Current File : //opt/alt/python37/lib64/python3.7/site-packages/numpy/core/tests/test_scalarmath.py
from __future__ import division, absolute_import, print_function
import sys
import warnings
import itertools
import operator
import numpy as np
from numpy.testing.utils import _gen_alignment_data
from numpy.testing import (
TestCase, run_module_suite, assert_, assert_equal, assert_raises,
assert_almost_equal, assert_allclose, assert_array_equal, IS_PYPY,
suppress_warnings
)
types = [np.bool_, np.byte, np.ubyte, np.short, np.ushort, np.intc, np.uintc,
np.int_, np.uint, np.longlong, np.ulonglong,
np.single, np.double, np.longdouble, np.csingle,
np.cdouble, np.clongdouble]
floating_types = np.floating.__subclasses__()
# This compares scalarmath against ufuncs.
class TestTypes(TestCase):
def test_types(self, level=1):
for atype in types:
a = atype(1)
assert_(a == 1, "error with %r: got %r" % (atype, a))
def test_type_add(self, level=1):
# list of types
for k, atype in enumerate(types):
a_scalar = atype(3)
a_array = np.array([3], dtype=atype)
for l, btype in enumerate(types):
b_scalar = btype(1)
b_array = np.array([1], dtype=btype)
c_scalar = a_scalar + b_scalar
c_array = a_array + b_array
# It was comparing the type numbers, but the new ufunc
# function-finding mechanism finds the lowest function
# to which both inputs can be cast - which produces 'l'
# when you do 'q' + 'b'. The old function finding mechanism
# skipped ahead based on the first argument, but that
# does not produce properly symmetric results...
assert_equal(c_scalar.dtype, c_array.dtype,
"error with types (%d/'%c' + %d/'%c')" %
(k, np.dtype(atype).char, l, np.dtype(btype).char))
def test_type_create(self, level=1):
for k, atype in enumerate(types):
a = np.array([1, 2, 3], atype)
b = atype([1, 2, 3])
assert_equal(a, b)
def test_leak(self):
# test leak of scalar objects
# a leak would show up in valgrind as still-reachable of ~2.6MB
for i in range(200000):
np.add(1, 1)
class TestBaseMath(TestCase):
def test_blocked(self):
# test alignments offsets for simd instructions
# alignments for vz + 2 * (vs - 1) + 1
for dt, sz in [(np.float32, 11), (np.float64, 7), (np.int32, 11)]:
for out, inp1, inp2, msg in _gen_alignment_data(dtype=dt,
type='binary',
max_size=sz):
exp1 = np.ones_like(inp1)
inp1[...] = np.ones_like(inp1)
inp2[...] = np.zeros_like(inp2)
assert_almost_equal(np.add(inp1, inp2), exp1, err_msg=msg)
assert_almost_equal(np.add(inp1, 2), exp1 + 2, err_msg=msg)
assert_almost_equal(np.add(1, inp2), exp1, err_msg=msg)
np.add(inp1, inp2, out=out)
assert_almost_equal(out, exp1, err_msg=msg)
inp2[...] += np.arange(inp2.size, dtype=dt) + 1
assert_almost_equal(np.square(inp2),
np.multiply(inp2, inp2), err_msg=msg)
# skip true divide for ints
if dt != np.int32 or (sys.version_info.major < 3 and not sys.py3kwarning):
assert_almost_equal(np.reciprocal(inp2),
np.divide(1, inp2), err_msg=msg)
inp1[...] = np.ones_like(inp1)
np.add(inp1, 2, out=out)
assert_almost_equal(out, exp1 + 2, err_msg=msg)
inp2[...] = np.ones_like(inp2)
np.add(2, inp2, out=out)
assert_almost_equal(out, exp1 + 2, err_msg=msg)
def test_lower_align(self):
# check data that is not aligned to element size
# i.e doubles are aligned to 4 bytes on i386
d = np.zeros(23 * 8, dtype=np.int8)[4:-4].view(np.float64)
o = np.zeros(23 * 8, dtype=np.int8)[4:-4].view(np.float64)
