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편집 파일: test_umath_complex.py

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()