def test_half_correctness(self):
"""Take every finite float16, and check the casting functions with
a manual conversion."""
# Create an array of all finite float16s
a_bits = self.finite_f16.view(dtype=uint16)
# Convert to 64-bit float manually
a_sgn = (-1.0)**((a_bits & 0x8000) >> 15)
a_exp = np.array((a_bits & 0x7c00) >> 10, dtype=np.int32) - 15
a_man = (a_bits & 0x03ff) * 2.0**(-10)
# Implicit bit of normalized floats
a_man[a_exp != -15] += 1
# Denormalized exponent is -14
a_exp[a_exp == -15] = -14
a_manual = a_sgn * a_man * 2.0**a_exp
a32_fail = np.nonzero(self.finite_f32 != a_manual)[0]
if len(a32_fail) != 0:
bad_index = a32_fail[0]
assert_equal(
self.finite_f32, a_manual,
"First non-equal is half value %x -> %g != %g" %
(self.finite_f16[bad_index], self.finite_f32[bad_index],
a_manual[bad_index]))
a64_fail = np.nonzero(self.finite_f64 != a_manual)[0]
if len(a64_fail) != 0:
bad_index = a64_fail[0]
assert_equal(
self.finite_f64, a_manual,
"First non-equal is half value %x -> %g != %g" %
(self.finite_f16[bad_index], self.finite_f64[bad_index],
a_manual[bad_index]))
def _unique1d(ar,
return_index=False,
return_inverse=False,
return_counts=False):
"""
Find the unique elements of an array, ignoring shape.
"""
ar = np.asanyarray(ar).flatten()
optional_indices = return_index or return_inverse
if optional_indices:
perm = ar.argsort(kind='mergesort' if return_index else 'quicksort')
aux = ar[perm]
else:
ar.sort()
aux = ar
mask = np.empty(aux.shape, dtype=np.bool_)
mask[:1] = True
mask[1:] = aux[1:] != aux[:-1]
ret = (aux[mask], )
if return_index:
ret += (perm[mask], )
if return_inverse:
imask = np.cumsum(mask) - 1
inv_idx = np.empty(mask.shape, dtype=np.intp)
inv_idx[perm] = imask
ret += (inv_idx, )
if return_counts:
idx = np.concatenate(np.nonzero(mask) + ([mask.size], ))
ret += (np.diff(idx), )
return ret
def trimcoef(c, tol=0):
"""
Remove "small" "trailing" coefficients from a polynomial.
"Small" means "small in absolute value" and is controlled by the
parameter `tol`; "trailing" means highest order coefficient(s), e.g., in
``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``)
both the 3-rd and 4-th order coefficients would be "trimmed."
Parameters
----------
c : array_like
1-d array of coefficients, ordered from lowest order to highest.
tol : number, optional
Trailing (i.e., highest order) elements with absolute value less
than or equal to `tol` (default value is zero) are removed.
Returns
-------
trimmed : ndarray
1-d array with trailing zeros removed. If the resulting series
would be empty, a series containing a single zero is returned.
Raises
------
ValueError
If `tol` < 0
See Also
--------
trimseq
Examples
--------
>>> from numpy1.polynomial import polyutils as pu
>>> pu.trimcoef((0,0,3,0,5,0,0))
array([ 0., 0., 3., 0., 5.])
>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed
array([ 0.])
>>> i = complex(0,1) # works for complex
>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)
array([ 0.0003+0.j , 0.0010-0.001j])
"""
if tol < 0:
raise ValueError("tol must be non-negative")
[c] = as_series([c])
[ind] = np.nonzero(np.abs(c) > tol)
if len(ind) == 0:
return c[:1] * 0
else:
return c[:ind[-1] + 1].copy()
def test_half_ordering(self):
"""Make sure comparisons are working right"""
# All non-NaN float16 values in reverse order
a = self.nonan_f16[::-1].copy()
# 32-bit float copy
b = np.array(a, dtype=float32)
# Should sort the same
a.sort()
b.sort()
assert_equal(a, b)
# Comparisons should work
assert_((a[:-1] <= a[1:]).all())
assert_(not (a[:-1] > a[1:]).any())
assert_((a[1:] >= a[:-1]).all())
assert_(not (a[1:] < a[:-1]).any())
# All != except for +/-0
assert_equal(np.nonzero(a[:-1] < a[1:])[0].size, a.size - 2)
assert_equal(np.nonzero(a[1:] > a[:-1])[0].size, a.size - 2)
def _get_multi_index(self, arr, indices):
"""Mimic multi dimensional indexing.
