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feat: add blas/base/ctrsm
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‎lib/node_modules/@stdlib/blas/base/ctrsm/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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# ctrsm
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> Solve one of the matrix equations `op(A)*X = alpha*B` or `X*op(A) = alpha*B`.
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<section class="usage">
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## Usage
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```javascript
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var ctrsm = require( '@stdlib/blas/base/ctrsm' );
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```
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#### ctrsm( order, side, uplo, transa, diag, M, N, alpha, A, LDA, B, LDB )
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Solves one of the matrix equations `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`, `op(A) = A^T`, or `op(A) = A^H`. The matrix `X` is overwritten on `B`.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var A = new Complex64Array( [ 2.0, 0.0, 1.0, 0.0, 0.0, 0.0, 2.0, 0.0 ] );
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var B = new Complex64Array( [ 4.0, 0.0, 2.0, 0.0 ] );
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var alpha = new Complex64( 1.0, 0.0 );
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ctrsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 1, alpha, A, 2, B, 1 );
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// B => <Complex64Array>[ 1.5, 0.0, 1.0, 0.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **side**: specifies whether `A` appears on the `'left'` or `'right'` of `X`.
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- **uplo**: specifies whether the `'upper'` or `'lower'` triangular part of `A` is used.
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- **transa**: transpose operation applied to `A` (`'no-transpose'`, `'transpose'`, or `'conjugate-transpose'`).
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- **diag**: specifies whether `A` is `'unit'` or `'non-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 of type `Complex64`.
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- **A**: input triangular matrix stored in a `Complex64Array`.
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of `A`).
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- **B**: input/output matrix stored in a `Complex64Array`. On exit, overwritten with solution `X`.
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- **LDB**: stride of the first dimension of `B` (a.k.a., leading dimension of `B`).
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#### ctrsm.ndarray( ord, sd, ul, ta, dg, M, N, aRe, aIm, A, sa1, oa, B, sb1, ob )
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Solves one of the matrix equations using alternative indexing semantics.
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```javascript
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var Complex64Array = require( '@stdlib/array/complex64' );
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var A = new Complex64Array( [ 2.0, 0.0, 1.0, 0.0, 0.0, 0.0, 2.0, 0.0 ] );
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var B = new Complex64Array( [ 4.0, 0.0, 2.0, 0.0 ] );
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ctrsm.ndarray( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 1, 1.0, 0.0, A, 2, 0, B, 1, 0 );
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// B => <Complex64Array>[ 1.5, 0.0, 1.0, 0.0 ]
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```
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The function accepts the following additional parameters:
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- **aRe**: real part of scalar constant `alpha`.
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- **aIm**: imaginary part of scalar constant `alpha`.
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- **sa1**: stride of the first dimension of `A`.
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- **oa**: starting index for `A`.
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- **sb1**: stride of the first dimension of `B`.
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- **ob**: starting index for `B`.
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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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- `ctrsm()` corresponds to the [BLAS][blas] level 3 function [`ctrsm`][blas-ctrsm].
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- Neither routine tests for singularity or near-singularity of `A`. Such tests must be performed before calling these routines.
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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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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var ctrsm = require( '@stdlib/blas/base/ctrsm' );
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var N = 3;
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var opts = {
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'dtype': 'complex64'
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};
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var A = discreteUniform( N * N, -10, 10, opts );
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var B = discreteUniform( N * N, -10, 10, opts );
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var alpha = new Complex64( 1.0, 0.0 );
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ctrsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', N, N, alpha, A, N, B, N );
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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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<!-- 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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* * *
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## See Also
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- <span class="package-name">[`@stdlib/blas/base/strsm`][@stdlib/blas/base/strsm]</span><span class="delimiter">: </span><span class="description">solve one of the matrix equations `op(A)*X = alpha*B` or `X*op(A) = alpha*B` where `A` is a real single-precision triangular matrix.</span>
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- <span class="package-name">[`@stdlib/blas/base/dtrsm`][@stdlib/blas/base/dtrsm]</span><span class="delimiter">: </span><span class="description">solve one of the matrix equations `op(A)*X = alpha*B` or `X*op(A) = alpha*B` where `A` is a real double-precision triangular matrix.</span>
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- <span class="package-name">[`@stdlib/blas/base/ztrsm`][@stdlib/blas/base/ztrsm]</span><span class="delimiter">: </span><span class="description">solve one of the matrix equations `op(A)*X = alpha*B` or `X*op(A) = alpha*B` where `A` is a complex double-precision triangular matrix.</span>
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</section>
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<!-- /.related -->
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<section class="links">
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[blas]: http://www.netlib.org/blas
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[blas-ctrsm]: https://www.netlib.org/lapack/explore-html/d1/d54/group__complex__blas__level3_ga7dbc51a6f35e10bc3c63dfc62c1d6db8.html
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[@stdlib/blas/base/strsm]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/strsm
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[@stdlib/blas/base/dtrsm]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/dtrsm
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[@stdlib/blas/base/ztrsm]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/base/ztrsm
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/base/ctrsm/benchmark/benchmark.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 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 Complex64Array = require( '@stdlib/array/complex64' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var ctrsm = require( './../lib' );
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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 - matrix dimension
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* @returns {Function} benchmark function
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*/
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function createBenchmark( N ) {
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var alpha;
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var abuf;
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var bbuf;
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var A;
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var B;
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abuf = uniform( N*N*2, -100.0, 100.0, options );
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bbuf = uniform( N*N*2, -100.0, 100.0, options );
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A = new Complex64Array( abuf.buffer );
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B = new Complex64Array( bbuf.buffer );
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alpha = new Complex64( 1.0, 0.0 );
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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 i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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ctrsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', N, N, alpha, A, N, B, N );
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if ( isnanf( bbuf[ i%(N*N*2) ] ) ) {
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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( bbuf[ i%(N*N*2) ] ) ) {
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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 = 3; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( format( '%s:order=row-major,side=left,uplo=upper,trans=no-transpose,diag=non-unit,M=%d,N=%d', pkg, len, len ), f );
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}
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}
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main();

‎lib/node_modules/@stdlib/blas/base/ctrsm/benchmark/benchmark.native.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 resolve = require( 'path' ).resolve;
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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 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 Complex64Array = require( '@stdlib/array/complex64' );
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var Complex64 = require( '@stdlib/complex/float32/ctor' );
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var tryRequire = require( '@stdlib/utils/try-require' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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// VARIABLES //
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var ctrsm = tryRequire( resolve( __dirname, './../lib/ctrsm.native.js' ) );
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var opts = {
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'skip': ( ctrsm instanceof Error )
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};
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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 - matrix dimension
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* @returns {Function} benchmark function
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*/
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function createBenchmark( N ) {
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var alpha;
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var abuf;
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var bbuf;
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var A;
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var B;
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abuf = uniform( N*N*2, -100.0, 100.0, options );
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bbuf = uniform( N*N*2, -100.0, 100.0, options );
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A = new Complex64Array( abuf.buffer );
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B = new Complex64Array( bbuf.buffer );
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alpha = new Complex64( 1.0, 0.0 );
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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 i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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ctrsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', N, N, alpha, A, N, B, N );
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if ( isnanf( bbuf[ i%(N*N*2) ] ) ) {
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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( bbuf[ i%(N*N*2) ] ) ) {
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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 = 3; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( format( '%s::native:order=row-major,side=left,uplo=upper,trans=no-transpose,diag=non-unit,M=%d,N=%d', pkg, len, len ), opts, f );
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}
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}
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main();

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