def test_dtypes(self):
# Test with different data types
for dtype in [np.int16, np.uint16, np.int32,
np.uint32, np.int64, np.uint64]:
coords = np.array(
[[1, 0, 1, 2, 3, 4], [1, 6, 1, 3, 2, 0]], dtype=dtype)
shape = (5, 8)
uncoords = 8*coords[0]+coords[1]
assert_equal(np.ravel_multi_index(coords, shape), uncoords)
assert_equal(coords, np.unravel_index(uncoords, shape))
uncoords = coords[0]+5*coords[1]
assert_equal(
np.ravel_multi_index(coords, shape, order='F'), uncoords)
assert_equal(coords, np.unravel_index(uncoords, shape, order='F'))
coords = np.array(
[[1, 0, 1, 2, 3, 4], [1, 6, 1, 3, 2, 0], [1, 3, 1, 0, 9, 5]],
dtype=dtype)
shape = (5, 8, 10)
uncoords = 10*(8*coords[0]+coords[1])+coords[2]
assert_equal(np.ravel_multi_index(coords, shape), uncoords)
assert_equal(coords, np.unravel_index(uncoords, shape))
uncoords = coords[0]+5*(coords[1]+8*coords[2])
assert_equal(
np.ravel_multi_index(coords, shape, order='F'), uncoords)
assert_equal(coords, np.unravel_index(uncoords, shape, order='F'))
def test_clipmodes(self):
# Test clipmodes
assert_equal(
np.ravel_multi_index([5, 1, -1, 2], (4, 3, 7, 12), mode='wrap'),
np.ravel_multi_index([1, 1, 6, 2], (4, 3, 7, 12)))
assert_equal(np.ravel_multi_index([5, 1, -1, 2], (4, 3, 7, 12),
mode=(
'wrap', 'raise', 'clip', 'raise')),
np.ravel_multi_index([1, 1, 0, 2], (4, 3, 7, 12)))
assert_raises(
ValueError, np.ravel_multi_index, [5, 1, -1, 2], (4, 3, 7, 12))
def test_basic(self):
assert_equal(np.unravel_index(2, (2, 2)), (1, 0))
assert_equal(np.ravel_multi_index((1, 0), (2, 2)), 2)
assert_equal(np.unravel_index(254, (17, 94)), (2, 66))
assert_equal(np.ravel_multi_index((2, 66), (17, 94)), 254)
assert_raises(ValueError, np.unravel_index, -1, (2, 2))
assert_raises(TypeError, np.unravel_index, 0.5, (2, 2))
assert_raises(ValueError, np.unravel_index, 4, (2, 2))
assert_raises(ValueError, np.ravel_multi_index, (-3, 1), (2, 2))
assert_raises(ValueError, np.ravel_multi_index, (2, 1), (2, 2))
assert_raises(ValueError, np.ravel_multi_index, (0, -3), (2, 2))
assert_raises(ValueError, np.ravel_multi_index, (0, 2), (2, 2))
assert_raises(TypeError, np.ravel_multi_index, (0.1, 0.), (2, 2))
assert_equal(np.unravel_index((2*3 + 1)*6 + 4, (4, 3, 6)), [2, 1, 4])
assert_equal(
np.ravel_multi_index([2, 1, 4], (4, 3, 6)), (2*3 + 1)*6 + 4)
arr = np.array([[3, 6, 6], [4, 5, 1]])
assert_equal(np.ravel_multi_index(arr, (7, 6)), [22, 41, 37])
assert_equal(
np.ravel_multi_index(arr, (7, 6), order='F'), [31, 41, 13])
assert_equal(
np.ravel_multi_index(arr, (4, 6), mode='clip'), [22, 23, 19])
assert_equal(np.ravel_multi_index(arr, (4, 4), mode=('clip', 'wrap')),
[12, 13, 13])
assert_equal(np.ravel_multi_index((3, 1, 4, 1), (6, 7, 8, 9)), 1621)
assert_equal(np.unravel_index(np.array([22, 41, 37]), (7, 6)),
[[3, 6, 6], [4, 5, 1]])
assert_equal(
np.unravel_index(np.array([31, 41, 13]), (7, 6), order='F'),
[[3, 6, 6], [4, 5, 1]])
assert_equal(np.unravel_index(1621, (6, 7, 8, 9)), [3, 1, 4, 1])
def test_big_indices(self):
# ravel_multi_index for big indices (issue #7546)
if np.intp == np.int64:
arr = ([1, 29], [3, 5], [3, 117], [19, 2],
[2379, 1284], [2, 2], [0, 1])
assert_equal(
np.ravel_multi_index(arr, (41, 7, 120, 36, 2706, 8, 6)),
[5627771580, 117259570957])
# test overflow checking for too big array (issue #7546)
dummy_arr = ([0],[0])
half_max = np.iinfo(np.intp).max // 2
assert_equal(
np.ravel_multi_index(dummy_arr, (half_max, 2)), [0])
assert_raises(ValueError,
np.ravel_multi_index, dummy_arr, (half_max+1, 2))
assert_equal(
np.ravel_multi_index(dummy_arr, (half_max, 2), order='F'), [0])
assert_raises(ValueError,
np.ravel_multi_index, dummy_arr, (half_max+1, 2), order='F')
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 histogramdd(sample,
bins=10,
range=None,
normed=None,
weights=None,
density=None):
"""
Compute the multidimensional histogram of some data.
