Python numpy 模块，nextafter() 实例源码
我们从Python开源项目中，提取了以下48个代码示例，用于说明如何使用numpy.nextafter()。
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def _sample(self, n_samples):
# samples must be sampled from (-1, 1) rather than [-1, 1)
loc, scale = self.loc, self.scale
if not self.is_reparameterized:
loc = tf.stop_gradient(loc)
scale = tf.stop_gradient(scale)
shape = tf.concat([[n_samples], self.batch_shape], 0)
uniform_samples = tf.random_uniform(
shape=shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
self.dtype.as_numpy_dtype(0.)),
maxval=1.,
dtype=self.dtype)
samples = loc - scale * tf.sign(uniform_samples) * \
tf.log1p(-tf.abs(uniform_samples))
static_n_samples = n_samples if isinstance(n_samples, int) else None
samples.set_shape(
tf.TensorShape([static_n_samples]).concatenate(
self.get_batch_shape()))
return samples
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def test_standard_scaler_trasform_with_partial_fit():
# Check some postconditions after applying partial_fit and transform
X = X_2d[:100, :]
scaler_incr = StandardScaler()
for i, batch in enumerate(gen_batches(X.shape[0], 1)):
X_sofar = X[:(i + 1), :]
chunks_copy = X_sofar.copy()
scaled_batch = StandardScaler().fit_transform(X_sofar)
scaler_incr = scaler_incr.partial_fit(X[batch])
scaled_incr = scaler_incr.transform(X_sofar)
assert_array_almost_equal(scaled_batch, scaled_incr)
assert_array_almost_equal(X_sofar, chunks_copy) # No change
right_input = scaler_incr.inverse_transform(scaled_incr)
assert_array_almost_equal(X_sofar, right_input)
zero = np.zeros(X.shape[1])
epsilon = np.nextafter(0, 1)
assert_array_less(zero, scaler_incr.var_ + epsilon) # as less or equal
assert_array_less(zero, scaler_incr.scale_ + epsilon)
# (i+1) because the Scaler has been already fitted
assert_equal((i + 1), scaler_incr.n_samples_seen_)
def _sample_n(self, n, seed=None):
sample_shape = array_ops.concat(([n], array_ops.shape(self.logits)), 0)
logits = self.logits * array_ops.ones(sample_shape)
if logits.get_shape().ndims == 2:
logits_2d = logits
else:
logits_2d = array_ops.reshape(logits, [-1, self.event_size])
np_dtype = self.dtype.as_numpy_dtype()
minval = np.nextafter(np_dtype(0), np_dtype(1))
uniform = random_ops.random_uniform(shape=array_ops.shape(logits_2d),
minval=minval,
maxval=1,
dtype=self.dtype,
seed=seed)
gumbel = - math_ops.log(- math_ops.log(uniform))
noisy_logits = math_ops.div(gumbel + logits_2d, self.temperature)
samples = nn_ops.log_softmax(noisy_logits)
ret = array_ops.reshape(samples, sample_shape)
return ret
def test_spacing_nextafter(self):
"""Test np.spacing and np.nextafter"""
# All non-negative finite #'s
a = np.arange(0x7c00, dtype=uint16)
hinf = np.array((np.inf,), dtype=float16)
a_f16 = a.view(dtype=float16)
assert_equal(np.spacing(a_f16[:-1]), a_f16[1:]-a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
# switch to negatives
a |= 0x8000
assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
assert_equal(np.spacing(a_f16[1:]), a_f16[:-1]-a_f16[1:])
assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
def test_float_remainder_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 = np.remainder(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = np.remainder(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = np.remainder(fone, fzer)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
# MSVC 2008 returns NaN here, so disable the check.
#rem = np.remainder(fone, finf)
#assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(fone, fnan)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(finf, fone)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
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 = self.mod(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = self.mod(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = self.mod(fone, fzer)
assert_(np.isnan(rem), 'dt: %s' % dt)
# MSVC 2008 returns NaN here, so disable the check.
#rem = self.mod(fone, finf)
#assert_(rem == fone, 'dt: %s' % dt)
rem = self.mod(fone, fnan)
assert_(np.isnan(rem), 'dt: %s' % dt)
rem = self.mod(finf, fone)
assert_(np.isnan(rem), 'dt: %s' % dt)
def test_float_remainder_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 = np.remainder(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = np.remainder(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = np.remainder(fone, fzer)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
