feat: add lapack/base/dlassq

PR-URL: stdlib-js#2668
Ref: stdlib-js#2464
Co-authored-by: Athan Reines <kgryte@gmail.com>
Reviewed-by: Athan Reines <kgryte@gmail.com>

lib/node_modules/@stdlib/lapack/base/dlassq/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.
+
+-->
+
+# dlassq
+
+> Return an updated sum of squares represented in scaled form.
+
+<section class="intro">
+
+This routine returns the values $s_{textrm{out}}$ and $\textrm{ss}_{\textrm{out}}$ such that
+
+<!-- <equation class="equation" label="eq:sum_of_squares" align="center" raw="s_{\textrm{out}}^2 \cdot \textrm{ss}_{\textrm{out}} = x_0^2 + \ldots + x_{N-1}^2 + s_{\textrm{in}}^2 \cdot \textrm{ss}_{\textrm{in}}" alt="Sum of squares represented in scaled form"> -->
+
+<div class="equation" align="center" data-raw-text="s_{\textrm{out}}^2 \cdot \textrm{ss}_{\textrm{out}} = x_0^2 + \ldots + x_{N-1}^2 + s_{\textrm{in}}^2 \cdot \textrm{ss}_{\textrm{in}}" data-equation="eq:sum_of_squares">
+    <img src="" alt="Sum of squares represented in scaled form">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+where $x_i = X_{(i-1) \cdot \textrm{sx}}$ and $\textrm{sx}$ is the stride of `X`. The value of $\textrm{ss}_{\textrm{in}}$ is assumed to be nonnegative.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlassq = require( '@stdlib/lapack/base/dlassq' );
+```
+
+#### dlassq( N, X, strideX, scale, sumsq )
+
+Returns an updated sum of squares represented in scaled form.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+
+var out = dlassq( 4, X, 1, 1.0, 0.0 );
+// returns <Float64Array>[ 1.0, 30.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **X**: input [`Float64Array`][mdn-float64array].
+-   **strideX**: stride length for `X`.
+-   **scale**: scaling factor.
+-   **sumsq**: basic sum of squares from which output is factored out.
+
+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 X0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+
+// Create an offset view:
+var X1 = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+// Compute the sum of squares:
+var out = dlassq( X1.length, X1, 1, 1.0, 0.0 );
+// returns <Float64Array>[ 1.0, 30.0 ]
+```
+
+The returned [`Float64Array`][mdn-float64array] contains an updated scale factor and an updated sum of squares, respectively.
+
+#### dlassq.ndarray( N, X, sx, ox, scale, sumsq, out, so, oo )
+
+Returns an updated sum of squares represented in scaled form using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
+var out = new Float64Array( [ 0.0, 0.0 ] );
+
+dlassq.ndarray( 4, X, 1, 0, 1.0, 0.0, out, 1, 0 );
+// out => <Float64Array>[ 1.0, 30.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **ox**: starting index for `X`.
+-   **out**: output [`Float64Array`][mdn-float64array]
+-   **so**: stride length for `out`.
+-   **oo**: starting index for `out`.
+
+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,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var X = new Float64Array( [ 1.0, 0.0, 2.0, 0.0, 3.0, 0.0, 4.0 ] );
+var out = new Float64Array( [ 0.0, 0.0, 999.9, 0.0, 999.9 ] );
+
+dlassq.ndarray( 4, X, 2, 0, 1.0, 0.0, out, 2, 1 );
+// out => <Float64Array>[ 0.0, 1.0, 999.9, 30.0, 999.9 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlassq()` corresponds to the [LAPACK][LAPACK] function [`dlassq`][lapack-dlassq].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var dlassq = require( '@stdlib/lapack/base/dlassq' );
+
+var X = discreteUniform( 10, -10, 10, {
+    'dtype': 'float64'
+});
+console.log( X );
+
+var out = dlassq( X.length, X, 1, 1.0, 0.0 );
+console.log( out );
+```
+
+</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-dlassq]: https://www.netlib.org/lapack/explore-html/d8/d76/group__lassq_gae8f40b0a34771b4f2d9c863de3af7be5.html#gae8f40b0a34771b4f2d9c863de3af7be5
+
+[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/dlassq/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 pkg = require( './../package.json' ).name;
+var dlassq = require( './../lib/dlassq.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var x = uniform( len, -100.0, 100.0, options );
+	return benchmark;
+
+	function benchmark( b ) {
+		var out;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			out = dlassq( x.length, x, 1, 1.0, 0.0 );
+			if ( isnan( out[ 0 ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( out[ 1 ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		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 = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();