dpnp.matmul

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

Matrix product of two arrays.

For full documentation refer to numpy.matmul.

Parameters:

x1 ({dpnp.ndarray, usm_ndarray}) -- First input array.
x2 ({dpnp.ndarray, usm_ndarray}) -- Second input array.
out ({None, dpnp.ndarray, usm_ndarray}, optional) -- Alternative output array in which to place the result. It must have a shape that matches the signature (n,k),(k,m)->(n,m) but the type (of the calculated values) will be cast if necessary. Default: None.
dtype ({None, dtype}, optional) -- Type to use in computing the matrix product. By default, the returned array will have data type that is determined by considering Promotion Type Rule and device capabilities.
casting ({"no", "equiv", "safe", "same_kind", "unsafe"}, optional) -- Controls what kind of data casting may occur. Default: "same_kind".
order ({"C", "F", "A", "K", None}, optional) -- Memory layout of the newly output array, if parameter out is None. Default: "K".
axes ({list of tuples}, optional) -- A list of tuples with indices of axes the matrix product should operate on. For instance, for the signature of (i,j),(j,k)->(i,k), the base elements are 2d matrices and these are taken to be stored in the two last axes of each argument. The corresponding axes keyword would be [(-2, -1), (-2, -1), (-2, -1)]. Default: None.

Returns:

out -- Returns the matrix 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, signature, extobj, and axis are only supported with their default value. Otherwise NotImplementedError exception will be raised.

See also

dpnp.linalg.matmul: Array API compatible version.
dpnp.vdot: Complex-conjugating dot product.
dpnp.tensordot: Sum products over arbitrary axes.
dpnp.einsum: Einstein summation convention.
dpnp.dot: Alternative matrix product with different broadcasting rules.

Examples

For 2-D arrays it is the matrix product:

>>> import dpnp as np
>>> a = np.array([[1, 0], [0, 1]])
>>> b = np.array([[4, 1], [2, 2]])
>>> np.matmul(a, b)
array([[4, 1],
       [2, 2]])

For 2-D mixed with 1-D, the result is the usual.

>>> a = np.array([[1, 0], [0, 1]])
>>> b = np.array([1, 2])
>>> np.matmul(a, b)
array([1, 2])
>>> np.matmul(b, a)
array([1, 2])

Broadcasting is conventional for stacks of arrays

>>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4))
>>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2))
>>> np.matmul(a,b).shape
(2, 2, 2)
>>> np.matmul(a, b)[0, 1, 1]
array(98)
>>> np.sum(a[0, 1, :] * b[0 , :, 1])
array(98)

Vector, vector returns the scalar inner product, but neither argument is complex-conjugated:

>>> x1 = np.array([2j, 3j])
>>> x2 = np.array([2j, 3j])
>>> np.matmul(x1, x2)
array(-13+0j)

The @ operator can be used as a shorthand for matmul on dpnp.ndarray.

>>> x1 @ x2
array(-13+0j)