Module « numpy.matlib »

Fonction matmul - module numpy.matlib

Signature de la fonction matmul

Description

matmul.__doc__

matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

Matrix product of two arrays.

Parameters
----------
x1, x2 : array_like
    Input arrays, scalars not allowed.
out : ndarray, optional
    A location into which the result is stored. If provided, it must have
    a shape that matches the signature `(n,k),(k,m)->(n,m)`. If not
    provided or None, a freshly-allocated array is returned.
**kwargs
    For other keyword-only arguments, see the
    :ref:`ufunc docs <ufuncs.kwargs>`.

    .. versionadded:: 1.16
       Now handles ufunc kwargs

Returns
-------
y : ndarray
    The matrix product of the inputs.
    This is a scalar only when both x1, x2 are 1-d vectors.

Raises
------
ValueError
    If the last dimension of `x1` is not the same size as
    the second-to-last dimension of `x2`.

    If a scalar value is passed in.

See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
einsum : Einstein summation convention.
dot : alternative matrix product with different broadcasting rules.

Notes
-----

The behavior depends on the arguments in the following way.

- If both arguments are 2-D they are multiplied like conventional
  matrices.
- If either argument is N-D, N > 2, it is treated as a stack of
  matrices residing in the last two indexes and broadcast accordingly.
- If the first argument is 1-D, it is promoted to a matrix by
  prepending a 1 to its dimensions. After matrix multiplication
  the prepended 1 is removed.
- If the second argument is 1-D, it is promoted to a matrix by
  appending a 1 to its dimensions. After matrix multiplication
  the appended 1 is removed.

``matmul`` differs from ``dot`` in two important ways:

- Multiplication by scalars is not allowed, use ``*`` instead.
- Stacks of matrices are broadcast together as if the matrices
  were elements, respecting the signature ``(n,k),(k,m)->(n,m)``:

  >>> a = np.ones([9, 5, 7, 4])
  >>> c = np.ones([9, 5, 4, 3])
  >>> np.dot(a, c).shape
  (9, 5, 7, 9, 5, 3)
  >>> np.matmul(a, c).shape
  (9, 5, 7, 3)
  >>> # n is 7, k is 4, m is 3

The matmul function implements the semantics of the `@` operator introduced
in Python 3.5 following PEP465.

Examples
--------
For 2-D arrays it is the matrix product:

>>> a = np.array([[1, 0],
...               [0, 1]])
>>> b = np.array([[4, 1],
...               [2, 2]])
>>> np.matmul(a, b)
array([[4, 1],
       [2, 2]])

For 2-D mixed with 1-D, the result is the usual.

>>> a = np.array([[1, 0],
...               [0, 1]])
>>> b = np.array([1, 2])
>>> np.matmul(a, b)
array([1, 2])
>>> np.matmul(b, a)
array([1, 2])


Broadcasting is conventional for stacks of arrays

>>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4))
>>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2))
>>> np.matmul(a,b).shape
(2, 2, 2)
>>> np.matmul(a, b)[0, 1, 1]
98
>>> sum(a[0, 1, :] * b[0 , :, 1])
98

Vector, vector returns the scalar inner product, but neither argument
is complex-conjugated:

>>> np.matmul([2j, 3j], [2j, 3j])
(-13+0j)

Scalar multiplication raises an error.

>>> np.matmul([1,2], 3)
Traceback (most recent call last):
...
ValueError: matmul: Input operand 1 does not have enough dimensions ...

The ``@`` operator can be used as a shorthand for ``np.matmul`` on
ndarrays.

>>> x1 = np.array([2j, 3j])
>>> x2 = np.array([2j, 3j])
>>> x1 @ x2
(-13+0j)

.. versionadded:: 1.10.0