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Module « numpy »

Fonction inner - module numpy

Signature de la fonction inner

Description

help(numpy.inner)

inner(a, b, /)

Inner product of two arrays.

Ordinary inner product of vectors for 1-D arrays (without complex
conjugation), in higher dimensions a sum product over the last axes.

Parameters
----------
a, b : array_like
    If `a` and `b` are nonscalar, their last dimensions must match.

Returns
-------
out : ndarray
    If `a` and `b` are both
    scalars or both 1-D arrays then a scalar is returned; otherwise
    an array is returned.
    ``out.shape = (*a.shape[:-1], *b.shape[:-1])``

Raises
------
ValueError
    If both `a` and `b` are nonscalar and their last dimensions have
    different sizes.

See Also
--------
tensordot : Sum products over arbitrary axes.
dot : Generalised matrix product, using second last dimension of `b`.
vecdot : Vector dot product of two arrays.
einsum : Einstein summation convention.

Notes
-----
For vectors (1-D arrays) it computes the ordinary inner-product::

    np.inner(a, b) = sum(a[:]*b[:])

More generally, if ``ndim(a) = r > 0`` and ``ndim(b) = s > 0``::

    np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))

or explicitly::

    np.inner(a, b)[i0,...,ir-2,j0,...,js-2]
         = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])

In addition `a` or `b` may be scalars, in which case::

   np.inner(a,b) = a*b

Examples
--------
Ordinary inner product for vectors:

>>> import numpy as np
>>> a = np.array([1,2,3])
>>> b = np.array([0,1,0])
>>> np.inner(a, b)
2

Some multidimensional examples:

>>> a = np.arange(24).reshape((2,3,4))
>>> b = np.arange(4)
>>> c = np.inner(a, b)
>>> c.shape
(2, 3)
>>> c
array([[ 14,  38,  62],
       [ 86, 110, 134]])

>>> a = np.arange(2).reshape((1,1,2))
>>> b = np.arange(6).reshape((3,2))
>>> c = np.inner(a, b)
>>> c.shape
(1, 1, 3)
>>> c
array([[[1, 3, 5]]])

An example where `b` is a scalar:

>>> np.inner(np.eye(2), 7)
array([[7., 0.],
       [0., 7.]])

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