xorbits.numpy.matmul#

xorbits.numpy.matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj, axes, axis])[源代码]#

Matrix product of two arrays.

参数

  • x1 (array_like) – Input arrays, scalars not allowed.

  • x2 (array_like) – Input arrays, scalars not allowed.

  • out (ndarray, 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.

    1.16(numpy) 新版功能: Now handles ufunc kwargs

返回

y – The matrix product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors.

返回类型

ndarray

引发

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.

参见

vdot

Complex-conjugating dot product.

tensordot

Sum products over arbitrary axes.

einsum

Einstein summation convention.

dot

alternative matrix product with different broadcasting rules.

提示

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 from dot 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).

实际案例

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 for np.matmul on ndarrays.

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

1.10.0(numpy) 新版功能.

This docstring was copied from numpy.