feat: add lapack/base/dlascl

lib/node_modules/@stdlib/lapack/base/dlascl/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# dlascl
+
+> LAPACK routine to multiply a double-precision floating-point M-by-N matrix `A` by a double-precision floating-point scalar.
+
+<section class="intro">
+
+The `dlascl` routine multiplies each element of an M-by-N matrix `A` by a scalar `α`
+
+<!-- <equation class="equation" label="eq:scaling_operation" align="center" raw="B = \alpha \cdot A = \alpha \cdot \left[ a_{1,1} a_{1,2} \ldots a_{0,N} \quad \ldots \right] = \left[ \alpha a_{1,1} \alpha a_{1,2} \ldots \alpha a_{0,N} \quad \ldots \right]" alt="Equation for matrix scaling operation."> -->
+
+```math
+B = \alpha \cdot A = \alpha \cdot \left[ a_{1,1} a_{1,2} \ldots a_{0,N} \quad \ldots \right] = \left[ \alpha a_{1,1} \alpha a_{1,2} \ldots \alpha a_{0,N} \quad \ldots \right]
+```
+
+<!-- </equation> -->
+
+In order to more readily avoid underflow/overflow, this routine chooses to represent `α` as the product of
+
+<!-- <equation class="equation" label="eq:alpha_representation" align="center" raw="\alpha = \beta \cdot \frac{1}{\gamma}" alt="Equation for alpha representation as beta over gamma."> -->
+
+```math
+\alpha = \beta \cdot \frac{1}{\gamma}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlascl = require( '@stdlib/lapack/base/dlascl' );
+```
+
+#### dlascl( order, type, KL, KU, γ, β, M, N, A, LDA )
+
+Multiplies a double-precision floating-point M-by-N matrix `A` by a double-precision floating-point scalar.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
+
+dlascl( 'row-major', 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2 );
+// A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **type**: specifies the type of matrix `A`. Must be one of the following: `'general'`, `'upper'`, `'lower'`, `'upper-hessenberg'`, `'symmetric-banded-lower'`, `'symmetric-banded-upper'`, or `'banded'`.
+-   **KL**: lower bandwidth of `A` (i.e., the number of sub-diagonals). Referenced only if type is `'symmetric-banded-lower'` or `'banded'`.
+-   **KU**: upper bandwidth of `A` (i.e., the number of super-diagonals). Referenced only if type is `'symmetric-banded-upper'` or `'banded'`.
+-   **γ**: the matrix `A` is multiplied by `β/γ`.
+-   **β**: the matrix `A` is multiplied by `β/γ`.
+-   **M**: number of rows in matrix `A`.
+-   **N**: number of columns in matrix `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+
+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 array:
+var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+// Create offset view:
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlascl( 'row-major', 'general', 0, 0, 1.0, 2.0, 3, 2, A1, 2 );
+// A0 => <Float64Array>[ 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
+```
+
+#### dlascl.ndarray( type, KL, KU, γ, β, M, N, A, strideA1, strideA2, offsetA )
+
+Multiplies a double-precision floating-point M-by-N matrix `A` by a double-precision floating-point scalar using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
+
+dlascl.ndarray( 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2, 1, 0 );
+// A => <Float64Array>[ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
+```
+
+The function has the following parameters:
+
+-   **type**: specifies the type of matrix `A`. Must be one of the following: `'general'`, `'upper'`, `'lower'`, `'upper-hessenberg'`, `'symmetric-banded-lower'`, `'symmetric-banded-upper'`, or `'banded'`.
+-   **KL**: lower bandwidth of `A` (i.e., the number of sub-diagonals). Referenced only if type is `'symmetric-banded-lower'` or `'banded'`.
+-   **KU**: upper bandwidth of `A` (i.e., the number of super-diagonals). Referenced only if type is `'symmetric-banded-upper'` or `'banded'`.
+-   **γ**: the matrix `A` is multiplied by `β/γ`.
+-   **β**: the matrix `A` is multiplied by `β/γ`.
+-   **M**: number of rows in matrix `A`.
+-   **N**: number of columns in matrix `A`.
+-   **A**: input [`Float64Array`][mdn-float64array].
+-   **strideA1**: stride of the first dimension of `A`.
+-   **strideA2**: stride of the second dimension of `A`.
+-   **offsetA**: starting index for `A`.
+
+
+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' );
+
+var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+dlascl.ndarray( 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2, 1, 1 );
+// A => <Float64Array>[ 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlascl()` corresponds to the [LAPACK][lapack] routine [`dlascl`][lapack-dlascl].
+-   If `type` is `'banded'`, `'symmetric-banded-lower'`, or `'symmetric-banded-upper'`, the matrix should be stored in the [band storage][lapack-band-storage] format.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlascl = require( '@stdlib/lapack/base/dlascl' );
+
+// Define a matrix A (3x2 in row-major order):
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+console.log( 'Initial A (row-major): ', A );
+
+dlascl( 'row-major', 'general', 0, 0, 1.0, 2.0, 3, 2, A, 2 );
+console.log( 'Scaled A (row-major): ', A );
+```
+
+</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">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dlascl]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d43/group__aux_o_t_h_e_rauxiliary_ga7bce4c35ec5a86ee0bfdd15c476d99c8.html
+
+[lapack-band-storage]: https://www.netlib.org/lapack/lug/node124.html
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dlascl/benchmark/benchmark.js

@@ -0,0 +1,117 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 dlascl = require( './../lib/dlascl.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+	'row-major',
+	'column-major'
+];
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {PositiveInteger} N - number of rows/columns
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, N ) {
+	var LDA;
+	var A;
+
+	LDA = N;
+
+	A = uniform( N*N, -10.0, 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 = dlascl( order, 'general', 0, 0, 1.0, 2.0, N, N, A, LDA );
+			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 ord;
+	var N;
+	var f;
+	var i;
+	var k;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( k = 0; k < LAYOUTS.length; k++ ) {
+		ord = LAYOUTS[ k ];
+		for ( i = min; i <= max; i++ ) {
+			N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+			f = createBenchmark( ord, N );
+			bench( pkg+'::square_matrix:order='+ord+',size='+(N*N), f );
+		}
+	}
+}
+
+main();