# MSVC 2008 returns NaN here, so disable the check.
#rem = np.remainder(fone, finf)
#assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(fone, fnan)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(finf, fone)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
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 = self.mod(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = self.mod(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = self.mod(fone, fzer)
assert_(np.isnan(rem), 'dt: %s' % dt)
# MSVC 2008 returns NaN here, so disable the check.
#rem = self.mod(fone, finf)
#assert_(rem == fone, 'dt: %s' % dt)
rem = self.mod(fone, fnan)
assert_(np.isnan(rem), 'dt: %s' % dt)
rem = self.mod(finf, fone)
assert_(np.isnan(rem), 'dt: %s' % dt)
def loglikelihood(num_points, num_dims, clusters, distances_dict_values_cl):
ll = 0
variance = cluster_variance(num_points, clusters, distances_dict_values_cl) or np.nextafter(0, 1)
# print 'var', variance
for cluster in clusters:
fRn = len(cluster)
t1 = fRn * np.log(fRn)
t2 = fRn * np.log(num_points)
t3 = ((fRn * num_dims) / 2.0) * np.log((2.0 * np.pi) * variance)
t4 = (fRn - 1.0) / 2.0
ll += t1 - t2 - t3 - t4
return ll
def _sample_n(self, n, seed=None):
shape = array_ops.concat(0, ([n], self.batch_shape()))
# Sample uniformly-at-random from the open-interval (-1, 1).
uniform_samples = random_ops.random_uniform(
shape=shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
self.dtype.as_numpy_dtype(0.)),
maxval=1.,
dtype=self.dtype,
seed=seed)
return (self.loc - self.scale * math_ops.sign(uniform_samples) *
math_ops.log(1. - math_ops.abs(uniform_samples)))
def _sample_n(self, n, seed=None):
shape = array_ops.concat(0, ([n], array_ops.shape(self._lam)))
# Sample uniformly-at-random from the open-interval (0, 1).
sampled = random_ops.random_uniform(
shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(0.),
self.dtype.as_numpy_dtype(1.)),
maxval=array_ops.ones((), dtype=self.dtype),
seed=seed,
dtype=self.dtype)
return -math_ops.log(sampled) / self._lam
def _sample_n(self, n, seed=None):
shape = array_ops.concat(0, ([n], self.batch_shape()))
# Sample uniformly-at-random from the open-interval (-1, 1).
uniform_samples = random_ops.random_uniform(
shape=shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
self.dtype.as_numpy_dtype(0.)),
maxval=1.,
dtype=self.dtype,
seed=seed)
return (self.loc - self.scale * math_ops.sign(uniform_samples) *
math_ops.log(1. - math_ops.abs(uniform_samples)))
def _sample_n(self, n, seed=None):
shape = array_ops.concat(0, ([n], array_ops.shape(self._lam)))
# Sample uniformly-at-random from the open-interval (0, 1).
sampled = random_ops.random_uniform(
shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(0.),
self.dtype.as_numpy_dtype(1.)),
maxval=array_ops.ones((), dtype=self.dtype),
seed=seed,
dtype=self.dtype)
return -math_ops.log(sampled) / self._lam
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
def test_uniform_range_bounds(self):
fmin = np.finfo('float').min
fmax = np.finfo('float').max
func = mt19937.uniform
assert_raises(OverflowError, func, -np.inf, 0)
assert_raises(OverflowError, func, 0, np.inf)
assert_raises(OverflowError, func, fmin, fmax)
assert_raises(OverflowError, func, [-np.inf], [0])
assert_raises(OverflowError, func, [0], [np.inf])
# (fmax / 1e17) - fmin is within range, so this should not throw
# account for i386 extended precision DBL_MAX / 1e17 + DBL_MAX >
# DBL_MAX by increasing fmin a bit
mt19937.uniform(low=np.nextafter(fmin, 1), high=fmax / 1e17)
def test_float_remainder_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 = np.remainder(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = np.remainder(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = np.remainder(fone, fzer)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
# MSVC 2008 returns NaN here, so disable the check.
#rem = np.remainder(fone, finf)
#assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(fone, fnan)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(finf, fone)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
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 = self.mod(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = self.mod(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = self.mod(fone, fzer)
assert_(np.isnan(rem), 'dt: %s' % dt)