assert_almost_equal(d + d, d * 2)
np.add(d, d, out=o)
np.add(np.ones_like(d), d, out=o)
np.add(d, np.ones_like(d), out=o)
np.add(np.ones_like(d), d)
np.add(d, np.ones_like(d))
class TestPower(TestCase):
def test_small_types(self):
for t in [np.int8, np.int16, np.float16]:
a = t(3)
b = a ** 4
assert_(b == 81, "error with %r: got %r" % (t, b))
def test_large_types(self):
for t in [np.int32, np.int64, np.float32, np.float64, np.longdouble]:
a = t(51)
b = a ** 4
msg = "error with %r: got %r" % (t, b)
if np.issubdtype(t, np.integer):
assert_(b == 6765201, msg)
else:
assert_almost_equal(b, 6765201, err_msg=msg)
def test_integers_to_negative_integer_power(self):
# Note that the combination of uint64 with a signed integer
# has common type np.float. The other combinations should all
# raise a ValueError for integer ** negative integer.
exp = [np.array(-1, dt)[()] for dt in 'bhilq']
# 1 ** -1 possible special case
base = [np.array(1, dt)[()] for dt in 'bhilqBHILQ']
for i1, i2 in itertools.product(base, exp):
if i1.dtype.name != 'uint64':
assert_raises(ValueError, operator.pow, i1, i2)
else:
res = operator.pow(i1, i2)
assert_(res.dtype.type is np.float64)
assert_almost_equal(res, 1.)
# -1 ** -1 possible special case
base = [np.array(-1, dt)[()] for dt in 'bhilq']
for i1, i2 in itertools.product(base, exp):
if i1.dtype.name != 'uint64':
assert_raises(ValueError, operator.pow, i1, i2)
else:
res = operator.pow(i1, i2)
assert_(res.dtype.type is np.float64)
assert_almost_equal(res, -1.)
# 2 ** -1 perhaps generic
base = [np.array(2, dt)[()] for dt in 'bhilqBHILQ']
for i1, i2 in itertools.product(base, exp):
if i1.dtype.name != 'uint64':
assert_raises(ValueError, operator.pow, i1, i2)
else:
res = operator.pow(i1, i2)
assert_(res.dtype.type is np.float64)
assert_almost_equal(res, .5)
def test_mixed_types(self):
typelist = [np.int8, np.int16, np.float16,
np.float32, np.float64, np.int8,
np.int16, np.int32, np.int64]
for t1 in typelist:
for t2 in typelist:
a = t1(3)
b = t2(2)
result = a**b
msg = ("error with %r and %r:"
"got %r, expected %r") % (t1, t2, result, 9)
if np.issubdtype(np.dtype(result), np.integer):
assert_(result == 9, msg)
else:
assert_almost_equal(result, 9, err_msg=msg)
def test_modular_power(self):
# modular power is not implemented, so ensure it errors
a = 5
b = 4
c = 10
expected = pow(a, b, c)
for t in (np.int32, np.float32, np.complex64):
# note that 3-operand power only dispatches on the first argument
assert_raises(TypeError, operator.pow, t(a), b, c)
assert_raises(TypeError, operator.pow, np.array(t(a)), b, c)
def floordiv_and_mod(x, y):
return (x // y, x % y)
def _signs(dt):
if dt in np.typecodes['UnsignedInteger']:
return (+1,)
else:
return (+1, -1)
class TestModulus(TestCase):
def test_modulus_basic(self):
dt = np.typecodes['AllInteger'] + np.typecodes['Float']
for op in [floordiv_and_mod, divmod]:
for dt1, dt2 in itertools.product(dt, dt):
for sg1, sg2 in itertools.product(_signs(dt1), _signs(dt2)):
fmt = 'op: %s, dt1: %s, dt2: %s, sg1: %s, sg2: %s'
msg = fmt % (op.__name__, dt1, dt2, sg1, sg2)
a = np.array(sg1*71, dtype=dt1)[()]
b = np.array(sg2*19, dtype=dt2)[()]
div, rem = op(a, b)
assert_equal(div*b + rem, a, err_msg=msg)
if sg2 == -1:
assert_(b < rem <= 0, msg)
else:
assert_(b > rem >= 0, msg)
def test_float_modulus_exact(self):
