numpy.matmul¶

numpy.
matmul
(a, b, out=None)¶ Matrix product of two arrays.
The behavior depends on the arguments in the following way.
 If both arguments are 2D they are multiplied like conventional matrices.
 If either argument is ND, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly.
 If the first argument is 1D, 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 1D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.
Multiplication by a scalar is not allowed, use
*
instead. Note that multiplying a stack of matrices with a vector will result in a stack of vectors, but matmul will not recognize it as such.matmul
differs fromdot
in two important ways. Multiplication by scalars is not allowed.
 Stacks of matrices are broadcast together as if the matrices were elements.
Warning
This function is preliminary and included in NumPy 1.10.0 for testing and documentation. Its semantics will not change, but the number and order of the optional arguments will.
New in version 1.10.0.
Parameters: a : array_like
First argument.
b : array_like
Second argument.
out : ndarray, optional
Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be Ccontiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.
Returns: output : ndarray
Returns the dot product of a and b. If a and b are both 1D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.
Raises: ValueError
If the last dimension of a is not the same size as the secondtolast dimension of b.
If scalar value is passed.
See also
Notes
The matmul function implements the semantics of the @ operator introduced in Python 3.5 following PEP465.
Examples
For 2D arrays it is the matrix product:
>>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.matmul(a, b) array([[4, 1], [2, 2]])
For 2D mixed with 1D, the result is the usual.
>>> a = [[1, 0], [0, 1]] >>> b = [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 complexconjugated:
>>> np.matmul([2j, 3j], [2j, 3j]) (13+0j)
Scalar multiplication raises an error.
>>> np.matmul([1,2], 3) Traceback (most recent call last): ... ValueError: Scalar operands are not allowed, use '*' instead