tensorly
.matmul
- matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj, axes, axis])
Matrix product of two arrays.
- Parameters:
- x1, x2array_like
Input arrays, scalars not allowed.
- outndarray, optional
A location into which the result is stored. If provided, it must have a shape that matches the signature (n,k),(k,m)->(n,m). If not provided or None, a freshly-allocated array is returned.
- **kwargs
For other keyword-only arguments, see the ufunc docs.
New in version 1.16: Now handles ufunc kwargs
- Returns:
- yndarray
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
Notes
The behavior depends on the arguments in the following way.
If both arguments are 2-D they are multiplied like conventional matrices.
If either argument is N-D, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly.
If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.
matmul
differs fromdot
in two important ways:Multiplication by scalars is not allowed, use
*
instead.Stacks of matrices are broadcast together as if the matrices were elements, respecting the signature
(n,k),(k,m)->(n,m)
:>>> a = np.ones([9, 5, 7, 4]) >>> c = np.ones([9, 5, 4, 3]) >>> np.dot(a, c).shape (9, 5, 7, 9, 5, 3) >>> np.matmul(a, c).shape (9, 5, 7, 3) >>> # n is 7, k is 4, m is 3
The matmul function implements the semantics of the
@
operator introduced in Python 3.5 following PEP 465.It uses an optimized BLAS library when possible (see numpy.linalg).
Examples
For 2-D arrays it is the matrix product:
>>> 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] 98 >>> sum(a[0, 1, :] * b[0 , :, 1]) 98
Vector, vector returns the scalar inner product, but neither argument is complex-conjugated:
>>> np.matmul([2j, 3j], [2j, 3j]) (-13+0j)
Scalar multiplication raises an error.
>>> np.matmul([1,2], 3) Traceback (most recent call last): ... ValueError: matmul: Input operand 1 does not have enough dimensions ...
The
@
operator can be used as a shorthand fornp.matmul
on ndarrays.>>> x1 = np.array([2j, 3j]) >>> x2 = np.array([2j, 3j]) >>> x1 @ x2 (-13+0j)
New in version 1.10.0.