feat: add lapack/base/dlasv2

lib/node_modules/@stdlib/lapack/base/dlasv2/README.md

@@ -0,0 +1,262 @@
+<!--
+
+@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.
+
+-->
+
+# dlasv2
+
+> Compute the singular value decomposition of a 2x2 upper triangular matrix.
+
+<section class="intro">
+
+The singular value decomposition of a 2x2 upper triangular matrix $ \begin{bmatrix} F & G \\ 0 & H \end{bmatrix}$ is given by
+
+<!-- <equation class="equation" label="eq:dlasv2_svd" align="center" raw="\left[\begin{array}{rr} \mathrm{CSL} & \mathrm{SNL} \\ -\mathrm{SNL} & \mathrm{CSL} \end{array}\right] \left[\begin{array}{rr} F & G \\ 0 & H \end{array}\right] \left[\begin{array}{rr} \mathrm{CSR} & -\mathrm{SNR} \\ \mathrm{SNR} & \mathrm{CSR} \end{array}\right] = \left[\begin{array}{rr} \mathrm{SSMAX} & 0 \\ 0 & \mathrm{SSMIN} \end{array}\right]" alt="Singular value decomposition of a 2x2 upper triangular matrix."> -->
+
+```math
+\left[\begin{array}{rr}\mathrm{CSL} & \mathrm{SNL} \\
+-\mathrm{SNL} & \mathrm{CSL}\end{array}\right]
+
+\left[\begin{array}{rr}F & G \\
+0 & H\end{array}\right]
+
+\left[\begin{array}{rr}\mathrm{CSR} & -\mathrm{SNR} \\
+\mathrm{SNR} & \mathrm{CSR}\end{array}\right]
+
+=
+
+\left[\begin{array}{rr}\mathrm{SSMAX} & 0 \\
+0 & \mathrm{SSMIN}\end{array}\right]
+```
+
+<!-- </equation> -->
+
+where `CSL`,`SNL`,`CSR`,`SNR` define orthogonal rotations and $\mathrm{SSMAX}^2, \mathrm{SSMIN}^2$ are the eigenvalues of $A^{T}A$.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlasv2 = require( '@stdlib/lapack/base/dlasv2' );
+```
+
+#### dlasv2( F, G, H, out )
+
+Computes the singular value decomposition of a 2x2 upper triangular matrix.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var out = new Float64Array( 6 );
+
+var v = dlasv2( 2.0, 3.0, 4.0, out );
+// returns <Float64Array>[ ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
+
+var bool = ( v === out );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **F**: the (0,0) element of matrix.
+-   **G**: the (0,1) element of matrix.
+-   **H**: the (1,1) element of matrix.
+-   **out**: [`Float64Array`][@stdlib/array/float64] output array containing `SSMIN`, `SSMAX`, `SNR`, `CSR`, `SNL`, and `CSL` respectively.
+
+On return, `abs(SSMAX)` is the larger singular value, `abs(SSMIN)` is the smaller singular value, and (`CSL`,`SNL`) and (`CSR`,`SNR`) are the left and right singular vectors for `abs(SSMAX)` as described in the decomposition.
+
+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 OUT0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+// Create offset views...
+var OUT1 = new Float64Array( OUT0.buffer, OUT0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlasv2( 2.0, 3.0, 4.0, OUT1 );
+// OUT0 => <Float64Array>[ 0.0, ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
+```
+
+#### dlasv2.ndarray( F, G, H, out, strideOut, offsetOut )
+
+Computes the singular value decomposition of a 2x2 upper triangular matrix using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var out = new Float64Array( 6 );
+
+dlasv2.ndarray( 2.0, 3.0, 4.0, out, 1, 0 );
+// out => <Float64Array>[ ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideOut**: stride length for `Out`.
+-   **offsetOut**:  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 out = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+dlasv2.ndarray( 2.0, 3.0, 4.0, out, 1, 1 );
+// out => <Float64Array>[ 0.0, ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlasv2()` corresponds to the [LAPACK][LAPACK] routine [`dlasv2`][lapack-dlasv2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlasv2 = require( '@stdlib/lapack/base/dlasv2' );
+
+var out = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+dlasv2( 1.0, 1e6, 2.0, out );
+console.log( out );
+
+dlasv2.ndarray( 1.0, 1e6, 2.0, out, 1, 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-dlasv2]: https://www.netlib.org/lapack/explore-html/d8/da7/group__lasv2_ga96f9f244300d82921950e2c393b4b20f.html#ga96f9f244300d82921950e2c393b4b20f
+
+[@stdlib/array/float64]: https://stdlib.io/docs/api/latest/@stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dlasv2/benchmark/benchmark.js

@@ -0,0 +1,69 @@
+/**
+* @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 Float64Array = require( '@stdlib/array/float64' );
+var format = require( '@stdlib/string/format' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var dlasv2 = require( './../lib/dlasv2.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// MAIN //
+
+bench( format( '%s', pkg ), function benchmark( b ) {
+	var out;
+	var N;
+	var f;
+	var g;
+	var h;
+	var i;
+
+	N = 100;
+	f = uniform( N, -500.0, 500.0, options );
+	g = uniform( N, -500.0, 500.0, options );
+	h = uniform( N, -500.0, 500.0, options );
+
+	out = new Float64Array( 6 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		dlasv2( f[ i%f.length ], g[ i%g.length ], h[ i%h.length ], out );
+		if ( isnan( out[ i%out.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( out[ i%out.length ] ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});