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shape_base.py
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shape_base.py
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from __future__ import division, absolute_import, print_function
__all__ = ['atleast_1d', 'atleast_2d', 'atleast_3d', 'block', 'hstack',
'stack', 'vstack']
import functools
import operator
import warnings
from . import numeric as _nx
from . import overrides
from .numeric import array, asanyarray, newaxis
from .multiarray import normalize_axis_index
array_function_dispatch = functools.partial(
overrides.array_function_dispatch, module='numpy')
def _atleast_1d_dispatcher(*arys):
return arys
@array_function_dispatch(_atleast_1d_dispatcher)
def atleast_1d(*arys):
"""
Convert inputs to arrays with at least one dimension.
Scalar inputs are converted to 1-dimensional arrays, whilst
higher-dimensional inputs are preserved.
Parameters
----------
arys1, arys2, ... : array_like
One or more input arrays.
Returns
-------
ret : ndarray
An array, or list of arrays, each with ``a.ndim >= 1``.
Copies are made only if necessary.
See Also
--------
atleast_2d, atleast_3d
Examples
--------
>>> np.atleast_1d(1.0)
array([1.])
>>> x = np.arange(9.0).reshape(3,3)
>>> np.atleast_1d(x)
array([[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]])
>>> np.atleast_1d(x) is x
True
>>> np.atleast_1d(1, [3, 4])
[array([1]), array([3, 4])]
"""
res = []
for ary in arys:
ary = asanyarray(ary)
if ary.ndim == 0:
result = ary.reshape(1)
else:
result = ary
res.append(result)
if len(res) == 1:
return res[0]
else:
return res
def _atleast_2d_dispatcher(*arys):
return arys
@array_function_dispatch(_atleast_2d_dispatcher)
def atleast_2d(*arys):
"""
View inputs as arrays with at least two dimensions.
Parameters
----------
arys1, arys2, ... : array_like
One or more array-like sequences. Non-array inputs are converted
to arrays. Arrays that already have two or more dimensions are
preserved.
Returns
-------
res, res2, ... : ndarray
An array, or list of arrays, each with ``a.ndim >= 2``.
Copies are avoided where possible, and views with two or more
dimensions are returned.
See Also
--------
atleast_1d, atleast_3d
Examples
--------
>>> np.atleast_2d(3.0)
array([[3.]])
>>> x = np.arange(3.0)
>>> np.atleast_2d(x)
array([[0., 1., 2.]])
>>> np.atleast_2d(x).base is x
True
>>> np.atleast_2d(1, [1, 2], [[1, 2]])
[array([[1]]), array([[1, 2]]), array([[1, 2]])]
"""
res = []
for ary in arys:
ary = asanyarray(ary)
if ary.ndim == 0:
result = ary.reshape(1, 1)
elif ary.ndim == 1:
result = ary[newaxis,:]
else:
result = ary
res.append(result)
if len(res) == 1:
return res[0]
else:
return res
def _atleast_3d_dispatcher(*arys):
return arys
@array_function_dispatch(_atleast_3d_dispatcher)
def atleast_3d(*arys):
"""
View inputs as arrays with at least three dimensions.
Parameters
----------
arys1, arys2, ... : array_like
One or more array-like sequences. Non-array inputs are converted to
arrays. Arrays that already have three or more dimensions are
preserved.
Returns
-------
res1, res2, ... : ndarray
An array, or list of arrays, each with ``a.ndim >= 3``. Copies are
avoided where possible, and views with three or more dimensions are
returned. For example, a 1-D array of shape ``(N,)`` becomes a view
of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a
view of shape ``(M, N, 1)``.
See Also
--------
atleast_1d, atleast_2d
Examples
--------
>>> np.atleast_3d(3.0)
array([[[3.]]])
