numpy.matvec#

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

Matrix-vector dot product of two arrays.

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

\[\mathbf{A} \cdot \mathbf{b} = \sum_{j=0}^{n-1} A_{ij} v_j\]

where the sum is over the last dimensions in x1 and x2 (unless axes is specified). (For a matrix-vector product with the vector conjugated, use np.vecmat(x2, x1.mT).)

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 matrix-vector product of the inputs.

Raises:

ValueError

If the last dimensions of x1 and x2 are not the same size.

If a scalar value is passed in.

See also

vecdot: Vector-vector product.
vecmat: Vector-matrix product.
matmul: Matrix-matrix product.
einsum: Einstein summation convention.

Examples

Rotate a set of vectors from Y to X along Z.

>>> a = np.array([[0., 1., 0.],
...               [-1., 0., 0.],
...               [0., 0., 1.]])
>>> v = np.array([[1., 0., 0.],
...               [0., 1., 0.],
...               [0., 0., 1.],
...               [0., 6., 8.]])
>>> np.matvec(a, v)
array([[ 0., -1.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  0.,  1.],
       [ 6.,  0.,  8.]])