# test that float results are exact for small integers. This also
# holds for the same integers scaled by powers of two.
nlst = list(range(-127, 0))
plst = list(range(1, 128))
dividend = nlst + [0] + plst
divisor = nlst + plst
arg = list(itertools.product(dividend, divisor))
tgt = list(divmod(*t) for t in arg)
a, b = np.array(arg, dtype=int).T
# convert exact integer results from Python to float so that
# signed zero can be used, it is checked.
tgtdiv, tgtrem = np.array(tgt, dtype=float).T
tgtdiv = np.where((tgtdiv == 0.0) & ((b < 0) ^ (a < 0)), -0.0, tgtdiv)
tgtrem = np.where((tgtrem == 0.0) & (b < 0), -0.0, tgtrem)
for op in [floordiv_and_mod, divmod]:
for dt in np.typecodes['Float']:
msg = 'op: %s, dtype: %s' % (op.__name__, dt)
fa = a.astype(dt)
fb = b.astype(dt)
# use list comprehension so a_ and b_ are scalars
div, rem = zip(*[op(a_, b_) for a_, b_ in zip(fa, fb)])
assert_equal(div, tgtdiv, err_msg=msg)
assert_equal(rem, tgtrem, err_msg=msg)
def test_float_modulus_roundoff(self):
# gh-6127
dt = np.typecodes['Float']
for op in [floordiv_and_mod, divmod]:
for dt1, dt2 in itertools.product(dt, dt):
for sg1, sg2 in itertools.product((+1, -1), (+1, -1)):
fmt = 'op: %s, dt1: %s, dt2: %s, sg1: %s, sg2: %s'
msg = fmt % (op.__name__, dt1, dt2, sg1, sg2)
a = np.array(sg1*78*6e-8, dtype=dt1)[()]
b = np.array(sg2*6e-8, dtype=dt2)[()]
div, rem = op(a, b)
# Equal assertion should hold when fmod is used
assert_equal(div*b + rem, a, err_msg=msg)
if sg2 == -1:
assert_(b < rem <= 0, msg)
else:
assert_(b > rem >= 0, msg)
def test_float_modulus_corner_cases(self):
# Check remainder magnitude.
for dt in np.typecodes['Float']:
b = np.array(1.0, dtype=dt)
a = np.nextafter(np.array(0.0, dtype=dt), -b)
rem = operator.mod(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = operator.mod(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "invalid value encountered in remainder")
for dt in np.typecodes['Float']:
fone = np.array(1.0, dtype=dt)
fzer = np.array(0.0, dtype=dt)
finf = np.array(np.inf, dtype=dt)
fnan = np.array(np.nan, dtype=dt)
rem = operator.mod(fone, fzer)
assert_(np.isnan(rem), 'dt: %s' % dt)
# MSVC 2008 returns NaN here, so disable the check.
#rem = operator.mod(fone, finf)
#assert_(rem == fone, 'dt: %s' % dt)
rem = operator.mod(fone, fnan)
assert_(np.isnan(rem), 'dt: %s' % dt)
rem = operator.mod(finf, fone)
assert_(np.isnan(rem), 'dt: %s' % dt)
class TestComplexDivision(TestCase):
def test_zero_division(self):
with np.errstate(all="ignore"):
for t in [np.complex64, np.complex128]:
a = t(0.0)
b = t(1.0)
assert_(np.isinf(b/a))
b = t(complex(np.inf, np.inf))
assert_(np.isinf(b/a))
b = t(complex(np.inf, np.nan))
assert_(np.isinf(b/a))
b = t(complex(np.nan, np.inf))
assert_(np.isinf(b/a))
b = t(complex(np.nan, np.nan))
assert_(np.isnan(b/a))
b = t(0.)
