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from __future__ import division, absolute_import, print_function
import sys
import platform
import numpy as np
import numpy.core.umath as ncu
from numpy.testing import (
TestCase, run_module_suite, assert_equal, assert_array_equal,
assert_almost_equal, dec
)
# TODO: branch cuts (use Pauli code)
# TODO: conj 'symmetry'
# TODO: FPU exceptions
# At least on Windows the results of many complex functions are not conforming
# to the C99 standard. See ticket 1574.
# Ditto for Solaris (ticket 1642) and OS X on PowerPC.
with np.errstate(all='ignore'):
functions_seem_flaky = ((np.exp(complex(np.inf, 0)).imag != 0)
or (np.log(complex(np.NZERO, 0)).imag != np.pi))
# TODO: replace with a check on whether platform-provided C99 funcs are used
skip_complex_tests = (not sys.platform.startswith('linux') or functions_seem_flaky)
def platform_skip(func):
return dec.skipif(skip_complex_tests,
"Numpy is using complex functions (e.g. sqrt) provided by your"
"platform's C library. However, they do not seem to behave according"
"to C99 -- so C99 tests are skipped.")(func)
class TestCexp(object):
def test_simple(self):
check = check_complex_value
f = np.exp
yield check, f, 1, 0, np.exp(1), 0, False
yield check, f, 0, 1, np.cos(1), np.sin(1), False
ref = np.exp(1) * np.complex(np.cos(1), np.sin(1))
yield check, f, 1, 1, ref.real, ref.imag, False
@platform_skip
def test_special_values(self):
# C99: Section G 6.3.1
check = check_complex_value
f = np.exp
# cexp(+-0 + 0i) is 1 + 0i
yield check, f, np.PZERO, 0, 1, 0, False
yield check, f, np.NZERO, 0, 1, 0, False
# cexp(x + infi) is nan + nani for finite x and raises 'invalid' FPU
# exception
yield check, f, 1, np.inf, np.nan, np.nan
yield check, f, -1, np.inf, np.nan, np.nan
yield check, f, 0, np.inf, np.nan, np.nan
# cexp(inf + 0i) is inf + 0i
yield check, f, np.inf, 0, np.inf, 0
# cexp(-inf + yi) is +0 * (cos(y) + i sin(y)) for finite y
yield check, f, -np.inf, 1, np.PZERO, np.PZERO
yield check, f, -np.inf, 0.75 * np.pi, np.NZERO, np.PZERO
# cexp(inf + yi) is +inf * (cos(y) + i sin(y)) for finite y
yield check, f, np.inf, 1, np.inf, np.inf
yield check, f, np.inf, 0.75 * np.pi, -np.inf, np.inf
# cexp(-inf + inf i) is +-0 +- 0i (signs unspecified)
def _check_ninf_inf(dummy):
msgform = "cexp(-inf, inf) is (%f, %f), expected (+-0, +-0)"
with np.errstate(invalid='ignore'):
z = f(np.array(np.complex(-np.inf, np.inf)))
if z.real != 0 or z.imag != 0:
raise AssertionError(msgform % (z.real, z.imag))
