def test_density(self):
# Check that the integral of the density equals 1.
n = 100
v = np.random.rand(n)
a, b = histogram(v, density=True)
area = np.sum(a * np.diff(b))
assert_almost_equal(area, 1)
# Check with non-constant bin widths
v = np.arange(10)
bins = [0, 1, 3, 6, 10]
a, b = histogram(v, bins, density=True)
assert_array_equal(a, .1)
assert_equal(np.sum(a * np.diff(b)), 1)
# Test that passing False works too
a, b = histogram(v, bins, density=False)
assert_array_equal(a, [1, 2, 3, 4])
# Variale bin widths are especially useful to deal with
# infinities.
v = np.arange(10)
bins = [0, 1, 3, 6, np.inf]
a, b = histogram(v, bins, density=True)
assert_array_equal(a, [.1, .1, .1, 0.])
# Taken from a bug report from N. Becker on the numpy-discussion
# mailing list Aug. 6, 2010.
counts, dmy = np.histogram([1, 2, 3, 4], [0.5, 1.5, np.inf],
density=True)
assert_equal(counts, [.25, 0])
def test_memmap_subclass(self):
class MemmapSubClass(memmap):
pass
fp = MemmapSubClass(self.tmpfp, dtype=self.dtype, shape=self.shape)
fp[:] = self.data
# We keep previous behavior for subclasses of memmap, i.e. the
# ufunc and __getitem__ output is never turned into a ndarray
assert_(sum(fp, axis=0).__class__ is MemmapSubClass)
assert_(sum(fp).__class__ is MemmapSubClass)
assert_(fp[1:, :-1].__class__ is MemmapSubClass)
assert (fp[[0, 1]].__class__ is MemmapSubClass)
def test_logseries_convergence(self):
# Test for ticket #923
N = 1000
np.random.seed(0)
rvsn = np.random.logseries(0.8, size=N)
# these two frequency counts should be close to theoretical
# numbers with this large sample
# theoretical large N result is 0.49706795
freq = np.sum(rvsn == 1) / float(N)
msg = "Frequency was %f, should be > 0.45" % freq
assert_(freq > 0.45, msg)
# theoretical large N result is 0.19882718
freq = np.sum(rvsn == 2) / float(N)
msg = "Frequency was %f, should be < 0.23" % freq
assert_(freq < 0.23, msg)
def test_sum(self):
"""Test whether matrix.sum(axis=1) preserves orientation.
Fails in NumPy <= 0.9.6.2127.
"""
M = matrix([[1, 2, 0, 0], [3, 4, 0, 0], [1, 2, 1, 2], [3, 4, 3, 4]])
sum0 = matrix([8, 12, 4, 6])
sum1 = matrix([3, 7, 6, 14]).T
sumall = 30
assert_array_equal(sum0, M.sum(axis=0))
assert_array_equal(sum1, M.sum(axis=1))
assert_equal(sumall, M.sum())
assert_array_equal(sum0, np.sum(M, axis=0))
assert_array_equal(sum1, np.sum(M, axis=1))
assert_equal(sumall, np.sum(M))
def test_simple(self):
n = 100
v = np.random.rand(n)
(a, b) = histogram(v)
# check if the sum of the bins equals the number of samples
assert_equal(np.sum(a, axis=0), n)
# check that the bin counts are evenly spaced when the data is from
# a linear function
(a, b) = histogram(np.linspace(0, 10, 100))
assert_array_equal(a, 10)
def test_testAddSumProd(self):
# Test add, sum, product.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.add.reduce(x), add.reduce(x)))
assert_(eq(np.add.accumulate(x), add.accumulate(x)))
assert_(eq(4, sum(array(4), axis=0)))
assert_(eq(4, sum(array(4), axis=0)))
assert_(eq(np.sum(x, axis=0), sum(x, axis=0)))
assert_(eq(np.sum(filled(xm, 0), axis=0), sum(xm, axis=0)))
assert_(eq(np.sum(x, 0), sum(x, 0)))
assert_(eq(np.product(x, axis=0), product(x, axis=0)))
assert_(eq(np.product(x, 0), product(x, 0)))
assert_(eq(np.product(filled(xm, 1), axis=0),
product(xm, axis=0)))
if len(s) > 1:
assert_(eq(np.concatenate((x, y), 1),
concatenate((xm, ym), 1)))
assert_(eq(np.add.reduce(x, 1), add.reduce(x, 1)))
assert_(eq(np.sum(x, 1), sum(x, 1)))
assert_(eq(np.product(x, 1), product(x, 1)))
def test_normed(self):
sup = suppress_warnings()
with sup:
rec = sup.record(np.VisibleDeprecationWarning, '.*normed.*')
