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Module « numpy.matlib »

Fonction outer - module numpy.matlib

Signature de la fonction outer

def outer(a, b, out=None) 

Description

help(numpy.matlib.outer)

Compute the outer product of two vectors.

Given two vectors `a` and `b` of length ``M`` and ``N``, respectively,
the outer product [1]_ is::

  [[a_0*b_0  a_0*b_1 ... a_0*b_{N-1} ]
   [a_1*b_0    .
   [ ...          .
   [a_{M-1}*b_0            a_{M-1}*b_{N-1} ]]

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

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.
linalg.outer : An Array API compatible variation of ``np.outer``,
               which accepts 1-dimensional inputs only.
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:

>>> import numpy as np
>>> 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)

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