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Fonction outer - module numpy.matlib

Signature de la fonction outer

def outer(a, b, out=None) 

Description

outer.__doc__

    Compute the outer product of two vectors.

    Given two vectors, ``a = [a0, a1, ..., aM]`` and
    ``b = [b0, b1, ..., bN]``,
    the outer product [1]_ is::

      [[a0*b0  a0*b1 ... a0*bN ]
       [a1*b0    .
       [ ...          .
       [aM*b0            aM*bN ]]

    Parameters
    ----------
    a : (M,) array_like
        First input vector.  Input is flattened if
        not already 1-dimensional.
    b : (N,) array_like
        Second input vector.  Input is flattened if
        not already 1-dimensional.
    out : (M, N) ndarray, optional
        A location where the result is stored

        .. versionadded:: 1.9.0

    Returns
    -------
    out : (M, N) ndarray
        ``out[i, j] = a[i] * b[j]``

    See also
    --------
    inner
    einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.
    ufunc.outer : A generalization to dimensions other than 1D and other
                  operations. ``np.multiply.outer(a.ravel(), b.ravel())``
                  is the equivalent.
    tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))``
                is the equivalent.

    References
    ----------
    .. [1] : G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd
             ed., Baltimore, MD, Johns Hopkins University Press, 1996,
             pg. 8.

    Examples
    --------
    Make a (*very* coarse) grid for computing a Mandelbrot set:

    >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
    >>> rl
    array([[-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.],
           [-2., -1.,  0.,  1.,  2.]])
    >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
    >>> im
    array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
           [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
           [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
           [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
           [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
    >>> grid = rl + im
    >>> grid
    array([[-2.+2.j, -1.+2.j,  0.+2.j,  1.+2.j,  2.+2.j],
           [-2.+1.j, -1.+1.j,  0.+1.j,  1.+1.j,  2.+1.j],
           [-2.+0.j, -1.+0.j,  0.+0.j,  1.+0.j,  2.+0.j],
           [-2.-1.j, -1.-1.j,  0.-1.j,  1.-1.j,  2.-1.j],
           [-2.-2.j, -1.-2.j,  0.-2.j,  1.-2.j,  2.-2.j]])

    An example using a "vector" of letters:

    >>> x = np.array(['a', 'b', 'c'], dtype=object)
    >>> np.outer(x, [1, 2, 3])
    array([['a', 'aa', 'aaa'],
           ['b', 'bb', 'bbb'],
           ['c', 'cc', 'ccc']], dtype=object)