# Check that the integral of the density equals 1.
n = 100
v = np.random.rand(n)
a, b = histogram(v, normed=True)
area = np.sum(a * np.diff(b))
assert_almost_equal(area, 1)
assert_equal(len(rec), 1)
sup = suppress_warnings()
with sup:
rec = sup.record(np.VisibleDeprecationWarning, '.*normed.*')
# Check with non-constant bin widths (buggy but backwards
# compatible)
v = np.arange(10)
bins = [0, 1, 5, 9, 10]
a, b = histogram(v, bins, normed=True)
area = np.sum(a * np.diff(b))
assert_almost_equal(area, 1)
assert_equal(len(rec), 1)
def pad(array, pad_width, mode, **kwargs):
"""
Pads an array.
Parameters
----------
array : array_like of rank N
Input array
pad_width : {sequence, array_like, int}
Number of values padded to the edges of each axis.
((before_1, after_1), ... (before_N, after_N)) unique pad widths
for each axis.
((before, after),) yields same before and after pad for each axis.
(pad,) or int is a shortcut for before = after = pad width for all
axes.
mode : str or function
One of the following string values or a user supplied function.
'constant'
Pads with a constant value.
'edge'
Pads with the edge values of array.
'linear_ramp'
Pads with the linear ramp between end_value and the
array edge value.
'maximum'
Pads with the maximum value of all or part of the
vector along each axis.
'mean'
Pads with the mean value of all or part of the
vector along each axis.
'median'
Pads with the median value of all or part of the
vector along each axis.
'minimum'
Pads with the minimum value of all or part of the
vector along each axis.
'reflect'
Pads with the reflection of the vector mirrored on
the first and last values of the vector along each
axis.
'symmetric'
Pads with the reflection of the vector mirrored
along the edge of the array.
'wrap'
Pads with the wrap of the vector along the axis.
The first values are used to pad the end and the
end values are used to pad the beginning.
<function>
Padding function, see Notes.
stat_length : sequence or int, optional
Used in 'maximum', 'mean', 'median', and 'minimum'. Number of
values at edge of each axis used to calculate the statistic value.
((before_1, after_1), ... (before_N, after_N)) unique statistic
lengths for each axis.
((before, after),) yields same before and after statistic lengths
for each axis.
(stat_length,) or int is a shortcut for before = after = statistic
length for all axes.
Default is ``None``, to use the entire axis.
constant_values : sequence or int, optional
Used in 'constant'. The values to set the padded values for each
axis.
((before_1, after_1), ... (before_N, after_N)) unique pad constants
for each axis.
((before, after),) yields same before and after constants for each
axis.
(constant,) or int is a shortcut for before = after = constant for
all axes.
Default is 0.
end_values : sequence or int, optional
Used in 'linear_ramp'. The values used for the ending value of the
linear_ramp and that will form the edge of the padded array.
((before_1, after_1), ... (before_N, after_N)) unique end values
for each axis.
((before, after),) yields same before and after end values for each
axis.
(constant,) or int is a shortcut for before = after = end value for
all axes.
Default is 0.
reflect_type : {'even', 'odd'}, optional
Used in 'reflect', and 'symmetric'. The 'even' style is the
default with an unaltered reflection around the edge value. For
the 'odd' style, the extended part of the array is created by
subtracting the reflected values from two times the edge value.
Returns
-------
pad : ndarray
Padded array of rank equal to `array` with shape increased
according to `pad_width`.
Notes
-----
.. versionadded:: 1.7.0
For an array with rank greater than 1, some of the padding of later
axes is calculated from padding of previous axes. This is easiest to
think about with a rank 2 array where the corners of the padded array
are calculated by using padded values from the first axis.
The padding function, if used, should return a rank 1 array equal in
length to the vector argument with padded values replaced. It has the
following signature::
padding_func(vector, iaxis_pad_width, iaxis, kwargs)
where
vector : ndarray
A rank 1 array already padded with zeros. Padded values are
vector[:pad_tuple[0]] and vector[-pad_tuple[1]:].
iaxis_pad_width : tuple
A 2-tuple of ints, iaxis_pad_width[0] represents the number of
values padded at the beginning of vector where
iaxis_pad_width[1] represents the number of values padded at
the end of vector.
iaxis : int
The axis currently being calculated.
kwargs : dict
Any keyword arguments the function requires.