>>> x = np.arange(3.0)
>>> np.atleast_3d(x).shape
(1, 3, 1)
>>> x = np.arange(12.0).reshape(4,3)
>>> np.atleast_3d(x).shape
(4, 3, 1)
>>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself
True
>>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]):
... print(arr, arr.shape) # doctest: +SKIP
...
[[[1]
[2]]] (1, 2, 1)
[[[1]
[2]]] (1, 2, 1)
[[[1 2]]] (1, 1, 2)
"""
res = []
for ary in arys:
ary = asanyarray(ary)
if ary.ndim == 0:
result = ary.reshape(1, 1, 1)
elif ary.ndim == 1:
result = ary[newaxis,:, newaxis]
elif ary.ndim == 2:
result = ary[:,:, newaxis]
else:
result = ary
res.append(result)
if len(res) == 1:
return res[0]
else:
return res
def _arrays_for_stack_dispatcher(arrays, stacklevel=4):
if not hasattr(arrays, '__getitem__') and hasattr(arrays, '__iter__'):
warnings.warn('arrays to stack must be passed as a "sequence" type '
'such as list or tuple. Support for non-sequence '
'iterables such as generators is deprecated as of '
'NumPy 1.16 and will raise an error in the future.',
FutureWarning, stacklevel=stacklevel)
return ()
return arrays
def _vhstack_dispatcher(tup):
return _arrays_for_stack_dispatcher(tup)
@array_function_dispatch(_vhstack_dispatcher)
def vstack(tup):
"""
Stack arrays in sequence vertically (row wise).
This is equivalent to concatenation along the first axis after 1-D arrays
of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by
`vsplit`.
This function makes most sense for arrays with up to 3 dimensions. For
instance, for pixel-data with a height (first axis), width (second axis),
and r/g/b channels (third axis). The functions `concatenate`, `stack` and
`block` provide more general stacking and concatenation operations.
Parameters
----------
tup : sequence of ndarrays
The arrays must have the same shape along all but the first axis.
1-D arrays must have the same length.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays, will be at least 2-D.
See Also
--------
stack : Join a sequence of arrays along a new axis.
hstack : Stack arrays in sequence horizontally (column wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
concatenate : Join a sequence of arrays along an existing axis.
vsplit : Split array into a list of multiple sub-arrays vertically.
block : Assemble arrays from blocks.
Examples
--------
>>> a = np.array([1, 2, 3])
>>> b = np.array([2, 3, 4])
>>> np.vstack((a,b))
array([[1, 2, 3],
[2, 3, 4]])
>>> a = np.array([[1], [2], [3]])
>>> b = np.array([[2], [3], [4]])
>>> np.vstack((a,b))
array([[1],
[2],
[3],
[2],
[3],
[4]])
"""
return _nx.concatenate([atleast_2d(_m) for _m in tup], 0)
@array_function_dispatch(_vhstack_dispatcher)
def hstack(tup):
"""
Stack arrays in sequence horizontally (column wise).
This is equivalent to concatenation along the second axis, except for 1-D
arrays where it concatenates along the first axis. Rebuilds arrays divided
by `hsplit`.
This function makes most sense for arrays with up to 3 dimensions. For
instance, for pixel-data with a height (first axis), width (second axis),
and r/g/b channels (third axis). The functions `concatenate`, `stack` and
`block` provide more general stacking and concatenation operations.
Parameters
----------
tup : sequence of ndarrays
The arrays must have the same shape along all but the second axis,
except 1-D arrays which can be any length.
Returns
-------
stacked : ndarray
The array formed by stacking the given arrays.
See Also
--------
stack : Join a sequence of arrays along a new axis.
vstack : Stack arrays in sequence vertically (row wise).
dstack : Stack arrays in sequence depth wise (along third axis).
concatenate : Join a sequence of arrays along an existing axis.
hsplit : Split array along second axis.
block : Assemble arrays from blocks.