yield _check_ninf_inf, None
# cexp(inf + inf i) is +-inf + NaNi and raised invalid FPU ex.
def _check_inf_inf(dummy):
msgform = "cexp(inf, inf) is (%f, %f), expected (+-inf, nan)"
with np.errstate(invalid='ignore'):
z = f(np.array(np.complex(np.inf, np.inf)))
if not np.isinf(z.real) or not np.isnan(z.imag):
raise AssertionError(msgform % (z.real, z.imag))
yield _check_inf_inf, None
# cexp(-inf + nan i) is +-0 +- 0i
def _check_ninf_nan(dummy):
msgform = "cexp(-inf, nan) is (%f, %f), expected (+-0, +-0)"
with np.errstate(invalid='ignore'):
z = f(np.array(np.complex(-np.inf, np.nan)))
if z.real != 0 or z.imag != 0:
raise AssertionError(msgform % (z.real, z.imag))
yield _check_ninf_nan, None
# cexp(inf + nan i) is +-inf + nan
def _check_inf_nan(dummy):
msgform = "cexp(-inf, nan) is (%f, %f), expected (+-inf, nan)"
with np.errstate(invalid='ignore'):
z = f(np.array(np.complex(np.inf, np.nan)))
if not np.isinf(z.real) or not np.isnan(z.imag):
raise AssertionError(msgform % (z.real, z.imag))
yield _check_inf_nan, None
# cexp(nan + yi) is nan + nani for y != 0 (optional: raises invalid FPU
# ex)
yield check, f, np.nan, 1, np.nan, np.nan
yield check, f, np.nan, -1, np.nan, np.nan
yield check, f, np.nan, np.inf, np.nan, np.nan
yield check, f, np.nan, -np.inf, np.nan, np.nan
# cexp(nan + nani) is nan + nani
yield check, f, np.nan, np.nan, np.nan, np.nan
@dec.knownfailureif(True, "cexp(nan + 0I) is wrong on most implementations")
def test_special_values2(self):
# XXX: most implementations get it wrong here (including glibc <= 2.10)
# cexp(nan + 0i) is nan + 0i
check = check_complex_value
f = np.exp
yield check, f, np.nan, 0, np.nan, 0
class TestClog(TestCase):
def test_simple(self):
x = np.array([1+0j, 1+2j])
y_r = np.log(np.abs(x)) + 1j * np.angle(x)
y = np.log(x)
for i in range(len(x)):
assert_almost_equal(y[i], y_r[i])
@platform_skip
@dec.skipif(platform.machine() == "armv5tel", "See gh-413.")
def test_special_values(self):
xl = []
yl = []
# From C99 std (Sec 6.3.2)
# XXX: check exceptions raised
# --- raise for invalid fails.
# clog(-0 + i0) returns -inf + i pi and raises the 'divide-by-zero'
# floating-point exception.
with np.errstate(divide='raise'):
x = np.array([np.NZERO], dtype=np.complex)
y = np.complex(-np.inf, np.pi)
self.assertRaises(FloatingPointError, np.log, x)
with np.errstate(divide='ignore'):
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(+0 + i0) returns -inf + i0 and raises the 'divide-by-zero'
# floating-point exception.
with np.errstate(divide='raise'):
x = np.array([0], dtype=np.complex)
y = np.complex(-np.inf, 0)
self.assertRaises(FloatingPointError, np.log, x)
with np.errstate(divide='ignore'):
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(x + i inf returns +inf + i pi /2, for finite x.
x = np.array([complex(1, np.inf)], dtype=np.complex)
y = np.complex(np.inf, 0.5 * np.pi)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
x = np.array([complex(-1, np.inf)], dtype=np.complex)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(x + iNaN) returns NaN + iNaN and optionally raises the
# 'invalid' floating- point exception, for finite x.
with np.errstate(invalid='raise'):
x = np.array([complex(1., np.nan)], dtype=np.complex)
y = np.complex(np.nan, np.nan)
#self.assertRaises(FloatingPointError, np.log, x)
with np.errstate(invalid='ignore'):
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
with np.errstate(invalid='raise'):
x = np.array([np.inf + 1j * np.nan], dtype=np.complex)
#self.assertRaises(FloatingPointError, np.log, x)
with np.errstate(invalid='ignore'):
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(- inf + iy) returns +inf + ipi , for finite positive-signed y.
x = np.array([-np.inf + 1j], dtype=np.complex)
y = np.complex(np.inf, np.pi)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(+ inf + iy) returns +inf + i0, for finite positive-signed y.
x = np.array([np.inf + 1j], dtype=np.complex)
y = np.complex(np.inf, 0)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(- inf + i inf) returns +inf + i3pi /4.
x = np.array([complex(-np.inf, np.inf)], dtype=np.complex)
y = np.complex(np.inf, 0.75 * np.pi)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(+ inf + i inf) returns +inf + ipi /4.
x = np.array([complex(np.inf, np.inf)], dtype=np.complex)
y = np.complex(np.inf, 0.25 * np.pi)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(+/- inf + iNaN) returns +inf + iNaN.