assert_(np.isnan(b/a))
def test_signed_zeros(self):
with np.errstate(all="ignore"):
for t in [np.complex64, np.complex128]:
# tupled (numerator, denominator, expected)
# for testing as expected == numerator/denominator
data = (
(( 0.0,-1.0), ( 0.0, 1.0), (-1.0,-0.0)),
(( 0.0,-1.0), ( 0.0,-1.0), ( 1.0,-0.0)),
(( 0.0,-1.0), (-0.0,-1.0), ( 1.0, 0.0)),
(( 0.0,-1.0), (-0.0, 1.0), (-1.0, 0.0)),
(( 0.0, 1.0), ( 0.0,-1.0), (-1.0, 0.0)),
(( 0.0,-1.0), ( 0.0,-1.0), ( 1.0,-0.0)),
((-0.0,-1.0), ( 0.0,-1.0), ( 1.0,-0.0)),
((-0.0, 1.0), ( 0.0,-1.0), (-1.0,-0.0))
)
for cases in data:
n = cases[0]
d = cases[1]
ex = cases[2]
result = t(complex(n[0], n[1])) / t(complex(d[0], d[1]))
# check real and imag parts separately to avoid comparison
# in array context, which does not account for signed zeros
assert_equal(result.real, ex[0])
assert_equal(result.imag, ex[1])
def test_branches(self):
with np.errstate(all="ignore"):
for t in [np.complex64, np.complex128]:
# tupled (numerator, denominator, expected)
# for testing as expected == numerator/denominator
data = list()
# trigger branch: real(fabs(denom)) > imag(fabs(denom))
# followed by else condition as neither are == 0
data.append((( 2.0, 1.0), ( 2.0, 1.0), (1.0, 0.0)))
# trigger branch: real(fabs(denom)) > imag(fabs(denom))
# followed by if condition as both are == 0
# is performed in test_zero_division(), so this is skipped
# trigger else if branch: real(fabs(denom)) < imag(fabs(denom))
data.append((( 1.0, 2.0), ( 1.0, 2.0), (1.0, 0.0)))
for cases in data:
n = cases[0]
d = cases[1]
ex = cases[2]
result = t(complex(n[0], n[1])) / t(complex(d[0], d[1]))
# check real and imag parts separately to avoid comparison
# in array context, which does not account for signed zeros
assert_equal(result.real, ex[0])
assert_equal(result.imag, ex[1])
class TestConversion(TestCase):
def test_int_from_long(self):
l = [1e6, 1e12, 1e18, -1e6, -1e12, -1e18]
li = [10**6, 10**12, 10**18, -10**6, -10**12, -10**18]
for T in [None, np.float64, np.int64]:
a = np.array(l, dtype=T)
assert_equal([int(_m) for _m in a], li)
a = np.array(l[:3], dtype=np.uint64)
assert_equal([int(_m) for _m in a], li[:3])
def test_iinfo_long_values(self):
for code in 'bBhH':
res = np.array(np.iinfo(code).max + 1, dtype=code)
tgt = np.iinfo(code).min
assert_(res == tgt)
for code in np.typecodes['AllInteger']:
res = np.array(np.iinfo(code).max, dtype=code)
tgt = np.iinfo(code).max
assert_(res == tgt)
for code in np.typecodes['AllInteger']:
res = np.typeDict[code](np.iinfo(code).max)
tgt = np.iinfo(code).max
assert_(res == tgt)
def test_int_raise_behaviour(self):
