numpy.vecdot

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

Vector dot product of two arrays.

Let \(\mathbf{a}\) be a vector in x1 and \(\mathbf{b}\) be a corresponding vector in x2. The dot product is defined as:

\[\mathbf{a} \cdot \mathbf{b} = \sum_{i=0}^{n-1} \overline{a_i}b_i\]

where the sum is over the last dimension (unless axis is specified) and where \(\overline{a_i}\) denotes the complex conjugate if \(a_i\) is complex and the identity otherwise.

New in version 2.0.0.

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 last 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 dot product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors.

Raises:

ValueError

If the last dimension of x1 is not the same size as the last dimension of x2.

If a scalar value is passed in.

See also

vdot

same but flattens arguments first

matmul

Matrix-matrix product.

vecmat

Vector-matrix product.

matvec

Matrix-vector product.

einsum

Einstein summation convention.

Examples

Try it in your browser!

>>> import numpy as np

Get the projected size along a given normal for an array of vectors.

>>> v = np.array([[0., 5., 0.], [0., 0., 10.], [0., 6., 8.]])
>>> n = np.array([0., 0.6, 0.8])
>>> np.vecdot(v, n)
array([ 3.,  8., 10.])

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