feat: add lapack/base/dlasq6

lib/node_modules/@stdlib/lapack/base/dgttrf/test/test.js

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2025 The Stdlib Authors.
+* 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.

lib/node_modules/@stdlib/lapack/base/dlasq6/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.
+
+-->
+
+# dlasq6
+
+> Compute one dqd transform in ping-pong form.
+
+<section class="intro">
+
+The `dlasq6` routine computes one dqd (shift equal to zero) transform in ping-pong form. This routine performs one dqd transform, updates the `Z` ( QD ) array in place, and returns the values `DMIN`, `DMIN1`, `DMIN2`, `DN`, `DNM1`, and `DNM2`.
+
+Where:
+
+-   `d` is the current transformed diagonal element of the implicit tridiagonal matrix during iteration.
+-   `DMIN` is the minimum value of `d` over the whole transform.
+-   `DMIN1` is the minimum value of `d`, excluding `d[ N0 ]`.
+-   `DMIN2` is the minimum value of `d`, excluding `d[ N0 ]` and `d[ N0-1 ]`.
+-   `DN` is the final value `d[ N0 ]`.
+-   `DNM1` is the value `d[ N0-1 ]`.
+-   `DNM2` is the value `d[ N0-2 ]`.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlasq6 = require( '@stdlib/lapack/base/dlasq6' );
+```
+
+#### dlasq6( I0, N0, Z, PP, out )
+
+Computes one dqd transform in ping-pong form.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var out = new Float64Array( 6 );
+var Z = new Float64Array( [5, 0, 7, 0, 9, 0, 3, 0, 11, 0, 4, 0, 20, 0, 0, 0] );
+
+var v = dlasq6( 0, 3, Z, 0, out );
+// returns <Float64Array>[ 3.75, 3.75, 3.75, ~12.088, ~6.111, 3.75 ]
+
+var bool = ( v === out );
+// returns true
+```
+
+The function has the following parameters:
+
+-   **I0**: the first index.
+-   **N0**: the last index.
+-   **Z**: [`Float64Array`][@stdlib/array/float64] QD array.
+-   **PP**: ping-pong flag, where `0` corresponds to ping and `1` corresponds to pong.
+-   **out**: [`Float64Array`][@stdlib/array/float64] output array containing `DMIN`, `DMIN1`, `DMIN2`, `DN`, `DNM1`, and `DNM2` respectively.
+
+On return, `Z` is updated in place and `out` contains the final scalar values from the transform.
+
+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 Z0 = new Float64Array( [0, 5, 0, 7, 0, 9, 0, 3, 0, 11, 0, 4, 0, 20, 0, 0, 0] ); // eslint-disable-line max-len
+var out0 = new Float64Array( 7 );
+
+// Create offset views...
+var Z = new Float64Array( Z0.buffer, Z0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var out = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlasq6( 0, 3, Z, 0, out );
+// out0 => <Float64Array>[ 0.0, 3.75, 3.75, 3.75, ~12.088, ~6.111, 3.75 ]
+```
+
+#### dlasq6.ndarray( I0, N0, Z, strideZ, offsetZ, PP, out, strideOut, offsetOut )
+
+Computes one dqd transform in ping-pong form using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var out = new Float64Array( 6 );
+var Z = new Float64Array( [5, 0, 7, 0, 9, 0, 3, 0, 11, 0, 4, 0, 20, 0, 0, 0] );
+
+dlasq6.ndarray( 0, 3, Z, 1, 0, 0, out, 1, 0 );
+// out => <Float64Array>[ 3.75, 3.75, 3.75, ~12.088, ~6.111, 3.75 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideZ**: stride length for `Z`.
+-   **offsetZ**: starting index for `Z`.
+-   **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 ] );
+var Z = new Float64Array( [5, 0, 7, 0, 9, 0, 3, 0, 11, 0, 4, 0, 20, 0, 0, 0] );
+
+dlasq6.ndarray( 0, 3, Z, 1, 0, 0, out, 1, 0 );
+// out => <Float64Array>[ 3.75, 3.75, 3.75, ~12.088, ~6.111, 3.75 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dlasq6()` corresponds to the [LAPACK][LAPACK] routine [`dlasq6`][lapack-dlasq6].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlasq6 = require( '@stdlib/lapack/base/dlasq6' );
+
+var Z = new Float64Array( [6, 0, 3, 0, 8, 0, 2, 0, 10, 0, 4, 0, 18, 0, 0, 0] );
+var out = new Float64Array( 6 );
+
+dlasq6( 0, 3, Z, 0, out );
+console.log( out );
+
+// Redefine the `Z` array as it gets updated.
+Z = new Float64Array( [6, 0, 3, 0, 8, 0, 2, 0, 10, 0, 4, 0, 18, 0, 0, 0] );
+
+dlasq6.ndarray( 0, 3, Z, 1, 0, 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-dlasq6]: https://www.netlib.org/lapack/explore-html/d9/d79/group__lasq6_ga2f0fd49aec60432f288625107131fdbe.html#ga2f0fd49aec60432f288625107131fdbe
+
+[@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/dlasq6/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 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 Float64Array = require( '@stdlib/array/float64' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dlasq6 = require( './../lib/dlasq6.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 out = new Float64Array( 6 );
+	var N0 = floor( (len / 4) - 1 );
+	var N = len;
+	var Z = uniform( N, -10.0, 10.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var y;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			y = dlasq6( 0, N0, Z, 0, out, 1, 0 );
+			if ( isnan( out[ i%6 ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( y ) ) {
+			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( format( '%s:len=%d', pkg, len ), f );
+	}
+}
+
+main();