numpy.core.shape_base

Parameters

arrays : nested list of arrays

The arrays to check

parent_index : list of int

The full index of arrays within the nested lists passed to _block_check_depths_match at the top of the recursion.

Returns

first_index : list of int

The full index of an element from the bottom of the nesting in arrays. If any element at the bottom is an empty list, this will refer to it, and the last index along the empty axis will be None.

max_arr_ndim : int

The maximum of the ndims of the arrays nested in arrays.

final_size: int

The number of elements in the final array. This is used the motivate the choice of algorithm used using benchmarking wisdom.

Parameters

arrays : nested list of arrays

The arrays to check

max_depth : list of int

The number of nested lists

result_ndim : int

The number of dimensions in thefinal array.

Returns

shape : tuple of int

The shape that the final array will take on.

slices: list of tuple of slices

The slices into the full array required for assignment. These are required to be prepended with (Ellipsis, ) to obtain to correct final index.

arrays: list of ndarray

The data to assign to each slice of the full array

Returns

shape: tuple of int

This tuple satisfies: ` shape, _ = _concatenate_shapes([arr.shape for shape in arrs], axis) shape == concatenate(arrs, axis).shape `

slice_prefixes: tuple of (slice(start, end), )

For a list of arrays being concatenated, this returns the slice in the larger array at axis that needs to be sliced into.

For example, the following holds: ``` ret = concatenate([a, b, c], axis) _, (sl_a, sl_b, sl_c) = concatenate_slices([a, b, c], axis)

ret[(slice(None),) * axis + sl_a] == a ret[(slice(None),) * axis + sl_b] == b ret[(slice(None),) * axis + sl_c] == c ```

These are called slice prefixes since they are used in the recursive blocking algorithm to compute the left-most slices during the recursion. Therefore, they must be prepended to rest of the slice that was computed deeper in the recursion.

These are returned as tuples to ensure that they can quickly be added to existing slice tuple without creating a new tuple every time.

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])]

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]])]

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)

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.

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 along an existing axis. stack : Join a sequence of arrays along a new axis. vstack : Stack arrays in sequence vertically (row wise). hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. vsplit : Split an array into multiple sub-arrays vertically (row-wise).

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([4, 5, 6])
>>> np.block([a, b, 10])             # hstack([a, b, 10])
array([ 1,  2,  3,  4,  5,  6, 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([4, 5, 6])
>>> np.block([[a], [b]])             # vstack([a, b])
array([[1, 2, 3],
       [4, 5, 6]])

>>> 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]])

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

concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. block : Assemble an nd-array from nested lists of blocks. vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. hsplit : Split an array into multiple sub-arrays horizontally (column-wise).

Examples

>>> a = np.array((1,2,3))
>>> b = np.array((4,5,6))
>>> np.hstack((a,b))
array([1, 2, 3, 4, 5, 6])
>>> a = np.array([[1],[2],[3]])
>>> b = np.array([[4],[5],[6]])
>>> np.hstack((a,b))
array([[1, 4],
       [2, 5],
       [3, 6]])

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. block : Assemble an nd-array from nested lists of blocks. split : Split array into a list of multiple sub-arrays of equal size.

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([4, 5, 6])
>>> np.stack((a, b))
array([[1, 2, 3],
       [4, 5, 6]])

>>> np.stack((a, b), axis=-1)
array([[1, 4],
       [2, 5],
       [3, 6]])

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

concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. block : Assemble an nd-array from nested lists of blocks. hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. vsplit : Split an array into multiple sub-arrays vertically (row-wise).

Examples

>>> a = np.array([1, 2, 3])
>>> b = np.array([4, 5, 6])
>>> np.vstack((a,b))
array([[1, 2, 3],
       [4, 5, 6]])

>>> a = np.array([[1], [2], [3]])
>>> b = np.array([[4], [5], [6]])
>>> np.vstack((a,b))
array([[1],
       [2],
       [3],
       [4],
       [5],
       [6]])