Parameters
----------
arr : ndarray
Array to be indexed.
indices : tuple of index objects
Returns
-------
out : ndarray
An array equivalent to the indexing operation (but always a copy).
`arr[indices]` should be identical.
no_copy : bool
Whether the indexing operation requires a copy. If this is `True`,
`np.may_share_memory(arr, arr[indices])` should be `True` (with
some exceptions for scalars and possibly 0-d arrays).
Notes
-----
While the function may mostly match the errors of normal indexing this
is generally not the case.
"""
in_indices = list(indices)
indices = []
# if False, this is a fancy or boolean index
no_copy = True
# number of fancy/scalar indexes that are not consecutive
num_fancy = 0
# number of dimensions indexed by a "fancy" index
fancy_dim = 0
# NOTE: This is a funny twist (and probably OK to change).
# The boolean array has illegal indexes, but this is
# allowed if the broadcast fancy-indices are 0-sized.
# This variable is to catch that case.
error_unless_broadcast_to_empty = False
# We need to handle Ellipsis and make arrays from indices, also
# check if this is fancy indexing (set no_copy).
ndim = 0
ellipsis_pos = None # define here mostly to replace all but first.
for i, indx in enumerate(in_indices):
if indx is None:
continue
if isinstance(indx, np.ndarray) and indx.dtype == bool:
no_copy = False
if indx.ndim == 0:
raise IndexError
# boolean indices can have higher dimensions
ndim += indx.ndim
fancy_dim += indx.ndim
continue
if indx is Ellipsis:
if ellipsis_pos is None:
ellipsis_pos = i
continue # do not increment ndim counter
raise IndexError
if isinstance(indx, slice):
ndim += 1
continue
if not isinstance(indx, np.ndarray):
# This could be open for changes in numpy.
# numpy should maybe raise an error if casting to intp
# is not safe. It rejects np.array([1., 2.]) but not
# [1., 2.] as index (same for ie. np.take).
# (Note the importance of empty lists if changing this here)
try:
indx = np.array(indx, dtype=np.intp)
except ValueError:
raise IndexError
in_indices[i] = indx
elif indx.dtype.kind != 'b' and indx.dtype.kind != 'i':
raise IndexError('arrays used as indices must be of '
'integer (or boolean) type')
if indx.ndim != 0:
no_copy = False
ndim += 1
fancy_dim += 1
if arr.ndim - ndim < 0:
# we can't take more dimensions then we have, not even for 0-d
# arrays. since a[()] makes sense, but not a[(),]. We will
# raise an error later on, unless a broadcasting error occurs
# first.
raise IndexError
if ndim == 0 and None not in in_indices:
# Well we have no indexes or one Ellipsis. This is legal.
return arr.copy(), no_copy
if ellipsis_pos is not None:
in_indices[ellipsis_pos:ellipsis_pos+1] = ([slice(None, None)] *
(arr.ndim - ndim))
for ax, indx in enumerate(in_indices):
if isinstance(indx, slice):
# convert to an index array
indx = np.arange(*indx.indices(arr.shape[ax]))
indices.append(['s', indx])
continue
elif indx is None:
# this is like taking a slice with one element from a new axis:
indices.append(['n', np.array([0], dtype=np.intp)])
arr = arr.reshape((arr.shape[:ax] + (1,) + arr.shape[ax:]))
continue
if isinstance(indx, np.ndarray) and indx.dtype == bool:
if indx.shape != arr.shape[ax:ax+indx.ndim]:
raise IndexError
try:
flat_indx = np.ravel_multi_index(np.nonzero(indx),
arr.shape[ax:ax+indx.ndim], mode='raise')
except Exception:
error_unless_broadcast_to_empty = True
# fill with 0s instead, and raise error later
flat_indx = np.array([0]*indx.sum(), dtype=np.intp)
# concatenate axis into a single one:
if indx.ndim != 0:
arr = arr.reshape((arr.shape[:ax]
+ (np.prod(arr.shape[ax:ax+indx.ndim]),)
+ arr.shape[ax+indx.ndim:]))
indx = flat_indx
else:
