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Fonction block - module numpy.matlib

Signature de la fonction block

def block(arrays) 

Description

block.__doc__

    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.

    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([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]])