def overflow_error_func(dtype):
np.typeDict[dtype](np.iinfo(dtype).max + 1)
for code in 'lLqQ':
assert_raises(OverflowError, overflow_error_func, code)
def test_longdouble_int(self):
# gh-627
x = np.longdouble(np.inf)
assert_raises(OverflowError, x.__int__)
x = np.clongdouble(np.inf)
assert_raises(OverflowError, x.__int__)
def test_numpy_scalar_relational_operators(self):
# All integer
for dt1 in np.typecodes['AllInteger']:
assert_(1 > np.array(0, dtype=dt1)[()], "type %s failed" % (dt1,))
assert_(not 1 < np.array(0, dtype=dt1)[()], "type %s failed" % (dt1,))
for dt2 in np.typecodes['AllInteger']:
assert_(np.array(1, dtype=dt1)[()] > np.array(0, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
assert_(not np.array(1, dtype=dt1)[()] < np.array(0, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
#Unsigned integers
for dt1 in 'BHILQP':
assert_(-1 < np.array(1, dtype=dt1)[()], "type %s failed" % (dt1,))
assert_(not -1 > np.array(1, dtype=dt1)[()], "type %s failed" % (dt1,))
assert_(-1 != np.array(1, dtype=dt1)[()], "type %s failed" % (dt1,))
#unsigned vs signed
for dt2 in 'bhilqp':
assert_(np.array(1, dtype=dt1)[()] > np.array(-1, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
assert_(not np.array(1, dtype=dt1)[()] < np.array(-1, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
assert_(np.array(1, dtype=dt1)[()] != np.array(-1, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
#Signed integers and floats
for dt1 in 'bhlqp' + np.typecodes['Float']:
assert_(1 > np.array(-1, dtype=dt1)[()], "type %s failed" % (dt1,))
assert_(not 1 < np.array(-1, dtype=dt1)[()], "type %s failed" % (dt1,))
assert_(-1 == np.array(-1, dtype=dt1)[()], "type %s failed" % (dt1,))
for dt2 in 'bhlqp' + np.typecodes['Float']:
assert_(np.array(1, dtype=dt1)[()] > np.array(-1, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
assert_(not np.array(1, dtype=dt1)[()] < np.array(-1, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
assert_(np.array(-1, dtype=dt1)[()] == np.array(-1, dtype=dt2)[()],
"type %s and %s failed" % (dt1, dt2))
def test_scalar_comparison_to_none(self):
# Scalars should just return False and not give a warnings.
# The comparisons are flagged by pep8, ignore that.
with warnings.catch_warnings(record=True) as w:
warnings.filterwarnings('always', '', FutureWarning)
assert_(not np.float32(1) == None)
assert_(not np.str_('test') == None)
# This is dubious (see below):
assert_(not np.datetime64('NaT') == None)
assert_(np.float32(1) != None)
assert_(np.str_('test') != None)
# This is dubious (see below):
assert_(np.datetime64('NaT') != None)
assert_(len(w) == 0)
