outer(a, b, out=None)

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

Returns

out : (M, N) ndarray

out[i, j] = a[i] * b[j]

Compute the outer product of two vectors.

See Also

einsum

einsum('i,j->ij', a.ravel(), b.ravel()) is the equivalent.

inner

tensordot

np.tensordot(a.ravel(), b.ravel(), axes=((), ())) 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.

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)

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._decomp_svd.svdvals numpy.kron dask.array.einsumfuncs.einsum scipy.linalg._decomp_update.qr_update dask.array.ufunc.ufunc.outer scipy.signal._signaltools.fftconvolve numpy.cross scipy.spatial._geometric_slerp.geometric_slerp numpy.core._multiarray_umath.c_einsum dask.array.routines.outer numpy.einsum

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