flopscope.

flopscope.numpy.linalg.matmul

fnp.linalg.matmul(x1: 'ArrayLike', x2: 'ArrayLike', /) -> 'FlopscopeArray'[flopscope source][numpy source]

Computes the matrix product.

Adapted from NumPy docs np.linalg.matmul

Arealinalg
Typecustom
NumPy Refnp.linalg.matmul
Cost
delegates to flops.matmul
Flopscope Context

Delegates to `fnp.matmul` which charges `m*k*n` FLOPs (FMA=1).

This function is Array API compatible, contrary to flops.matmul.

Parameters

x1:array_like

The first input array.

x2:array_like

The second input array.

Returns

out:ndarray

The matrix 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 second-to-last dimension of x2.

If a scalar value is passed in.

See also

Examples

For 2-D arrays it is the matrix product:

>>> a = flops.array([[1, 0],
... [0, 1]])
>>> b = flops.array([[4, 1],
... [2, 2]])
>>> flops.linalg.matmul(a, b)
array([[4, 1],
       [2, 2]])

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

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

Broadcasting is conventional for stacks of arrays

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

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

>>> flops.linalg.matmul([2j, 3j], [2j, 3j])
(-13+0j)

Scalar multiplication raises an error.

>>> flops.linalg.matmul([1,2], 3)
Traceback (most recent call last):
...
ValueError: matmul: Input operand 1 does not have enough dimensions ...