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Add Cholesky function specification #110

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Merged
merged 7 commits into from
May 12, 2021
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Add Cholesky function specification #110

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e196ff5
Add Cholesky spec
kgryte Jan 14, 2021
10b19ea
Update description
kgryte Jan 14, 2021
b1728af
Return an array rather than a tuple
kgryte Mar 24, 2021
5755fb5
Merge branch 'main' of https://github.com/pydata-apis/array-api into …
kgryte Mar 24, 2021
1218c1b
Update dtype requirements
kgryte Mar 24, 2021
b476125
Update dtype requirements
kgryte Mar 25, 2021
717078a
Move API to submodule
kgryte Apr 26, 2021
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24 changes: 21 additions & 3 deletions spec/API_specification/linear_algebra_functions.md
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Expand Up @@ -15,10 +15,28 @@ A conforming implementation of the array API standard must provide and support t

<!-- NOTE: please keep the functions in alphabetical order -->

(function-cholesky)=
### cholesky()
(function-linalg-cholesky)=
### linalg.cholesky(x, /, *, upper=False)

TODO
Returns the Cholesky decomposition of a symmetric positive-definite matrix (or a stack of symmetric positive-definite matrices) `x`.

<!-- NOTE: once complex numbers are supported, each square matrix must be Hermitian. -->

#### Parameters

- **x**: _&lt;array&gt;_

- input array having shape `(..., M, M)` and whose innermost two dimensions form square matrices. Should have a floating-point data type.

- **upper**: _bool_

- If `True`, the result must be the upper-triangular Cholesky factor. If `False`, the result must be the lower-triangular Cholesky factor. Default: `False`.

#### Returns

- **out**: _&lt;array&gt;_

- an array containing the Cholesky factors for each square matrix. The returned array must have a floating-point data type determined by {ref}`type-promotion` and shape as `x`.

(function-cross)=
### cross(x1, x2, /, *, axis=-1)
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