# MSVC 2008 returns NaN here, so disable the check.
#rem = self.mod(fone, finf)
#assert_(rem == fone, 'dt: %s' % dt)
rem = self.mod(fone, fnan)
assert_(np.isnan(rem), 'dt: %s' % dt)
rem = self.mod(finf, fone)
assert_(np.isnan(rem), 'dt: %s' % dt)
def test_float_remainder_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 = np.remainder(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = np.remainder(-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 = np.remainder(fone, fzer)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
# MSVC 2008 returns NaN here, so disable the check.
#rem = np.remainder(fone, finf)
#assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(fone, fnan)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(finf, fone)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
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 = self.mod(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = self.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 = self.mod(fone, fzer)
assert_(np.isnan(rem), 'dt: %s' % dt)
# MSVC 2008 returns NaN here, so disable the check.
#rem = self.mod(fone, finf)
#assert_(rem == fone, 'dt: %s' % dt)
rem = self.mod(fone, fnan)
assert_(np.isnan(rem), 'dt: %s' % dt)
rem = self.mod(finf, fone)
assert_(np.isnan(rem), 'dt: %s' % dt)
def _uniform_inclusive(loc=0.0, scale=1.0):
# like scipy.stats.distributions but inclusive of `high`
# XXX scale + 1. might not actually be a float after scale if
# XXX scale is very large.
return uniform(loc=loc, scale=np.nextafter(scale, scale + 1.))
def test_real_bounds():
# should give same answer as using check_limits() but this is easier
# to read
a = Real(1., 2.1)
assert_false(0.99 in a)
assert_true(1. in a)
assert_true(2.09 in a)
assert_true(2.1 in a)
assert_false(np.nextafter(2.1, 3.) in a)
def _sample_n(self, n, seed=None):
shape = array_ops.concat(([n], self.batch_shape()), 0)
# Sample uniformly-at-random from the open-interval (-1, 1).
uniform_samples = random_ops.random_uniform(
shape=shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
self.dtype.as_numpy_dtype(0.)),
maxval=1.,
dtype=self.dtype,
seed=seed)
return (self.loc - self.scale * math_ops.sign(uniform_samples) *
math_ops.log(1. - math_ops.abs(uniform_samples)))
def _sample_n(self, n, seed=None):
shape = array_ops.concat(([n], array_ops.shape(self.mean())), 0)
np_dtype = self.dtype.as_numpy_dtype()
minval = np.nextafter(np_dtype(0), np_dtype(1))
uniform = random_ops.random_uniform(shape=shape,
minval=minval,
maxval=1,
dtype=self.dtype,
seed=seed)
sampled = -math_ops.log(-math_ops.log(uniform))
return sampled * self.scale + self.loc
def _sample_n(self, n, seed=None):
shape = array_ops.concat(([n], array_ops.shape(self.mean())), 0)
np_dtype = self.dtype.as_numpy_dtype()
minval = np.nextafter(np_dtype(0), np_dtype(1))
uniform = random_ops.random_uniform(shape=shape,
minval=minval,
maxval=1,
dtype=self.dtype,
seed=seed)
sampled = math_ops.log(uniform) - math_ops.log(1-uniform)
return sampled * self.scale + self.loc
def _sample_n(self, n, seed=None):
shape = array_ops.concat(([n], array_ops.shape(self._lam)), 0)
# Sample uniformly-at-random from the open-interval (0, 1).
sampled = random_ops.random_uniform(
shape,
minval=np.nextafter(self.dtype.as_numpy_dtype(0.),
self.dtype.as_numpy_dtype(1.)),
maxval=array_ops.ones((), dtype=self.dtype),
seed=seed,
dtype=self.dtype)
return -math_ops.log(sampled) / self._lam
def test_float_remainder_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 = np.remainder(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = np.remainder(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = np.remainder(fone, fzer)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