x = np.array([complex(np.inf, np.nan)], dtype=np.complex)
y = np.complex(np.inf, np.nan)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
x = np.array([complex(-np.inf, np.nan)], dtype=np.complex)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(NaN + iy) returns NaN + iNaN and optionally raises the
# 'invalid' floating-point exception, for finite y.
x = np.array([complex(np.nan, 1)], dtype=np.complex)
y = np.complex(np.nan, np.nan)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(NaN + i inf) returns +inf + iNaN.
x = np.array([complex(np.nan, np.inf)], dtype=np.complex)
y = np.complex(np.inf, np.nan)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(NaN + iNaN) returns NaN + iNaN.
x = np.array([complex(np.nan, np.nan)], dtype=np.complex)
y = np.complex(np.nan, np.nan)
assert_almost_equal(np.log(x), y)
xl.append(x)
yl.append(y)
# clog(conj(z)) = conj(clog(z)).
xa = np.array(xl, dtype=np.complex)
ya = np.array(yl, dtype=np.complex)
with np.errstate(divide='ignore'):
for i in range(len(xa)):
assert_almost_equal(np.log(xa[i].conj()), ya[i].conj())
class TestCsqrt(object):
def test_simple(self):
# sqrt(1)
yield check_complex_value, np.sqrt, 1, 0, 1, 0
# sqrt(1i)
yield check_complex_value, np.sqrt, 0, 1, 0.5*np.sqrt(2), 0.5*np.sqrt(2), False
# sqrt(-1)
yield check_complex_value, np.sqrt, -1, 0, 0, 1
def test_simple_conjugate(self):
ref = np.conj(np.sqrt(np.complex(1, 1)))
def f(z):
return np.sqrt(np.conj(z))
yield check_complex_value, f, 1, 1, ref.real, ref.imag, False
#def test_branch_cut(self):
# _check_branch_cut(f, -1, 0, 1, -1)
@platform_skip
def test_special_values(self):
# C99: Sec G 6.4.2
check = check_complex_value
f = np.sqrt
# csqrt(+-0 + 0i) is 0 + 0i
yield check, f, np.PZERO, 0, 0, 0
yield check, f, np.NZERO, 0, 0, 0
# csqrt(x + infi) is inf + infi for any x (including NaN)
yield check, f, 1, np.inf, np.inf, np.inf
yield check, f, -1, np.inf, np.inf, np.inf
yield check, f, np.PZERO, np.inf, np.inf, np.inf
yield check, f, np.NZERO, np.inf, np.inf, np.inf
yield check, f, np.inf, np.inf, np.inf, np.inf
yield check, f, -np.inf, np.inf, np.inf, np.inf
yield check, f, -np.nan, np.inf, np.inf, np.inf
# csqrt(x + nani) is nan + nani for any finite x
yield check, f, 1, np.nan, np.nan, np.nan
yield check, f, -1, np.nan, np.nan, np.nan
yield check, f, 0, np.nan, np.nan, np.nan
# csqrt(-inf + yi) is +0 + infi for any finite y > 0
yield check, f, -np.inf, 1, np.PZERO, np.inf
# csqrt(inf + yi) is +inf + 0i for any finite y > 0
yield check, f, np.inf, 1, np.inf, np.PZERO
# csqrt(-inf + nani) is nan +- infi (both +i infi are valid)
def _check_ninf_nan(dummy):
msgform = "csqrt(-inf, nan) is (%f, %f), expected (nan, +-inf)"
z = np.sqrt(np.array(np.complex(-np.inf, np.nan)))
#Fixme: ugly workaround for isinf bug.
