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feat: add blas/base/strsm
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‎lib/node_modules/@stdlib/blas/base/strsm/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# strsm
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> Solve matrix equation `op(A) * X = alpha * B` or `X * op(A) = alpha * B` where `alpha` is a scalar, `X` and `B` are `m` by `n` matrices, `A` is a unit, or non-unit, upper or lower triangular matrix and `op(A)` is one of `op(A) = A` or `op(A) = A^T`. The matrix `X` is overwritten on `B`.
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<section class = "usage">
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## Usage
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```javascript
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var strsm = require( '@stdlib/blas/base/strsm' );
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```
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#### strsm( order, side, uplo, transa, diag, m, n, alpha, A, LDA, B, LDB )
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Solves matrix equation `op(A) * X = alpha * B` or `X * op(A) = alpha * B` where `alpha` is a scalar, `X` and `B` are `m` by `n` matrices, `A` is a unit, or non-unit, upper or lower triangular matrix and `op(A)` is one of `op(A) = A` or `op(A) = A^T`. The matrix `X` is overwritten on `B`.
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```javascript
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var Float32Array = require( '@stdlib/array/loat32' );
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A = new Float32Array( [ 1.0, 3.0, 0.0, 4.0 ] );
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B = new Float32Array( [ 5.0, 7.0, 0.0, 8.0 ] );
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strsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, B, 2 );
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// B => <Float32Array>[ 30.0, 6.0, 0.0, 12.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout of `A` and `B`.
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- **side**: specifies whether `op( A )` appears on the left or right side of `X`.
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- **uplo**: specifies whether the upper or lower triangular part of the matrix `A` is supplied.
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- **transa**: specifies the form of `op( A )` to be used in the matrix multiplication.
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- **diag**: specifies whether or not `A` is unit triangular.
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- **m**: number of rows in `B`.
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- **n**: number of columns in `B`.
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- **alpha**: scalar constant.
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- **A**: input matrix `A`.
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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- **B**: input matrix `B`.
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- **LDB**: stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`).
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float32Array = require( '@stdlib/array/loat32' );
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// Initial arrays...
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var A0 = new Float32Array( [ 0.0, 1.0, 3.0, 0.0, 4.0 ] );
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var B0 = new Float32Array( [ 0.0, 5.0, 7.0, 0.0, 8.0 ] );
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// Create offset views...
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var A1 = new Float32Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var B1 = new Float32Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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strsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A1, 2, B1, 2 );
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// B0 => <Float32Array>[ 0.0, 30.0, 6.0, 0.0, 12.0 ]
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```
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#### strsm.ndarray( s, ul, t, d, m, n, α, A, sa1, sa2, oa, B, sb1, sb2, ob )
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Solves matrix equation `op(A) * X = alpha * B` or `X * op(A) = alpha * B` using alternative indexing semantics and where `alpha` is a scalar, `X` and `B` are `m` by `n` matrices, `A` is a unit, or non-unit, upper or lower triangular matrix and `op(A)` is one of `op(A) = A` or `op(A) = A^T`. The matrix `X` is overwritten on `B`.
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```javascript
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var Float32Array = require( '@stdlib/array/loat32' );
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A = new Float32Array( [ 0.0, 0.0, 1.0, 3.0, 0.0, 4.0 ] );
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B = new Float32Array( [ 0.0, 5.0, 7.0, 0.0, 8.0 ] );
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strsm.ndarray( 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, 1, 2, B, 2, 1, 1 );
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// B => <Float32Array>[ 0.0, 30.0, 6.0, 0.0, 12.0 ]
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```
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The function has the following parameters:
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- **side**: specifies whether `op( A )` appears on the left or right side of `X`.
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- **uplo**: specifies whether the upper or lower triangular part of the matrix `A` is supplied.
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- **transa**: specifies the form of `op( A )` to be used in the matrix multiplication.
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- **diag**: specifies whether or not `A` is unit triangular.
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- **m**: number of rows in `B`.
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- **n**: number of columns in `B`.
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- **alpha**: scalar constant.
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- **A**: input matrix `A`.
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- **sa1**: stride of the first dimension of `A`.
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- **sa2**: stride of the second dimension of `A`.
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- **oa**: starting index for `A`.
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- **B**: input matrix `B`.
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- **sb1**: stride of the first dimension of `B`.
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- **sb2**: stride of the second dimension of `B`.
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- **ob**: starting index for `B`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
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```javascript
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var Float32Array = require( '@stdlib/array/loat32' );
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A = new Float32Array( [ 0.0, 0.0, 1.0, 3.0, 0.0, 4.0 ] );
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B = new Float32Array( [ 0.0, 5.0, 7.0, 0.0, 8.0 ] );
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strsm.ndarray( 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, 1, 2, B, 2, 1, 1 );
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// B => <Float32Array>[ 0.0, 30.0, 6.0, 0.0, 12.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- `strsm()` corresponds to the [BLAS][blas] level 3 function [`strsm`][strsm].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var Float32Array = require( '@stdlib/array/loat32' );
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var strsm = require( '@stdlib/blas/base/strsm' );
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var A = new Float32Array( [ 1.0, 0.0, 3.0, 4.0 ] );
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var B = new Float32Array( [ 5.0, 0.0, 7.0, 8.0 ] );
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strsm( 'row-major', 'left', 'lower', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, B, 2 );
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console.log( B );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[blas]: http://www.netlib.org/blas
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[strsm]: https://www.netlib.org/lapack/explore-html/d2/d8b/strsm_8f.html
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/base/strsm/benchmark/benchmark_ca_cb_l_l_nt_nu.ndarray.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var zeros = require( '@stdlib/array/zeros' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var pkg = require( './../package.json' ).name;
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var strsm = require( './../lib/ndarray.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float32'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} N - array dimension size
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* @returns {Function} benchmark function
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*/
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function createBenchmark( N ) {
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var A = uniform( N*N, -10.0, 10.0, options );
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var B = zeros( N*N, options.dtype );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var z;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = strsm( 'left', 'lower', 'no-transpose', 'non-unit', N, N, 1.0, A, 1, N, 0, B, 1, N, 0 );
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if ( isnanf( z[ i%z.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnanf( z[ i%z.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 4; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = floor( pow( pow( 10, i ), 1.0/2.0 ) );
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f = createBenchmark( len );
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bench( pkg+':ndarray:order(A)=column-major,order(B)=column-major,side=left,uplo=lower,trans=false,diag=non-unit,size='+(len*len), f );
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}
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}
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main();

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