From cea4bb2219a3f2a4ef9e15946aa1c30afe5ffccd Mon Sep 17 00:00:00 2001 From: Aaron Meurer Date: Thu, 20 May 2021 15:34:52 -0600 Subject: [PATCH] Fix a typo in the spec --- spec/API_specification/linear_algebra_functions.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/spec/API_specification/linear_algebra_functions.md b/spec/API_specification/linear_algebra_functions.md index 97da8f110..3724c2c24 100644 --- a/spec/API_specification/linear_algebra_functions.md +++ b/spec/API_specification/linear_algebra_functions.md @@ -34,7 +34,7 @@ The `matmul` function must implement the same semantics as the built-in `@` oper - **x1**: _<array>_ - - first input array. Should have a numeric data type. Must have at least one dimension. If `x1` is one-dimensional having shape `(M)` and `x2` has more than one dimension, `x1` 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 `x1` has more than one dimension (including after vector-to-matrix promotion), `x1` must be compatible with `x2` (see {ref}`broadcasting`). If `x1` has shape `(..., M, K)`, the innermost two dimensions form matrices on which to perform matrix multiplication. + - first input array. Should have a numeric data type. Must have at least one dimension. If `x1` is one-dimensional having shape `(M)` and `x2` has more than one dimension, `x1` 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 `x1` has more than one dimension (including after vector-to-matrix promotion), `x1` must be compatible with `x2` (see {ref}`broadcasting`). If `x1` has shape `(..., M, K)`, the innermost two dimensions form matrices on which to perform matrix multiplication. - **x2**: _<array>_ @@ -58,7 +58,7 @@ The `matmul` function must implement the same semantics as the built-in `@` oper - if either `x1` or `x2` is a zero-dimensional array. - if `x1` is a one-dimensional array having shape `(N)`, `x2` is a one-dimensional array having shape `(M)`, and `N != M`. -- if `x1` is an array having shape `(..., M, K)`, `x2` is an array having shape `(..., L, N)`, and `K != L`. +- if `x1` is an array having shape `(..., M, K)`, `x2` is an array having shape `(..., L, N)`, and `K != L`. (function-tensordot)= ### tensordot(x1, x2, /, *, axes=2) @@ -78,13 +78,13 @@ Returns a tensor contraction of `x1` and `x2` over specific axes. - **axes**: _Union\[ int, Tuple\[ Sequence\[ int ], Sequence\[ int ] ] ]_ - number of axes (dimensions) to contract or explicit sequences of axes (dimensions) for `x1` and `x2`, respectively. - + If `axes` is an `int` equal to `N`, then contraction must be performed over the last `N` axes of `x1` and the first `N` axes of `x2` in order. The size of each corresponding axis (dimension) must match. Must be nonnegative. - If `N` equals `0`, the result is the tensor (outer) product. - If `N` equals `1`, the result is the tensor dot product. - If `N` equals `2`, the result is the tensor double contraction (default). - + If `axes` is a tuple of two sequences `(x1_axes, x2_axes)`, the first sequence must apply to `x` and the second sequence to `x2`. Both sequences must have the same length. Each axis (dimension) `x1_axes[i]` for `x1` must have the same size as the respective axis (dimension) `x2_axes[i]` for `x2`. Each sequence must consist of unique (nonnegative) integers that specify valid axes for each respective array. #### Returns @@ -135,7 +135,7 @@ Computes the (vector) dot product of two arrays. #### Returns -- **out**: _<array;>_ +- **out**: _<array>_ - if `x1` and `x2` are both one-dimensional arrays, a zero-dimensional containing the dot product; otherwise, a non-zero-dimensional array containing the dot products and having rank `N-1`, where `N` is the rank (number of dimensions) of the shape determined according to {ref}`broadcasting`. The returned array must have a data type determined by {ref}`type-promotion`.