Viewing file: test_umath_complex.py (17.31 KB) -rw-r--r-- Select action/file-type: (+) | (+) | (+) | Code (+) | Session (+) | (+) | SDB (+) | (+) | (+) | (+) | (+) | (+) |
from numpy.testing import * import numpy.core.umath as ncu import numpy as np
# TODO: branch cuts (use Pauli code) # TODO: conj 'symmetry' # TODO: FPU exceptions
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
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 ref = np.complex(np.cos(1.), np.sin(1.)) yield check, f, -np.inf, 1, np.PZERO, np.PZERO
ref = np.complex(np.cos(np.pi * 0.75), np.sin(np.pi * 0.75)) 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 ref = np.complex(np.cos(1.), np.sin(1.)) yield check, f, np.inf, 1, np.inf, np.inf
ref = np.complex(np.cos(np.pi * 0.75), np.sin(np.pi * 0.75)) 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): z = f(np.array(np.complex(-np.inf, np.inf))) if z.real != 0 or z.imag != 0: raise AssertionError( "cexp(-inf, inf) is (%f, %f), expected (+-0, +-0)" \ % (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): z = f(np.array(np.complex(np.inf, np.inf))) if not np.isinf(z.real) or not np.isnan(z.imag): raise AssertionError( "cexp(inf, inf) is (%f, %f), expected (+-inf, nan)" \ % (z.real, z.imag)) yield _check_inf_inf, None
# cexp(-inf + nan i) is +-0 +- 0i def _check_ninf_nan(dummy): z = f(np.array(np.complex(-np.inf, np.nan))) if z.real != 0 or z.imag != 0: raise AssertionError( "cexp(-inf, nan) is (%f, %f), expected (+-0, +-0)" \ % (z.real, z.imag)) yield _check_ninf_nan, None
# cexp(inf + nan i) is +-inf + nan def _check_inf_nan(dummy): z = f(np.array(np.complex(np.inf, np.nan))) if not np.isinf(z.real) or not np.isnan(z.imag): raise AssertionError( "cexp(-inf, nan) is (%f, %f), expected (+-inf, nan)" \ % (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 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])
@dec.knownfailureif(True, "clog(- inf + i inf) fails on Windows.") def test_special_values(self): xl = [] yl = []
# From C99 std (Sec 6.3.2) # XXX: check exceptions raised
# clog(-0 + i0) returns -inf + i pi and raises the 'divide-by-zero' # floating-point exception. x = np.array([np.NZERO], dtype=np.complex) y = np.complex(-np.inf, np.pi) 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. x = np.array([0], dtype=np.complex) y = np.complex(-np.inf, 0) 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. x = np.array([complex(1., 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)
x = np.array([np.inf + np.nan * 1j], dtype=np.complex) 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) for i in range(len(xa)): assert_almost_equal(np.log(np.conj(xa[i])), np.conj(np.log(xa[i])))
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)
def test_special_values(self): check = check_complex_value f = np.sqrt
# C99: Sec G 6.4.2 x, y = [], []
# 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): z = np.sqrt(np.array(np.complex(-np.inf, np.nan))) if not np.isnan(z.real) or not np.isinf(z.imag): raise AssertionError( "csqrt(-inf, nan) is (%f, %f), expected (nan, +-inf)" \ % (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 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 = 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 = 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 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) ya = 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) if exact: assert_equal(f(z1), z2) else: assert_almost_equal(f(z1), z2)
if __name__ == "__main__": run_module_suite()
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