feat: add blas/base/dtrsm

lib/node_modules/@stdlib/blas/base/dtrsm/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# dtrsm
+
+> 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`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dtrsm = require( '@stdlib/blas/base/dtrsm' );
+```
+
+#### dtrsm( order, side, uplo, transa, diag, m, n, alpha, A, LDA, B, LDB )
+
+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`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+A = new Float64Array( [ 1.0, 3.0, 0.0, 4.0 ] );
+B = new Float64Array( [ 5.0, 7.0, 0.0, 8.0 ] );
+
+dtrsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, B, 2 );
+// B => <Float64Array>[ 30.0, 6.0, 0.0, 12.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout of `A` and `B`.
+-   **side**: specifies whether `op( A )` appears on the left or right side of `X`.
+-   **uplo**: specifies whether the upper or lower triangular part of the matrix `A` is supplied.
+-   **transa**: specifies the form of `op( A )` to be used in the matrix multiplication.
+-   **diag**: specifies whether or not `A` is unit triangular.
+-   **m**: number of rows in `B`.
+-   **n**: number of columns in `B`.
+-   **alpha**: scalar constant.
+-   **A**: input matrix `A`.
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **B**: input matrix `B`.
+-   **LDB**: stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`).
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 3.0, 0.0, 4.0 ] );
+var B0 = new Float64Array( [ 0.0, 5.0, 7.0, 0.0, 8.0 ] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var B1 = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dtrsm( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A1, 2, B1, 2 );
+// B0 => <Float64Array>[ 0.0, 30.0, 6.0, 0.0, 12.0 ]
+```
+
+#### dtrsm.ndarray( o, s, ul, t, d, m, n, α, A, sa1, sa2, oa, B, sb1, sb2, ob )
+
+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`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+A = new Float64Array( [ 0.0, 0.0, 1.0, 3.0, 0.0, 4.0 ] );
+B = new Float64Array( [ 0.0, 5.0, 7.0, 0.0, 8.0 ] );
+
+dtrsm.ndarray( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, 1, 2, B, 2, 1, 1 );
+// B => <Float64Array>[ 0.0, 30.0, 6.0, 0.0, 12.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+-   **sb1**: stride of the first dimension of `B`.
+-   **sb2**: stride of the second dimension of `B`.
+-   **ob**: starting index for `B`.
+
+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,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+A = new Float64Array( [ 0.0, 0.0, 1.0, 3.0, 0.0, 4.0 ] );
+B = new Float64Array( [ 0.0, 5.0, 7.0, 0.0, 8.0 ] );
+
+dtrsm.ndarray( 'row-major', 'left', 'upper', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, 1, 2, B, 2, 1, 1 );
+// B => <Float64Array>[ 0.0, 30.0, 6.0, 0.0, 12.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dtrsm()` corresponds to the [BLAS][blas] level 3 function [`dtrsm`][dtrsm].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dtrsm = require( '@stdlib/blas/base/dtrsm' );
+
+var A = new Float64Array( [ 1.0, 0.0, 3.0, 4.0 ] );
+var B = new Float64Array( [ 5.0, 0.0, 7.0, 8.0 ] );
+
+dtrsm( 'row-major', 'left', 'lower', 'no-transpose', 'non-unit', 2, 2, 6.0, A, 2, B, 2 );
+console.log( B );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[blas]: http://www.netlib.org/blas
+
+[dtrsm]: https://www.netlib.org/lapack/explore-html/d9/de5/group__trsm_ga7120d931d7b1a15e12d50d328799df8a.html#ga7120d931d7b1a15e12d50d328799df8a
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/base/dtrsm/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pkg = require( './../package.json' ).name;
+var dtrsm = require( './../lib/dtrsm.js' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var A;
+	var B;
+
+	A = uniform( N*N, 1.0, 10.0, {
+		'dtype': 'float64'
+	});
+	B = uniform( N*N, 1.0, 10.0, {
+		'dtype': 'float64'
+	});
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			z = dtrsm( 'column-major', 'left', 'upper', 'no-transpose', 'non-unit', N, N, 1.0, A, N, B, N );
+			if ( isnan( z[ i%z.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z[ i%z.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var min;
+	var max;
+	var N;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( N );
+		bench( pkg+':order=column-major,size='+(N*N), f );
+	}
+}
+
+main();