Parameters
----------
sample : (N, D) array, or (D, N) array_like
The data to be histogrammed.
Note the unusual interpretation of sample when an array_like:
* When an array, each row is a coordinate in a D-dimensional space -
such as ``histogramgramdd(np.array([p1, p2, p3]))``.
* When an array_like, each element is the list of values for single
coordinate - such as ``histogramgramdd((X, Y, Z))``.
The first form should be preferred.
bins : sequence or int, optional
The bin specification:
* A sequence of arrays describing the bin edges along each dimension.
* The number of bins for each dimension (nx, ny, ... =bins)
* The number of bins for all dimensions (nx=ny=...=bins).
range : sequence, optional
A sequence of length D, each an optional (lower, upper) tuple giving
the outer bin edges to be used if the edges are not given explicitly in
`bins`.
An entry of None in the sequence results in the minimum and maximum
values being used for the corresponding dimension.
The default, None, is equivalent to passing a tuple of D None values.
density : bool, optional
If False, the default, returns the number of samples in each bin.
If True, returns the probability *density* function at the bin,
``bin_count / sample_count / bin_volume``.
normed : bool, optional
An alias for the density argument that behaves identically. To avoid
confusion with the broken normed argument to `histogram`, `density`
should be preferred.
weights : (N,) array_like, optional
An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.
Weights are normalized to 1 if normed is True. If normed is False,
the values of the returned histogram are equal to the sum of the
weights belonging to the samples falling into each bin.
Returns
-------
H : ndarray
The multidimensional histogram of sample x. See normed and weights
for the different possible semantics.
edges : list
A list of D arrays describing the bin edges for each dimension.
See Also
--------
histogram: 1-D histogram
histogram2d: 2-D histogram
Examples
--------
>>> r = np.random.randn(100,3)
>>> H, edges = np.histogramdd(r, bins = (5, 8, 4))
>>> H.shape, edges[0].size, edges[1].size, edges[2].size
((5, 8, 4), 6, 9, 5)
"""
try:
# Sample is an ND-array.
N, D = sample.shape
except (AttributeError, ValueError):
# Sample is a sequence of 1D arrays.
sample = np.atleast_2d(sample).T
N, D = sample.shape
nbin = np.empty(D, int)
edges = D * [None]
dedges = D * [None]
if weights is not None:
weights = np.asarray(weights)
try:
M = len(bins)
if M != D:
raise ValueError(
'The dimension of bins must be equal to the dimension of the '
' sample x.')
except TypeError:
# bins is an integer
bins = D * [bins]
# normalize the range argument
if range is None:
range = (None, ) * D
elif len(range) != D:
raise ValueError('range argument must have one entry per dimension')
# Create edge arrays
for i in _range(D):
if np.ndim(bins[i]) == 0:
if bins[i] < 1:
raise ValueError(
'`bins[{}]` must be positive, when an integer'.format(i))
smin, smax = _get_outer_edges(sample[:, i], range[i])
edges[i] = np.linspace(smin, smax, bins[i] + 1)
elif np.ndim(bins[i]) == 1:
edges[i] = np.asarray(bins[i])
if np.any(edges[i][:-1] > edges[i][1:]):
raise ValueError(
'`bins[{}]` must be monotonically increasing, when an array'
.format(i))
else:
raise ValueError(
'`bins[{}]` must be a scalar or 1d array'.format(i))
nbin[i] = len(edges[i]) + 1 # includes an outlier on each end
dedges[i] = np.diff(edges[i])
# Compute the bin number each sample falls into.
Ncount = tuple(
# avoid np.digitize to work around gh-11022
np.searchsorted(edges[i], sample[:, i], side='right')
for i in _range(D))
# Using digitize, values that fall on an edge are put in the right bin.
# For the rightmost bin, we want values equal to the right edge to be
# counted in the last bin, and not as an outlier.
for i in _range(D):
# Find which points are on the rightmost edge.
on_edge = (sample[:, i] == edges[i][-1])
# Shift these points one bin to the left.
Ncount[i][on_edge] -= 1
# Compute the sample indices in the flattened histogram matrix.
# This raises an error if the array is too large.
xy = np.ravel_multi_index(Ncount, nbin)
# Compute the number of repetitions in xy and assign it to the
# flattened histmat.
hist = np.bincount(xy, weights, minlength=nbin.prod())
# Shape into a proper matrix
hist = hist.reshape(nbin)
# This preserves the (bad) behavior observed in gh-7845, for now.
hist = hist.astype(float, casting='safe')
# Remove outliers (indices 0 and -1 for each dimension).
core = D * (slice(1, -1), )
hist = hist[core]
# handle the aliasing normed argument
if normed is None:
if density is None:
density = False
elif density is None:
# an explicit normed argument was passed, alias it to the new name
density = normed
else:
raise TypeError("Cannot specify both 'normed' and 'density'")
if density:
# calculate the probability density function
s = hist.sum()
for i in _range(D):
shape = np.ones(D, int)
shape[i] = nbin[i] - 2
hist = hist / dedges[i].reshape(shape)
hist /= s
if (hist.shape != nbin - 2).any():
raise RuntimeError("Internal Shape Error")
return hist, edges