diff --git a/spec/API_specification/linear_algebra_functions.md b/spec/API_specification/linear_algebra_functions.md index 129861b2c..d0c4b7234 100644 --- a/spec/API_specification/linear_algebra_functions.md +++ b/spec/API_specification/linear_algebra_functions.md @@ -257,15 +257,15 @@ The `matmul` function must implement the same semantics as the built-in `@` oper - **out**: _<array>_ - - if both `x1` and `x2` are one-dimensional arrays having shape `(N)`, a zero-dimensional array containing the inner product as its only element. - - if `x1` is a two-dimensional array having shape `(M, K)` and `x2` is a two-dimensional array having shape `(K, N)`, a two-dimensional array containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) and having shape `(M, N)`. - - if `x1` is a one-dimensional array having shape `(K)` and `x2` 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](https://en.wikipedia.org/wiki/Matrix_multiplication). - - if `x1` is an array having shape `(..., M, K)` and `x2` 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](https://en.wikipedia.org/wiki/Matrix_multiplication). - - if `x1` is a two-dimensional array having shape `(M, K)` and `x2` is an array having shape `(..., K, N)`, an array having shape `(..., M, N)` and containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) for each stacked matrix. - - if `x1` is an array having shape `(..., M, K)` and `x2` is a two-dimensional array having shape `(K, N)`, an array having shape `(..., M, N)` and containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) for each stacked matrix. - - if either `x1` or `x2` has more than two dimensions, an array having a shape determined by {ref}`broadcasting` `x1` against `x2` and containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) for each stacked matrix. - - The returned array must have a data type determined by {ref}`type-promotion`. + - if both `x1` and `x2` are one-dimensional arrays having shape `(N)`, a zero-dimensional array containing the inner product as its only element. + - if `x1` is a two-dimensional array having shape `(M, K)` and `x2` is a two-dimensional array having shape `(K, N)`, a two-dimensional array containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) and having shape `(M, N)`. + - if `x1` is a one-dimensional array having shape `(K)` and `x2` 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](https://en.wikipedia.org/wiki/Matrix_multiplication). + - if `x1` is an array having shape `(..., M, K)` and `x2` 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](https://en.wikipedia.org/wiki/Matrix_multiplication). + - if `x1` is a two-dimensional array having shape `(M, K)` and `x2` is an array having shape `(..., K, N)`, an array having shape `(..., M, N)` and containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) for each stacked matrix. + - if `x1` is an array having shape `(..., M, K)` and `x2` is a two-dimensional array having shape `(K, N)`, an array having shape `(..., M, N)` and containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) for each stacked matrix. + - if either `x1` or `x2` has more than two dimensions, an array having a shape determined by {ref}`broadcasting` `x1` against `x2` and containing the [conventional matrix product](https://en.wikipedia.org/wiki/Matrix_multiplication) for each stacked matrix. + + The returned array must have a data type determined by {ref}`type-promotion`. #### Raises