# MSVC 2008 returns NaN here, so disable the check.
#rem = np.remainder(fone, finf)
#assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(fone, fnan)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
rem = np.remainder(finf, fone)
assert_(np.isnan(rem), 'dt: %s, rem: %s' % (dt, rem))
def _test_nextafter(t):
one = t(1)
two = t(2)
zero = t(0)
eps = np.finfo(t).eps
assert_(np.nextafter(one, two) - one == eps)
assert_(np.nextafter(one, zero) - one < 0)
assert_(np.isnan(np.nextafter(np.nan, one)))
assert_(np.isnan(np.nextafter(one, np.nan)))
assert_(np.nextafter(one, one) == one)
def test_nextafter_vs_spacing():
# XXX: spacing does not handle long double yet
for t in [np.float32, np.float64]:
for _f in [1, 1e-5, 1000]:
f = t(_f)
f1 = t(_f + 1)
assert_(np.nextafter(f, f1) - f == np.spacing(f))
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 = self.mod(a, b)
assert_(rem <= b, 'dt: %s' % dt)
rem = self.mod(-a, -b)
assert_(rem >= -b, 'dt: %s' % dt)
# Check nans, inf
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.simplefilter('ignore', RuntimeWarning)
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 = self.mod(fone, fzer)
assert_(np.isnan(rem), 'dt: %s' % dt)
# MSVC 2008 returns NaN here, so disable the check.
#rem = self.mod(fone, finf)
#assert_(rem == fone, 'dt: %s' % dt)
rem = self.mod(fone, fnan)
assert_(np.isnan(rem), 'dt: %s' % dt)
rem = self.mod(finf, fone)
assert_(np.isnan(rem), 'dt: %s' % dt)
def similarity(data, vocab, normalize=False):
"""Return the similarity between some data and the vocabulary.
Computes the dot products between all data vectors and each
vocabulary vector. If ``normalize=True``, normalizes all vectors
to compute the cosine similarity.
Parameters
----------
data: array_like
The data used for comparison.
vocab: Vocabulary or array_like
Vocabulary (or list of vectors) to use to calculate
the similarity values.
normalize : bool, optional (Default: False)
Whether to normalize all vectors, to compute the cosine similarity.
"""
from nengo_spa.vocab import Vocabulary
if isinstance(data, SemanticPointer):
data = data.v
if isinstance(vocab, Vocabulary):
vectors = vocab.vectors
elif is_iterable(vocab):
if isinstance(next(iter(vocab)), SemanticPointer):
vocab = [p.v for p in vocab]
vectors = np.array(vocab, copy=False, ndmin=2)
else:
raise ValidationError("%r object is not a valid vocabulary"
% (type(vocab).__name__), attr='vocab')
dots = np.dot(vectors, data.T)
if normalize:
# Zero-norm vectors should return zero, so avoid divide-by-zero error
eps = np.nextafter(0, 1) # smallest float above zero
dnorm = np.maximum(npext.norm(data.T, axis=0, keepdims=True), eps)
vnorm = np.maximum(npext.norm(vectors, axis=1, keepdims=True), eps)
if len(dots.shape) == 1:
vnorm = np.squeeze(vnorm)
dots /= dnorm
dots /= vnorm
return dots.T
def _compute_mi_cc(x, y, n_neighbors):
"""Compute mutual information between two continuous variables.
Parameters
----------
x, y : ndarray, shape (n_samples,)
Samples of two continuous random variables, must have an identical
shape.
n_neighbors : int
Number of nearest neighbors to search for each point, see [1]_.
Returns
-------
mi : float
Estimated mutual information. If it turned out to be negative it is
replace by 0.
Notes
-----
True mutual information can't be negative. If its estimate by a numerical
method is negative, it means (providing the method is adequate) that the
mutual information is close to 0 and replacing it by 0 is a reasonable
strategy.
References
----------
.. [1] A. Kraskov, H. Stogbauer and P. Grassberger, "Estimating mutual
information". Phys. Rev. E 69, 2004.
"""
n_samples = x.size
x = x.reshape((-1, 1))
y = y.reshape((-1, 1))
xy = np.hstack((x, y))
# Here we rely on NearestNeighbors to select the fastest algorithm.
nn = NearestNeighbors(metric='chebyshev', n_neighbors=n_neighbors)
nn.fit(xy)
radius = nn.kneighbors()[0]
radius = np.nextafter(radius[:, -1], 0)
# Algorithm is selected explicitly to allow passing an array as radius
# later (not all algorithms support this).
nn.set_params(algorithm='kd_tree')
nn.fit(x)
ind = nn.radius_neighbors(radius=radius, return_distance=False)
nx = np.array([i.size for i in ind])
nn.fit(y)
ind = nn.radius_neighbors(radius=radius, return_distance=False)
ny = np.array([i.size for i in ind])
mi = (digamma(n_samples) + digamma(n_neighbors) -
np.mean(digamma(nx + 1)) - np.mean(digamma(ny + 1)))
return max(0, mi)