# This could be changed, a 0-d boolean index can
# make sense (even outside the 0-d indexed array case)
# Note that originally this is could be interpreted as
# integer in the full integer special case.
raise IndexError
else:
# If the index is a singleton, the bounds check is done
# before the broadcasting. This used to be different in <1.9
if indx.ndim == 0:
if indx >= arr.shape[ax] or indx < -arr.shape[ax]:
raise IndexError
if indx.ndim == 0:
# The index is a scalar. This used to be two fold, but if
# fancy indexing was active, the check was done later,
# possibly after broadcasting it away (1.7. or earlier).
# Now it is always done.
if indx >= arr.shape[ax] or indx < - arr.shape[ax]:
raise IndexError
if (len(indices) > 0 and
indices[-1][0] == 'f' and
ax != ellipsis_pos):
# NOTE: There could still have been a 0-sized Ellipsis
# between them. Checked that with ellipsis_pos.
indices[-1].append(indx)
else:
# We have a fancy index that is not after an existing one.
# NOTE: A 0-d array triggers this as well, while one may
# expect it to not trigger it, since a scalar would not be
# considered fancy indexing.
num_fancy += 1
indices.append(['f', indx])
if num_fancy > 1 and not no_copy:
# We have to flush the fancy indexes left
new_indices = indices[:]
axes = list(range(arr.ndim))
fancy_axes = []
new_indices.insert(0, ['f'])
ni = 0
ai = 0
for indx in indices:
ni += 1
if indx[0] == 'f':
new_indices[0].extend(indx[1:])
del new_indices[ni]
ni -= 1
for ax in range(ai, ai + len(indx[1:])):
fancy_axes.append(ax)
axes.remove(ax)
ai += len(indx) - 1 # axis we are at
indices = new_indices
# and now we need to transpose arr:
arr = arr.transpose(*(fancy_axes + axes))
# We only have one 'f' index now and arr is transposed accordingly.
# Now handle newaxis by reshaping...
ax = 0
for indx in indices:
if indx[0] == 'f':
if len(indx) == 1:
continue
# First of all, reshape arr to combine fancy axes into one:
orig_shape = arr.shape
orig_slice = orig_shape[ax:ax + len(indx[1:])]
arr = arr.reshape((arr.shape[:ax]
+ (np.prod(orig_slice).astype(int),)
+ arr.shape[ax + len(indx[1:]):]))
# Check if broadcasting works
res = np.broadcast(*indx[1:])
# unfortunately the indices might be out of bounds. So check
# that first, and use mode='wrap' then. However only if
# there are any indices...
if res.size != 0:
if error_unless_broadcast_to_empty:
raise IndexError
for _indx, _size in zip(indx[1:], orig_slice):
if _indx.size == 0:
continue
if np.any(_indx >= _size) or np.any(_indx < -_size):
raise IndexError
if len(indx[1:]) == len(orig_slice):
if np.product(orig_slice) == 0:
# Work around for a crash or IndexError with 'wrap'
# in some 0-sized cases.
try:
mi = np.ravel_multi_index(indx[1:], orig_slice,
mode='raise')
except Exception:
# This happens with 0-sized orig_slice (sometimes?)
# here it is a ValueError, but indexing gives a:
raise IndexError('invalid index into 0-sized')
else:
mi = np.ravel_multi_index(indx[1:], orig_slice,
mode='wrap')
else:
# Maybe never happens...
raise ValueError
arr = arr.take(mi.ravel(), axis=ax)
try:
arr = arr.reshape((arr.shape[:ax]
+ mi.shape
+ arr.shape[ax+1:]))
except ValueError:
# too many dimensions, probably
raise IndexError
ax += mi.ndim
continue
# If we are here, we have a 1D array for take:
arr = arr.take(indx[1], axis=ax)
ax += 1
return arr, no_copy
def test_bool(self):
bool_a = [True, False, True, True]
int_a, = np.nonzero(bool_a)
assert_equal(np.ix_(bool_a)[0], int_a)
def test_testMaPut(self):
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
m = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]
i = np.nonzero(m)[0]
put(ym, i, zm)
assert_(all(take(ym, i, axis=0) == zm))