Examples
--------
>>> a = [1, 2, 3, 4, 5]
>>> np.pad(a, (2,3), 'constant', constant_values=(4, 6))
array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6])
>>> np.pad(a, (2, 3), 'edge')
array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5])
>>> np.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))
array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4])
>>> np.pad(a, (2,), 'maximum')
array([5, 5, 1, 2, 3, 4, 5, 5, 5])
>>> np.pad(a, (2,), 'mean')
array([3, 3, 1, 2, 3, 4, 5, 3, 3])
>>> np.pad(a, (2,), 'median')
array([3, 3, 1, 2, 3, 4, 5, 3, 3])
>>> a = [[1, 2], [3, 4]]
>>> np.pad(a, ((3, 2), (2, 3)), 'minimum')
array([[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1],
[3, 3, 3, 4, 3, 3, 3],
[1, 1, 1, 2, 1, 1, 1],
[1, 1, 1, 2, 1, 1, 1]])
>>> a = [1, 2, 3, 4, 5]
>>> np.pad(a, (2, 3), 'reflect')
array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])
>>> np.pad(a, (2, 3), 'reflect', reflect_type='odd')
array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8])
>>> np.pad(a, (2, 3), 'symmetric')
array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])
>>> np.pad(a, (2, 3), 'symmetric', reflect_type='odd')
array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])
>>> np.pad(a, (2, 3), 'wrap')
array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])
>>> def pad_with(vector, pad_width, iaxis, kwargs):
... pad_value = kwargs.get('padder', 10)
... vector[:pad_width[0]] = pad_value
... vector[-pad_width[1]:] = pad_value
... return vector
>>> a = np.arange(6)
>>> a = a.reshape((2, 3))
>>> np.pad(a, 2, pad_with)
array([[10, 10, 10, 10, 10, 10, 10],
[10, 10, 10, 10, 10, 10, 10],
[10, 10, 0, 1, 2, 10, 10],
[10, 10, 3, 4, 5, 10, 10],
[10, 10, 10, 10, 10, 10, 10],
[10, 10, 10, 10, 10, 10, 10]])
>>> np.pad(a, 2, pad_with, padder=100)
array([[100, 100, 100, 100, 100, 100, 100],
[100, 100, 100, 100, 100, 100, 100],
[100, 100, 0, 1, 2, 100, 100],
[100, 100, 3, 4, 5, 100, 100],
[100, 100, 100, 100, 100, 100, 100],
[100, 100, 100, 100, 100, 100, 100]])
"""
if not np.asarray(pad_width).dtype.kind == 'i':
raise TypeError('`pad_width` must be of integral type.')
narray = np.array(array)
pad_width = _validate_lengths(narray, pad_width)
allowedkwargs = {
'constant': ['constant_values'],
'edge': [],
'linear_ramp': ['end_values'],
'maximum': ['stat_length'],
'mean': ['stat_length'],
'median': ['stat_length'],
'minimum': ['stat_length'],
'reflect': ['reflect_type'],
'symmetric': ['reflect_type'],
'wrap': [],
}
kwdefaults = {
'stat_length': None,
'constant_values': 0,
'end_values': 0,
'reflect_type': 'even',
}
if isinstance(mode, np.compat.basestring):
# Make sure have allowed kwargs appropriate for mode
for key in kwargs:
if key not in allowedkwargs[mode]:
raise ValueError('%s keyword not in allowed keywords %s' %
(key, allowedkwargs[mode]))
# Set kwarg defaults
for kw in allowedkwargs[mode]:
kwargs.setdefault(kw, kwdefaults[kw])
# Need to only normalize particular keywords.
for i in kwargs:
if i == 'stat_length':
kwargs[i] = _validate_lengths(narray, kwargs[i])
if i in ['end_values', 'constant_values']:
kwargs[i] = _normalize_shape(narray,
kwargs[i],
cast_to_int=False)
else:
# Drop back to old, slower np.apply_along_axis mode for user-supplied
# vector function
function = mode
# Create a new padded array
rank = list(range(narray.ndim))
total_dim_increase = [np.sum(pad_width[i]) for i in rank]
offset_slices = tuple(
slice(pad_width[i][0], pad_width[i][0] + narray.shape[i])
for i in rank)
new_shape = np.array(narray.shape) + total_dim_increase
newmat = np.zeros(new_shape, narray.dtype)
