From ec6719e71a12c974c077e0057b5a822d84c683ee Mon Sep 17 00:00:00 2001 From: Athan Reines Date: Wed, 3 Nov 2021 18:49:15 -0700 Subject: [PATCH] Loosen tolerance cutoff to accommodate non-SVD algorithms For further discussion, see https://github.com/data-apis/array-api/issues/216 --- spec/extensions/linear_algebra_functions.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/spec/extensions/linear_algebra_functions.md b/spec/extensions/linear_algebra_functions.md index 4f4a62b22..90e21d9a4 100644 --- a/spec/extensions/linear_algebra_functions.md +++ b/spec/extensions/linear_algebra_functions.md @@ -345,7 +345,7 @@ Returns the rank (i.e., number of non-zero singular values) of a matrix (or a st - **rtol**: _Optional\[ Union\[ float, <array> ] ]_ - - relative tolerance for small singular values. Singular values less than or equal to `rtol * largest_singular_value` are set to zero. If a `float`, the value is equivalent to a zero-dimensional array having a floating-point data type determined by {ref}`type-promotion` (as applied to `x`) and must be broadcast against each matrix. If an `array`, must have a floating-point data type and must be compatible with `shape(x)[:-2]` (see {ref}`broadcasting`). If `None`, the default value is `max(M, N) * eps`, where `eps` must be the machine epsilon associated with the floating-point data type determined by {ref}`type-promotion` (as applied to `x`). Default: `None`. + - relative tolerance for small singular values. Singular values approximately less than or equal to `rtol * largest_singular_value` are set to zero. If a `float`, the value is equivalent to a zero-dimensional array having a floating-point data type determined by {ref}`type-promotion` (as applied to `x`) and must be broadcast against each matrix. If an `array`, must have a floating-point data type and must be compatible with `shape(x)[:-2]` (see {ref}`broadcasting`). If `None`, the default value is `max(M, N) * eps`, where `eps` must be the machine epsilon associated with the floating-point data type determined by {ref}`type-promotion` (as applied to `x`). Default: `None`. #### Returns @@ -392,7 +392,7 @@ Returns the (Moore-Penrose) pseudo-inverse of a matrix (or a stack of matrices) - **rtol**: _Optional\[ Union\[ float, <array> ] ]_ - - relative tolerance for small singular values. Singular values less than or equal to `rtol * largest_singular_value` are set to zero. If a `float`, the value is equivalent to a zero-dimensional array having a floating-point data type determined by {ref}`type-promotion` (as applied to `x`) and must be broadcast against each matrix. If an `array`, must have a floating-point data type and must be compatible with `shape(x)[:-2]` (see {ref}`broadcasting`). If `None`, the default value is `max(M, N) * eps`, where `eps` must be the machine epsilon associated with the floating-point data type determined by {ref}`type-promotion` (as applied to `x`). Default: `None`. + - relative tolerance for small singular values. Singular values approximately less than or equal to `rtol * largest_singular_value` are set to zero. If a `float`, the value is equivalent to a zero-dimensional array having a floating-point data type determined by {ref}`type-promotion` (as applied to `x`) and must be broadcast against each matrix. If an `array`, must have a floating-point data type and must be compatible with `shape(x)[:-2]` (see {ref}`broadcasting`). If `None`, the default value is `max(M, N) * eps`, where `eps` must be the machine epsilon associated with the floating-point data type determined by {ref}`type-promotion` (as applied to `x`). Default: `None`. #### Returns