numpy.vecmat

numpy.vecmat(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis])=<ufunc 'vecmat'>

Vector-matrix dot product of two arrays.

Given a vector (or stack of vector) \(\mathbf{v}\) in x1 and a matrix (or stack of matrices) \(\mathbf{A}\) in x2, the vector-matrix product is defined as:

\[\mathbf{v} \cdot \mathbf{A} = \sum_{i=0}^{n-1} \overline{v_i}A_{ij}\]

where the sum is over the last dimension of x1 and the one-but-last dimensions in x2 (unless axes is specified) and where \(\overline{v_i}\) denotes the complex conjugate if \(v\) is complex and the identity otherwise. (For a non-conjugated vector-matrix product, use np.matvec(x2.mT, x1).)

New in version 2.2.0.

Parameters:

x1, x2array_like

Input arrays, scalars not allowed.

outndarray, optional

A location into which the result is stored. If provided, it must have the broadcasted shape of x1 and x2 with the summation axis removed. If not provided or None, a freshly-allocated array is used.

**kwargs

For other keyword-only arguments, see the ufunc docs.

Returns:

yndarray

The vector-matrix product of the inputs.

Raises:

ValueError

If the last dimensions of x1 and the one-but-last dimension of x2 are not the same size.

If a scalar value is passed in.

See also

vecdot

Vector-vector product.

matvec

Matrix-vector product.

matmul

Matrix-matrix product.

einsum

Einstein summation convention.

Examples

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Project a vector along X and Y.

>>> v = np.array([0., 4., 2.])
>>> a = np.array([[1., 0., 0.],
...               [0., 1., 0.],
...               [0., 0., 0.]])
>>> np.vecmat(v, a)
array([ 0.,  4., 0.])

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