# Insert the original array into the padded array
newmat[offset_slices] = narray
# This is the core of pad ...
for iaxis in rank:
np.apply_along_axis(function, iaxis, newmat, pad_width[iaxis],
iaxis, kwargs)
return newmat
# If we get here, use new padding method
newmat = narray.copy()
# API preserved, but completely new algorithm which pads by building the
# entire block to pad before/after `arr` with in one step, for each axis.
if mode == 'constant':
for axis, ((pad_before, pad_after), (before_val, after_val)) \
in enumerate(zip(pad_width, kwargs['constant_values'])):
newmat = _prepend_const(newmat, pad_before, before_val, axis)
newmat = _append_const(newmat, pad_after, after_val, axis)
elif mode == 'edge':
for axis, (pad_before, pad_after) in enumerate(pad_width):
newmat = _prepend_edge(newmat, pad_before, axis)
newmat = _append_edge(newmat, pad_after, axis)
elif mode == 'linear_ramp':
for axis, ((pad_before, pad_after), (before_val, after_val)) \
in enumerate(zip(pad_width, kwargs['end_values'])):
newmat = _prepend_ramp(newmat, pad_before, before_val, axis)
newmat = _append_ramp(newmat, pad_after, after_val, axis)
elif mode == 'maximum':
for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
in enumerate(zip(pad_width, kwargs['stat_length'])):
newmat = _prepend_max(newmat, pad_before, chunk_before, axis)
newmat = _append_max(newmat, pad_after, chunk_after, axis)
elif mode == 'mean':
for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
in enumerate(zip(pad_width, kwargs['stat_length'])):
newmat = _prepend_mean(newmat, pad_before, chunk_before, axis)
newmat = _append_mean(newmat, pad_after, chunk_after, axis)
elif mode == 'median':
for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
in enumerate(zip(pad_width, kwargs['stat_length'])):
newmat = _prepend_med(newmat, pad_before, chunk_before, axis)
newmat = _append_med(newmat, pad_after, chunk_after, axis)
elif mode == 'minimum':
for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \
in enumerate(zip(pad_width, kwargs['stat_length'])):
newmat = _prepend_min(newmat, pad_before, chunk_before, axis)
newmat = _append_min(newmat, pad_after, chunk_after, axis)
elif mode == 'reflect':
for axis, (pad_before, pad_after) in enumerate(pad_width):
if narray.shape[axis] == 0:
# Axes with non-zero padding cannot be empty.
if pad_before > 0 or pad_after > 0:
raise ValueError("There aren't any elements to reflect"
" in axis {} of `array`".format(axis))
# Skip zero padding on empty axes.
continue
# Recursive padding along any axis where `pad_amt` is too large
# for indexing tricks. We can only safely pad the original axis
# length, to keep the period of the reflections consistent.
if ((pad_before > 0) or
(pad_after > 0)) and newmat.shape[axis] == 1:
# Extending singleton dimension for 'reflect' is legacy
# behavior; it really should raise an error.
newmat = _prepend_edge(newmat, pad_before, axis)
newmat = _append_edge(newmat, pad_after, axis)
continue
method = kwargs['reflect_type']
safe_pad = newmat.shape[axis] - 1
while ((pad_before > safe_pad) or (pad_after > safe_pad)):
pad_iter_b = min(safe_pad, safe_pad * (pad_before // safe_pad))
pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad))
newmat = _pad_ref(newmat, (pad_iter_b, pad_iter_a), method,
axis)
pad_before -= pad_iter_b
pad_after -= pad_iter_a
safe_pad += pad_iter_b + pad_iter_a
newmat = _pad_ref(newmat, (pad_before, pad_after), method, axis)
elif mode == 'symmetric':
for axis, (pad_before, pad_after) in enumerate(pad_width):
# Recursive padding along any axis where `pad_amt` is too large
# for indexing tricks. We can only safely pad the original axis
# length, to keep the period of the reflections consistent.
method = kwargs['reflect_type']
safe_pad = newmat.shape[axis]
while ((pad_before > safe_pad) or (pad_after > safe_pad)):
pad_iter_b = min(safe_pad, safe_pad * (pad_before // safe_pad))
pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad))
newmat = _pad_sym(newmat, (pad_iter_b, pad_iter_a), method,
axis)
pad_before -= pad_iter_b
pad_after -= pad_iter_a
safe_pad += pad_iter_b + pad_iter_a
newmat = _pad_sym(newmat, (pad_before, pad_after), method, axis)
elif mode == 'wrap':
for axis, (pad_before, pad_after) in enumerate(pad_width):