Examples
--------
>>> a = np.array((1,2,3))
>>> b = np.array((2,3,4))
>>> np.hstack((a,b))
array([1, 2, 3, 2, 3, 4])
>>> a = np.array([[1],[2],[3]])
>>> b = np.array([[2],[3],[4]])
>>> np.hstack((a,b))
array([[1, 2],
[2, 3],
[3, 4]])
"""
arrs = [atleast_1d(_m) for _m in tup]
# As a special case, dimension 0 of 1-dimensional arrays is "horizontal"
if arrs and arrs[0].ndim == 1:
return _nx.concatenate(arrs, 0)
else:
return _nx.concatenate(arrs, 1)
def _stack_dispatcher(arrays, axis=None, out=None):
arrays = _arrays_for_stack_dispatcher(arrays, stacklevel=6)
if out is not None:
# optimize for the typical case where only arrays is provided
arrays = list(arrays)
arrays.append(out)
return arrays
@array_function_dispatch(_stack_dispatcher)
def stack(arrays, axis=0, out=None):
"""
Join a sequence of arrays along a new axis.
The ``axis`` parameter specifies the index of the new axis in the
dimensions of the result. For example, if ``axis=0`` it will be the first
dimension and if ``axis=-1`` it will be the last dimension.
.. versionadded:: 1.10.0
Parameters
----------
arrays : sequence of array_like
Each array must have the same shape.
axis : int, optional
The axis in the result array along which the input arrays are stacked.
out : ndarray, optional
If provided, the destination to place the result. The shape must be
correct, matching that of what stack would have returned if no
out argument were specified.
Returns
-------
stacked : ndarray
The stacked array has one more dimension than the input arrays.
See Also
--------
concatenate : Join a sequence of arrays along an existing axis.
split : Split array into a list of multiple sub-arrays of equal size.
block : Assemble arrays from blocks.
Examples
--------
>>> arrays = [np.random.randn(3, 4) for _ in range(10)]
>>> np.stack(arrays, axis=0).shape
(10, 3, 4)
>>> np.stack(arrays, axis=1).shape
(3, 10, 4)
>>> np.stack(arrays, axis=2).shape
(3, 4, 10)
>>> a = np.array([1, 2, 3])
>>> b = np.array([2, 3, 4])
>>> np.stack((a, b))
array([[1, 2, 3],
[2, 3, 4]])
>>> np.stack((a, b), axis=-1)
array([[1, 2],
[2, 3],
[3, 4]])
"""
arrays = [asanyarray(arr) for arr in arrays]
if not arrays:
raise ValueError('need at least one array to stack')
shapes = {arr.shape for arr in arrays}
if len(shapes) != 1:
raise ValueError('all input arrays must have the same shape')
result_ndim = arrays[0].ndim + 1
axis = normalize_axis_index(axis, result_ndim)
sl = (slice(None),) * axis + (_nx.newaxis,)
expanded_arrays = [arr[sl] for arr in arrays]
return _nx.concatenate(expanded_arrays, axis=axis, out=out)
def _block_dispatcher(arrays, out=None):
# Use type(...) is list to match the behavior of np.block(), which special
# cases list specifically rather than allowing for generic iterables or
# tuple. Also, we know that list.__array_function__ will never exist.
if type(arrays) is list:
for subarrays in arrays:
for subarray in _block_dispatcher(subarrays):
yield subarray
else:
yield arrays
if out is not None:
yield out
@array_function_dispatch(_block_dispatcher)
def block(arrays, out=None):
"""
Assemble an nd-array from nested lists of blocks.
Blocks in the innermost lists are concatenated (see `concatenate`) along
the last dimension (-1), then these are concatenated along the
second-last dimension (-2), and so on until the outermost list is reached.
Blocks can be of any dimension, but will not be broadcasted using the normal
rules. Instead, leading axes of size 1 are inserted, to make ``block.ndim``
the same for all blocks. This is primarily useful for working with scalars,
and means that code like ``np.block([v, 1])`` is valid, where
``v.ndim == 1``.