# For documentation purposes, this is why the datetime is dubious.
# At the time of deprecation this was no behaviour change, but
# it has to be considered when the deprecations are done.
assert_(np.equal(np.datetime64('NaT'), None))
#class TestRepr(TestCase):
# def test_repr(self):
# for t in types:
# val = t(1197346475.0137341)
# val_repr = repr(val)
# val2 = eval(val_repr)
# assert_equal( val, val2 )
class TestRepr(object):
def _test_type_repr(self, t):
finfo = np.finfo(t)
last_fraction_bit_idx = finfo.nexp + finfo.nmant
last_exponent_bit_idx = finfo.nexp
storage_bytes = np.dtype(t).itemsize*8
# could add some more types to the list below
for which in ['small denorm', 'small norm']:
# Values from http://en.wikipedia.org/wiki/IEEE_754
constr = np.array([0x00]*storage_bytes, dtype=np.uint8)
if which == 'small denorm':
byte = last_fraction_bit_idx // 8
bytebit = 7-(last_fraction_bit_idx % 8)
constr[byte] = 1 << bytebit
elif which == 'small norm':
byte = last_exponent_bit_idx // 8
bytebit = 7-(last_exponent_bit_idx % 8)
constr[byte] = 1 << bytebit
else:
raise ValueError('hmm')
val = constr.view(t)[0]
val_repr = repr(val)
val2 = t(eval(val_repr))
if not (val2 == 0 and val < 1e-100):
assert_equal(val, val2)
def test_float_repr(self):
# long double test cannot work, because eval goes through a python
# float
for t in [np.float32, np.float64]:
yield self._test_type_repr, t
if not IS_PYPY:
# sys.getsizeof() is not valid on PyPy
class TestSizeOf(TestCase):
def test_equal_nbytes(self):
for type in types:
x = type(0)
assert_(sys.getsizeof(x) > x.nbytes)
def test_error(self):
d = np.float32()
assert_raises(TypeError, d.__sizeof__, "a")
class TestMultiply(TestCase):
def test_seq_repeat(self):
# Test that basic sequences get repeated when multiplied with
# numpy integers. And errors are raised when multiplied with others.
# Some of this behaviour may be controversial and could be open for
# change.
for seq_type in (list, tuple):
seq = seq_type([1, 2, 3])
for numpy_type in np.typecodes["AllInteger"]:
i = np.dtype(numpy_type).type(2)
assert_equal(seq * i, seq * int(i))
assert_equal(i * seq, int(i) * seq)
for numpy_type in np.typecodes["All"].replace("V", ""):
if numpy_type in np.typecodes["AllInteger"]:
continue
i = np.dtype(numpy_type).type()
assert_raises(TypeError, operator.mul, seq, i)
assert_raises(TypeError, operator.mul, i, seq)
def test_no_seq_repeat_basic_array_like(self):
# Test that an array-like which does not know how to be multiplied
# does not attempt sequence repeat (raise TypeError).
# See also gh-7428.
class ArrayLike(object):
def __init__(self, arr):
self.arr = arr
def __array__(self):
return self.arr
# Test for simple ArrayLike above and memoryviews (original report)
for arr_like in (ArrayLike(np.ones(3)), memoryview(np.ones(3))):
assert_array_equal(arr_like * np.float32(3.), np.full(3, 3.))
assert_array_equal(np.float32(3.) * arr_like, np.full(3, 3.))
assert_array_equal(arr_like * np.int_(3), np.full(3, 3))
assert_array_equal(np.int_(3) * arr_like, np.full(3, 3))
class TestNegative(TestCase):
def test_exceptions(self):
a = np.ones((), dtype=np.bool_)[()]
assert_raises(TypeError, operator.neg, a)
def test_result(self):
types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
with suppress_warnings() as sup:
sup.filter(RuntimeWarning)
for dt in types:
a = np.ones((), dtype=dt)[()]
assert_equal(operator.neg(a) + a, 0)
class TestSubtract(TestCase):
def test_result(self):
types = np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?'
with suppress_warnings() as sup:
sup.filter(RuntimeWarning)
for dt in types:
a = np.ones((), dtype=dt)[()]
assert_equal(operator.sub(a, a), 0)
class TestAbs(TestCase):
def _test_abs_func(self, absfunc):
for tp in floating_types:
x = tp(-1.5)
assert_equal(absfunc(x), 1.5)
x = tp(0.0)
res = absfunc(x)
# assert_equal() checks zero signedness
assert_equal(res, 0.0)
x = tp(-0.0)
res = absfunc(x)
assert_equal(res, 0.0)
def test_builtin_abs(self):
self._test_abs_func(abs)
def test_numpy_abs(self):
self._test_abs_func(np.abs)
if __name__ == "__main__":
run_module_suite()
Mini Shell