__matmul__

array.__matmul__(other: array, /) → array

Computes the matrix product.

Note

The matmul function must implement the same semantics as the built-in @ operator (see PEP 465).

Parameters:

  • self (array) – array instance. Should have a numeric data type. Must have at least one dimension. If self is one-dimensional having shape (M,) and other has more than one dimension, self must be promoted to a two-dimensional array by prepending 1 to its dimensions (i.e., must have shape (1, M)). After matrix multiplication, the prepended dimensions in the returned array must be removed. If self has more than one dimension (including after vector-to-matrix promotion), shape(self)[:-2] must be compatible with shape(other)[:-2] (after vector-to-matrix promotion) (see Broadcasting). If self has shape (..., M, K), the innermost two dimensions form matrices on which to perform matrix multiplication.

  • other (array) – other array. Should have a numeric data type. Must have at least one dimension. If other is one-dimensional having shape (N,) and self has more than one dimension, other must be promoted to a two-dimensional array by appending 1 to its dimensions (i.e., must have shape (N, 1)). After matrix multiplication, the appended dimensions in the returned array must be removed. If other has more than one dimension (including after vector-to-matrix promotion), shape(other)[:-2] must be compatible with shape(self)[:-2] (after vector-to-matrix promotion) (see Broadcasting). If other has shape (..., K, N), the innermost two dimensions form matrices on which to perform matrix multiplication.

Note

If either x1 or x2 has a complex floating-point data type, neither argument must be complex-conjugated or transposed. If conjugation and/or transposition is desired, these operations should be explicitly performed prior to computing the matrix product.

Returns:

out (array) –

  • if both self and other are one-dimensional arrays having shape (N,), a zero-dimensional array containing the inner product as its only element.

  • if self is a two-dimensional array having shape (M, K) and other is a two-dimensional array having shape (K, N), a two-dimensional array containing the conventional matrix product and having shape (M, N).

  • if self is a one-dimensional array having shape (K,) and other is an array having shape (..., K, N), an array having shape (..., N) (i.e., prepended dimensions during vector-to-matrix promotion must be removed) and containing the conventional matrix product.

  • if self is an array having shape (..., M, K) and other is a one-dimensional array having shape (K,), an array having shape (..., M) (i.e., appended dimensions during vector-to-matrix promotion must be removed) and containing the conventional matrix product.

  • if self is a two-dimensional array having shape (M, K) and other is an array having shape (..., K, N), an array having shape (..., M, N) and containing the conventional matrix product for each stacked matrix.

  • if self is an array having shape (..., M, K) and other is a two-dimensional array having shape (K, N), an array having shape (..., M, N) and containing the conventional matrix product for each stacked matrix.

  • if either self or other has more than two dimensions, an array having a shape determined by Broadcasting shape(self)[:-2] against shape(other)[:-2] and containing the conventional matrix product for each stacked matrix.

  • The returned array must have a data type determined by Type Promotion Rules.

Notes

Note

Results must equal the results returned by the equivalent function matmul().

Raises

  • if either self or other is a zero-dimensional array.

  • if self is a one-dimensional array having shape (K,), other is a one-dimensional array having shape (L,), and K != L.

  • if self is a one-dimensional array having shape (K,), other is an array having shape (..., L, N), and K != L.

  • if self is an array having shape (..., M, K), other is a one-dimensional array having shape (L,), and K != L.

  • if self is an array having shape (..., M, K), other is an array having shape (..., L, N), and K != L.

Changed in version 2022.12: Added complex data type support.