-8
der1 = np.arctan(bicomplex(x + h * 1j, 0)).imag1 / h
np.testing.assert_allclose(der1, 1. / (1 + x**2))
der2 = bicomplex(x+h*1j, h).arctan().imag12/h**2
np.testing.assert_allclose(der2, -2*x/(1+x**2)**2)
# pass
def _test_first_derivative(name):
x = np.linspace(0.0001, 0.98, 5)
h = _default_base_step(x, scale=2)
f, df = get_function(name, n=1)
der = f(bicomplex(x + h * 1j, 0)).imag1 / h
der_true = df(x)
np.testing.assert_allclose(der, der_true, err_msg=('%s' % name))
def _test_second_derivative(name):
x = np.linspace(0.01, 0.98, 5)
h = _default_base_step(x, scale=2.5)
# h = 1e-8
f, df = get_function(name, n=2)
der = f(bicomplex(x + h * 1j, h)).imag12 / h**2
der_true = df(x)
np.testing.assert_allclose(der, der_true, err_msg=('%s' % name))
_function_names = ['cos', 'sin', 'tan', 'arccos', 'arcsin', 'arctan', 'cosh',
'sinh', 'tanh', 'exp', 'log', 'exp2', 'square', 'sqrt',
'log1p', 'expm1', 'log10', 'log2', 'arcsinh', 'arctanh']
[docs]class DerivativeTester(unittest.TestCase):
[docs] def test_all_first_derivatives(self):
for name in _function_names:
_test_first_derivative(name)
[docs] def test_all_second_derivatives(self):
for name in _function_names:
_test_second_derivative(name)
# for name in _function_names:
# for i, derivative in enumerate([_test_first_derivative,
# _test_second_derivative]):
# testname = 'test_n%d_derivative_%s' % (i+1, name)
# testfunc = partial(derivative, name)
# testfunc.__doc__ = testname
# setattr(DerivativeTester, testname, testfunc)
if __name__ == "__main__":
# import sys;sys.argv = ['', 'Test.testName']
unittest.main()