dpnp.vecdot

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

Computes the vector dot product.

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.

For full documentation refer to numpy.vecdot.

Parameters:

  • x1 ({dpnp.ndarray, usm_ndarray}) -- First input array.

  • x2 ({dpnp.ndarray, usm_ndarray}) -- Second input array.

  • out ({None, dpnp.ndarray, usm_ndarray}, 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.

    Default: None.

  • casting ({"no", "equiv", "safe", "same_kind", "unsafe"}, optional) --

    Controls what kind of data casting may occur.

    Default: "same_kind".

  • order ({None, "C", "F", "A", "K"}, optional) --

    Memory layout of the newly output array, if parameter out is None.

    Default: "K".

  • dtype ({None, str, dtype object}, optional) --

    Type to use in computing the vector dot product. By default, the returned array will have data type that is determined by considering Promotion Type Rule and device capabilities.

    Default: None.

  • axes ({None, list of tuples}, optional) --

    A list of tuples with indices of axes the dot product should operate on. For instance, for the signature of (i),(i)->(), the base elements are vectors and these are taken to be stored in the last axes of each argument. The corresponding axes keyword would be [(-1,), (-1,), ()].

    Default: None.

  • axis ({None, int}, optional) --

    Axis over which to compute the dot product. This is a short-cut for passing in axes with entries of (axis,) for each single-core-dimension argument and () for all others. For instance, for a signature (i),(i)->(), it is equivalent to passing in axes=[(axis,), (axis,), ()].

    Default: None.

Returns:

out -- The vector dot product of the inputs. This is a 0-d array only when both x1, x2 are 1-d vectors.

Return type:

dpnp.ndarray

Limitations

Keyword arguments subok, and signature are only supported with their default values. Otherwise NotImplementedError exception will be raised.

See also

dpnp.linalg.vecdot

Array API compatible version.

dpnp.vdot

Complex-conjugating dot product but flattens arguments first.

dpnp.matmul

Matrix-matrix product.

dpnp.vecmat

Vector-matrix product.

dpnp.matvec

Matrix-vector product.

dpnp.einsum

Einstein summation convention.

Examples

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

>>> import dpnp as np
>>> 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.])