with np.errstate(invalid='ignore'):
if not (np.isnan(z.real) and np.isinf(z.imag)):
raise AssertionError(msgform % (z.real, z.imag))
yield _check_ninf_nan, None
# csqrt(+inf + nani) is inf + nani
yield check, f, np.inf, np.nan, np.inf, np.nan
# csqrt(nan + yi) is nan + nani for any finite y (infinite handled in x
# + nani)
yield check, f, np.nan, 0, np.nan, np.nan
yield check, f, np.nan, 1, np.nan, np.nan
yield check, f, np.nan, np.nan, np.nan, np.nan
# XXX: check for conj(csqrt(z)) == csqrt(conj(z)) (need to fix branch
# cuts first)
class TestCpow(TestCase):
def setUp(self):
self.olderr = np.seterr(invalid='ignore')
def tearDown(self):
np.seterr(**self.olderr)
def test_simple(self):
x = np.array([1+1j, 0+2j, 1+2j, np.inf, np.nan])
y_r = x ** 2
y = np.power(x, 2)
for i in range(len(x)):
assert_almost_equal(y[i], y_r[i])
def test_scalar(self):
x = np.array([1, 1j, 2, 2.5+.37j, np.inf, np.nan])
y = np.array([1, 1j, -0.5+1.5j, -0.5+1.5j, 2, 3])
lx = list(range(len(x)))
# Compute the values for complex type in python
p_r = [complex(x[i]) ** complex(y[i]) for i in lx]
# Substitute a result allowed by C99 standard
p_r[4] = complex(np.inf, np.nan)
# Do the same with numpy complex scalars
n_r = [x[i] ** y[i] for i in lx]
for i in lx:
assert_almost_equal(n_r[i], p_r[i], err_msg='Loop %d\n' % i)
def test_array(self):
x = np.array([1, 1j, 2, 2.5+.37j, np.inf, np.nan])
y = np.array([1, 1j, -0.5+1.5j, -0.5+1.5j, 2, 3])
lx = list(range(len(x)))
# Compute the values for complex type in python
p_r = [complex(x[i]) ** complex(y[i]) for i in lx]
# Substitute a result allowed by C99 standard
p_r[4] = complex(np.inf, np.nan)
# Do the same with numpy arrays
n_r = x ** y
for i in lx:
assert_almost_equal(n_r[i], p_r[i], err_msg='Loop %d\n' % i)
class TestCabs(object):
def setUp(self):
self.olderr = np.seterr(invalid='ignore')
def tearDown(self):
np.seterr(**self.olderr)
def test_simple(self):
x = np.array([1+1j, 0+2j, 1+2j, np.inf, np.nan])
y_r = np.array([np.sqrt(2.), 2, np.sqrt(5), np.inf, np.nan])
y = np.abs(x)
for i in range(len(x)):
assert_almost_equal(y[i], y_r[i])
def test_fabs(self):
# Test that np.abs(x +- 0j) == np.abs(x) (as mandated by C99 for cabs)
x = np.array([1+0j], dtype=np.complex)
assert_array_equal(np.abs(x), np.real(x))
x = np.array([complex(1, np.NZERO)], dtype=np.complex)
assert_array_equal(np.abs(x), np.real(x))
x = np.array([complex(np.inf, np.NZERO)], dtype=np.complex)
assert_array_equal(np.abs(x), np.real(x))
x = np.array([complex(np.nan, np.NZERO)], dtype=np.complex)
assert_array_equal(np.abs(x), np.real(x))
def test_cabs_inf_nan(self):
x, y = [], []
# cabs(+-nan + nani) returns nan
x.append(np.nan)
y.append(np.nan)
yield check_real_value, np.abs, np.nan, np.nan, np.nan
x.append(np.nan)
y.append(-np.nan)
yield check_real_value, np.abs, -np.nan, np.nan, np.nan
# According to C99 standard, if exactly one of the real/part is inf and
# the other nan, then cabs should return inf
x.append(np.inf)
y.append(np.nan)
yield check_real_value, np.abs, np.inf, np.nan, np.inf
x.append(-np.inf)
y.append(np.nan)
yield check_real_value, np.abs, -np.inf, np.nan, np.inf
# cabs(conj(z)) == conj(cabs(z)) (= cabs(z))
def f(a):
return np.abs(np.conj(a))
def g(a, b):
return np.abs(np.complex(a, b))