When the nested list is two levels deep, this allows block matrices to be
constructed from their components.
.. versionadded:: 1.13.0
Parameters
----------
arrays : nested list of array_like or scalars (but not tuples)
If passed a single ndarray or scalar (a nested list of depth 0), this
is returned unmodified (and not copied).
Elements shapes must match along the appropriate axes (without
broadcasting), but leading 1s will be prepended to the shape as
necessary to make the dimensions match.
out : ndarray
ndarray to which to copy the blocks.
Returns
-------
block_array : ndarray
The array assembled from the given blocks.
The dimensionality of the output is equal to the greatest of:
* the dimensionality of all the inputs
* the depth to which the input list is nested
Raises
------
ValueError
* If list depths are mismatched - for instance, ``[[a, b], c]`` is
illegal, and should be spelt ``[[a, b], [c]]``
* If lists are empty - for instance, ``[[a, b], []]``
See Also
--------
concatenate : Join a sequence of arrays together.
stack : Stack arrays in sequence along a new dimension.
hstack : Stack arrays in sequence horizontally (column wise).
vstack : Stack arrays in sequence vertically (row wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
vsplit : Split array into a list of multiple sub-arrays vertically.
Notes
-----
When called with only scalars, ``np.block`` is equivalent to an ndarray
call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to
``np.array([[1, 2], [3, 4]])``.
This function does not enforce that the blocks lie on a fixed grid.
``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form::
AAAbb
AAAbb
cccDD
But is also allowed to produce, for some ``a, b, c, d``::
AAAbb
AAAbb
cDDDD
Since concatenation happens along the last axis first, `block` is _not_
capable of producing the following directly::
AAAbb
cccbb
cccDD
Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is
equivalent to ``np.block([[A, B, ...], [p, q, ...]])``.
Examples
--------
The most common use of this function is to build a block matrix
>>> A = np.eye(2) * 2
>>> B = np.eye(3) * 3
>>> np.block([
... [A, np.zeros((2, 3))],
... [np.ones((3, 2)), B ]
... ])
array([[2., 0., 0., 0., 0.],
[0., 2., 0., 0., 0.],
[1., 1., 3., 0., 0.],
[1., 1., 0., 3., 0.],
[1., 1., 0., 0., 3.]])
With a list of depth 1, `block` can be used as `hstack`
>>> np.block([1, 2, 3]) # hstack([1, 2, 3])
array([1, 2, 3])
>>> a = np.array([1, 2, 3])
>>> b = np.array([2, 3, 4])
>>> np.block([a, b, 10]) # hstack([a, b, 10])
array([ 1, 2, 3, 2, 3, 4, 10])
>>> A = np.ones((2, 2), int)
>>> B = 2 * A
>>> np.block([A, B]) # hstack([A, B])
array([[1, 1, 2, 2],
[1, 1, 2, 2]])
With a list of depth 2, `block` can be used in place of `vstack`:
>>> a = np.array([1, 2, 3])
>>> b = np.array([2, 3, 4])
>>> np.block([[a], [b]]) # vstack([a, b])
array([[1, 2, 3],
[2, 3, 4]])
>>> A = np.ones((2, 2), int)
>>> B = 2 * A
>>> np.block([[A], [B]]) # vstack([A, B])
array([[1, 1],
[1, 1],
[2, 2],
[2, 2]])
It can also be used in places of `atleast_1d` and `atleast_2d`
>>> a = np.array(0)
>>> b = np.array([1])
>>> np.block([a]) # atleast_1d(a)
array([0])
>>> np.block([b]) # atleast_1d(b)
array([1])
>>> np.block([[a]]) # atleast_2d(a)
array([[0]])
>>> np.block([[b]]) # atleast_2d(b)
array([[1]])
"""
# This function is benchmarked at
# https://pv.github.io/numpy-bench/#bench_shape_base.Block2D.time_block2d
return _nx.block(arrays, out=out)