feat: add lapack/base/dlaqsp

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# dlaqsp
+
+> Equilibrate a real symmetric matrix stored in packed format.
+
+<section class="intro">
+
+Given a vector of scaling factors `S`, the routine equilibrates a real symmetric matrix `A` stored in packed format such that
+
+<!-- <equation class="equation" label="eq:equilibration" align="center" raw="A = \text{diag}(S) \times A \times \text{diag}(S)" alt="Equilibration of a symmetric matrix."> -->
+
+```math
+A = \text{diag}(S) \times A \times \text{diag}(S)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlaqsp = require( '@stdlib/lapack/base/dlaqsp' );
+```
+
+#### dlaqsp( order, uplo, N, AP, S, scond, amax )
+
+Equilibrates a real symmetric matrix `A` stored in packed format using scaling factors `S`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var S = new Float64Array( [ 0.05, 2.0, 4.0 ] );
+
+var out = dlaqsp( 'column-major', 'upper', 3, AP, S, 0.0125, 6.0 );
+// AP => <Float64Array>[ ~0.0025, 0.2, 12.0, 0.8, 40.0, 96.0 ]
+// out => 'Y'
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout (either `'row-major'` or `'column-major'`).
+-   **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied (either `'upper'` or `'lower'`).
+-   **N**: order of matrix `A`.
+-   **AP**: packed form of symmetric matrix `A` as a [`Float64Array`][mdn-float64array].
+-   **S**: scale factors vector for `A` as a [`Float64Array`][mdn-float64array].
+-   **scond**: ratio of the smallest `S[i]` to the largest `S[i]`.
+-   **amax**: absolute value of the largest matrix entry.
+
+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 AP0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var S0 = new Float64Array( [ 0.0, 0.05, 2.0, 4.0 ] );
+
+// Create offset views:
+var AP1 = new Float64Array( AP0.buffer, AP0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var S1 = new Float64Array( S0.buffer, S0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var out = dlaqsp( 'column-major', 'upper', 3, AP1, S1, 0.0125, 6.0 );
+// AP1 => <Float64Array>[ ~0.0025, 0.2, 12.0, 0.8, 40.0, 96.0 ]
+// out => 'Y'
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dlaqsp.ndarray( order, uplo, N, AP, strideAP, offsetAP, S, strideS, offsetS, scond, amax )
+
+<!-- lint enable maximum-heading-length -->
+
+Equilibrates a real symmetric matrix `A` stored in packed format using scaling factors `S` and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var S = new Float64Array( [ 0.05, 2.0, 4.0 ] );
+
+var out = dlaqsp.ndarray( 'column-major', 'upper', 3, AP, 1, 0, S, 1, 0, 0.0125, 6.0 );
+// AP => <Float64Array>[ ~0.0025, 0.2, 12.0, 0.8, 40.0, 96.0 ]
+// out => 'Y'
+```
+
+The function has the following additional parameters:
+
+-   **strideAP**: stride length for `AP`.
+-   **offsetAP**: starting index for `AP`.
+-   **strideS**: stride length for `S`.
+-   **offsetS**: starting index for `S`.
+
+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 AP = new Float64Array( [ 9999.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var S = new Float64Array( [ 9999.0, 0.05, 2.0, 4.0 ] );
+
+var out = dlaqsp.ndarray( 'column-major', 'upper', 3, AP, 1, 1, S, 1, 1, 0.0125, 6.0 );
+// AP => <Float64Array>[ 9999.0, ~0.0025, 0.2, 12.0, 0.8, 40.0, 96.0 ]
+// out => 'Y'
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `AP` should contain `N*(N+1)/2` elements.
+-   If `scond` is greater than or equal to `0.1` and `amax` is neither too small nor too large (i.e., the matrix is close to neither underflow nor overflow), the matrix is considered to be sufficiently well-scaled, `AP` is left unchanged, and the function returns `'N'`. Otherwise, the function mutates `AP` in-place, replacing `A` by `diag(S)*A*diag(S)`, and returns `'Y'`.
+-   `dlaqsp()` corresponds to the [LAPACK][LAPACK] routine [`dlaqsp`][lapack-dlaqsp].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlaqsp = require( '@stdlib/lapack/base/dlaqsp' );
+
+// Define a symmetric matrix in packed format and a vector of scale factors:
+var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var S = new Float64Array( [ 0.05, 2.0, 4.0 ] );
+
+// Equilibrate the matrix, whose upper triangle is stored:
+var out = dlaqsp( 'column-major', 'upper', 3, AP, S, 0.0125, 6.0 );
+console.log( out );
+console.log( AP );
+
+AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+S = new Float64Array( [ 0.05, 2.0, 4.0 ] );
+
+// Equilibrate the matrix, whose lower triangle is stored:
+out = dlaqsp.ndarray( 'column-major', 'lower', 3, AP, 1, 0, S, 1, 0, 0.0125, 6.0 );
+console.log( out );
+console.log( AP );
+```
+
+</section>
+
+<!-- /.examples -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+### Usage
+
+```c
+// TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+### Examples
+
+```c
+// TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<section class="links">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dlaqsp]: https://www.netlib.org/lapack/explore-html/d1/d63/group__laqhp_ga60516a6dc31da01e46cfad594b906b40.html#ga60516a6dc31da01e46cfad594b906b40
+
+[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/dlaqsp/benchmark/benchmark.js

@@ -0,0 +1,108 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 isString = require( '@stdlib/assert/is-string' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dlaqsp = require( './../lib/dlaqsp.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - matrix order
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var AP;
+	var S;
+
+	AP = uniform( N * ( N + 1 ) / 2, -10.0, 10.0, options );
+	S = uniform( N, 0.5, 2.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var equed;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			equed = dlaqsp( 'column-major', 'upper', N, AP, S, 0.01, 10.0 );
+			if ( !isString( equed ) ) {
+				b.fail( 'should return a string' );
+			}
+		}
+		b.toc();
+		if ( !isString( equed ) ) {
+			b.fail( 'should return a string' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( len );
+		bench( format( '%s:size=%d', pkg, len * ( len + 1 ) / 2 ), f );
+	}
+}
+
+main();