xa = np.array(x, dtype=np.complex)
for i in range(len(xa)):
ref = g(x[i], y[i])
yield check_real_value, f, x[i], y[i], ref
class TestCarg(object):
def test_simple(self):
check_real_value(ncu._arg, 1, 0, 0, False)
check_real_value(ncu._arg, 0, 1, 0.5*np.pi, False)
check_real_value(ncu._arg, 1, 1, 0.25*np.pi, False)
check_real_value(ncu._arg, np.PZERO, np.PZERO, np.PZERO)
@dec.knownfailureif(True,
"Complex arithmetic with signed zero is buggy on most implementation")
def test_zero(self):
# carg(-0 +- 0i) returns +- pi
yield check_real_value, ncu._arg, np.NZERO, np.PZERO, np.pi, False
yield check_real_value, ncu._arg, np.NZERO, np.NZERO, -np.pi, False
# carg(+0 +- 0i) returns +- 0
yield check_real_value, ncu._arg, np.PZERO, np.PZERO, np.PZERO
yield check_real_value, ncu._arg, np.PZERO, np.NZERO, np.NZERO
# carg(x +- 0i) returns +- 0 for x > 0
yield check_real_value, ncu._arg, 1, np.PZERO, np.PZERO, False
yield check_real_value, ncu._arg, 1, np.NZERO, np.NZERO, False
# carg(x +- 0i) returns +- pi for x < 0
yield check_real_value, ncu._arg, -1, np.PZERO, np.pi, False
yield check_real_value, ncu._arg, -1, np.NZERO, -np.pi, False
# carg(+- 0 + yi) returns pi/2 for y > 0
yield check_real_value, ncu._arg, np.PZERO, 1, 0.5 * np.pi, False
yield check_real_value, ncu._arg, np.NZERO, 1, 0.5 * np.pi, False
# carg(+- 0 + yi) returns -pi/2 for y < 0
yield check_real_value, ncu._arg, np.PZERO, -1, 0.5 * np.pi, False
yield check_real_value, ncu._arg, np.NZERO, -1, -0.5 * np.pi, False
#def test_branch_cuts(self):
# _check_branch_cut(ncu._arg, -1, 1j, -1, 1)
def test_special_values(self):
# carg(-np.inf +- yi) returns +-pi for finite y > 0
yield check_real_value, ncu._arg, -np.inf, 1, np.pi, False
yield check_real_value, ncu._arg, -np.inf, -1, -np.pi, False
# carg(np.inf +- yi) returns +-0 for finite y > 0
yield check_real_value, ncu._arg, np.inf, 1, np.PZERO, False
yield check_real_value, ncu._arg, np.inf, -1, np.NZERO, False
# carg(x +- np.infi) returns +-pi/2 for finite x
yield check_real_value, ncu._arg, 1, np.inf, 0.5 * np.pi, False
yield check_real_value, ncu._arg, 1, -np.inf, -0.5 * np.pi, False
# carg(-np.inf +- np.infi) returns +-3pi/4
yield check_real_value, ncu._arg, -np.inf, np.inf, 0.75 * np.pi, False
yield check_real_value, ncu._arg, -np.inf, -np.inf, -0.75 * np.pi, False
# carg(np.inf +- np.infi) returns +-pi/4
yield check_real_value, ncu._arg, np.inf, np.inf, 0.25 * np.pi, False
yield check_real_value, ncu._arg, np.inf, -np.inf, -0.25 * np.pi, False
# carg(x + yi) returns np.nan if x or y is nan
yield check_real_value, ncu._arg, np.nan, 0, np.nan, False
yield check_real_value, ncu._arg, 0, np.nan, np.nan, False
yield check_real_value, ncu._arg, np.nan, np.inf, np.nan, False
yield check_real_value, ncu._arg, np.inf, np.nan, np.nan, False
def check_real_value(f, x1, y1, x, exact=True):
z1 = np.array([complex(x1, y1)])
if exact:
assert_equal(f(z1), x)
else:
assert_almost_equal(f(z1), x)
def check_complex_value(f, x1, y1, x2, y2, exact=True):
z1 = np.array([complex(x1, y1)])
z2 = np.complex(x2, y2)
with np.errstate(invalid='ignore'):
if exact:
assert_equal(f(z1), z2)
else:
assert_almost_equal(f(z1), z2)
if __name__ == "__main__":
run_module_suite()
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