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Module « numpy.matlib »

Fonction block - module numpy.matlib

Signature de la fonction block

def block(arrays) 

Description

help(numpy.matlib.block)

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.

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).
unstack : Split an array into a tuple of sub-arrays along an axis.

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:

>>> import numpy as np
>>> 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 place 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]])

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