# Recursive padding along any axis where `pad_amt` is too large
# for indexing tricks. We can only safely pad the original axis
# length, to keep the period of the reflections consistent.
safe_pad = newmat.shape[axis]
while ((pad_before > safe_pad) or (pad_after > safe_pad)):
pad_iter_b = min(safe_pad, safe_pad * (pad_before // safe_pad))
pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad))
newmat = _pad_wrap(newmat, (pad_iter_b, pad_iter_a), axis)
pad_before -= pad_iter_b
pad_after -= pad_iter_a
safe_pad += pad_iter_b + pad_iter_a
newmat = _pad_wrap(newmat, (pad_before, pad_after), axis)
return newmat
def sum_to_0d(x):
""" Sum x, returning a 0d array of the same class """
assert_equal(x.ndim, 1)
return np.squeeze(np.sum(x, keepdims=True))
def fft1(x):
L = len(x)
phase = -2j*np.pi*(np.arange(L)/float(L))
phase = np.arange(L).reshape(-1, 1) * phase
return np.sum(x*np.exp(phase), axis=1)
def stack_arrays(arrays,
defaults=None,
usemask=True,
asrecarray=False,
autoconvert=False):
"""
Superposes arrays fields by fields
Parameters
----------
arrays : array or sequence
Sequence of input arrays.
defaults : dictionary, optional
Dictionary mapping field names to the corresponding default values.
usemask : {True, False}, optional
Whether to return a MaskedArray (or MaskedRecords is
`asrecarray==True`) or a ndarray.
asrecarray : {False, True}, optional
Whether to return a recarray (or MaskedRecords if `usemask==True`)
or just a flexible-type ndarray.
autoconvert : {False, True}, optional
Whether automatically cast the type of the field to the maximum.
Examples
--------
>>> from numpy1.lib import recfunctions as rfn
>>> x = np.array([1, 2,])
>>> rfn.stack_arrays(x) is x
True
>>> z = np.array([('A', 1), ('B', 2)], dtype=[('A', '|S3'), ('B', float)])
>>> zz = np.array([('a', 10., 100.), ('b', 20., 200.), ('c', 30., 300.)],
... dtype=[('A', '|S3'), ('B', float), ('C', float)])
>>> test = rfn.stack_arrays((z,zz))
>>> test
masked_array(data = [('A', 1.0, --) ('B', 2.0, --) ('a', 10.0, 100.0) ('b', 20.0, 200.0)
('c', 30.0, 300.0)],
mask = [(False, False, True) (False, False, True) (False, False, False)
(False, False, False) (False, False, False)],
fill_value = ('N/A', 1e+20, 1e+20),
dtype = [('A', '|S3'), ('B', '<f8'), ('C', '<f8')])
"""
if isinstance(arrays, ndarray):
return arrays
elif len(arrays) == 1:
return arrays[0]
seqarrays = [np.asanyarray(a).ravel() for a in arrays]
nrecords = [len(a) for a in seqarrays]
ndtype = [a.dtype for a in seqarrays]
fldnames = [d.names for d in ndtype]
#
dtype_l = ndtype[0]
newdescr = get_fieldspec(dtype_l)
names = [n for n, d in newdescr]
for dtype_n in ndtype[1:]:
for fname, fdtype in get_fieldspec(dtype_n):
if fname not in names:
newdescr.append((fname, fdtype))
names.append(fname)
else:
nameidx = names.index(fname)
_, cdtype = newdescr[nameidx]
if autoconvert:
newdescr[nameidx] = (fname, max(fdtype, cdtype))
elif fdtype != cdtype:
raise TypeError("Incompatible type '%s' <> '%s'" %
(cdtype, fdtype))
# Only one field: use concatenate
if len(newdescr) == 1:
output = ma.concatenate(seqarrays)
else:
#
output = ma.masked_all((np.sum(nrecords), ), newdescr)
offset = np.cumsum(np.r_[0, nrecords])
seen = []
for (a, n, i, j) in zip(seqarrays, fldnames, offset[:-1], offset[1:]):
names = a.dtype.names
if names is None:
output['f%i' % len(seen)][i:j] = a
else:
for name in n:
output[name][i:j] = a[name]
if name not in seen:
seen.append(name)
#
return _fix_output(_fix_defaults(output, defaults),
usemask=usemask,
asrecarray=asrecarray)
def test_nansum(self):
tgt = np.sum(self.mat)
for mat in self.integer_arrays():
assert_equal(np.nansum(mat), tgt)
