feat: add lapack/base/dlasq2

lib/node_modules/@stdlib/lapack/base/dlasq2/README.md

@@ -0,0 +1,263 @@
+<!--
+
+@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.
+
+-->
+
+# dlasq2
+
+> Compute all eigenvalues of the symmetric positive definite tridiagonal matrix associated with the QD Array `Z` to high relative accuracy.
+
+<section class="intro">
+
+The `dlasq2` routine computes all the eigenvalues of the symmetric positive definite tri-diagonal matrix associated with the QD (quotient-difference) array `Z` to high relative accuracy, in the absence of denormalization, underflow and overflow.
+
+To see the relation of Z to the tridiagonal matrix, let `L` be a unit lower bidiagonal matrix with subdiagonals `Z(2,4,6,,..)` and let `U` be an upper bidiagonal matrix with 1's above and diagonal `Z(1,3,5,,..)`. The tridiagonal is `L*U` or, if you prefer, the symmetric tridiagonal to which it is similar.
+
+The QD array `Z` of length `4*N` contains pairs `(q_i, qq_i, e_i, ee_i)` for `i = 1, 2, ..., N`, where `q_i` and `e_i` are derived from the diagonal and off-diagonal elements of `T` and `qq_i` and `ee_i` are working storage.
+
+Upon successful completion, the first `N` indexed elements contain the eigenvalues in descending order, and `Z( 2*N+1 )` holds the trace, and `Z( 2*N+2 )` holds the sum of the eigenvalues.
+
+If `N > 2`, then `Z( 2*N+3 )` holds the iteration count, `Z( 2*N+4 )` holds `NDIVS/NIN^2`, and `Z( 2*N+5 )` holds the percentage of shifts that failed.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlasq2 = require( '@stdlib/lapack/base/dlasq2' );
+```
+
+#### dlasq2( N, Z )
+
+Computes all eigenvalues of the symmetric positive definite tridiagonal matrix associated with the QD Array `Z` to high relative accuracy.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var Z = new Float64Array( [ 100, 4, 81, 3, 64, 2.5, 49, 2, 36, 1.5, 25, 1, 16, 0.5, 9, 0 ] );
+
+var out = dlasq2( 4, Z );
+// Z => <Float64Array>[ ~115.713, ~83.153, ~62.17, ~42.464, ~83.153, ~20.987, ~0.0, ~0.0, 303.5, ~303.5, 15, 4.0625, 0.0, ~0.0, ~0.172, ~0.096 ]
+// out => 0
+```
+
+The function has the following parameters:
+
+-   **N**: number of rows/columns in the tridiagonal matrix.
+-   **Z**: the QD array as a [`Float64Array`][@stdlib/array/float64]. Must have at least `4*N` indexed elements. `Z` is overwritten during computation. Upon successful exit, the first `N` indexed elements of `Z` contain the eigenvalues in decreasing order.
+
+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, max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var Z0 = new Float64Array( [ 0.0, 100, 4, 81, 3, 64, 2.5, 49, 2, 36, 1.5, 25, 1, 16, 0.5, 9, 0 ] );
+
+// Create offset views...
+var Z1 = new Float64Array( Z0.buffer, Z0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlasq2( 4, Z1 );
+// Z0 => <Float64Array>[ 0.0, ~115.713, ~83.153, ~62.17, ~42.464, ~83.153, ~20.987, ~0.0, ~0.0, 303.5, ~303.5, 15, 4.0625, 0.0, ~0.0, ~0.172, ~0.096 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dlasq2.ndarray( N, Z, strideZ, offsetZ )
+
+Computes all eigenvalues of the symmetric positive definite tridiagonal matrix associated with the QD Array `Z` to high relative accuracy using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var Z = new Float64Array( [ 100, 4, 81, 3, 64, 2.5, 49, 2, 36, 1.5, 25, 1, 16, 0.5, 9, 0 ] );
+
+dlasq2.ndarray( 4, Z, 1, 0 );
+// Z => <Float64Array>[ ~115.713, ~83.153, ~62.17, ~42.464, ~83.153, ~20.987, ~0.0, ~0.0, 303.5, ~303.5, 15, 4.0625, 0.0, ~0.0, ~0.172, ~0.096 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideZ**: stride length for `Z`.
+-   **offsetZ**:  starting index for `Z`.
+
+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 Z = new Float64Array( [ 0.0, 100, 4, 81, 3, 64, 2.5, 49, 2, 36, 1.5, 25, 1, 16, 0.5, 9, 0 ] );
+
+dlasq2.ndarray( 4, Z, 1, 1 );
+// Z => <Float64Array>[ 0.0, ~115.713, ~83.153, ~62.17, ~42.464, ~83.153, ~20.987, ~0.0, ~0.0, 303.5, ~303.5, 15, 4.0625, 0.0, ~0.0, ~0.172, ~0.096 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input array `Z`.
+
+-   Both functions return a status code indicating success or failure. A status code indicates the following conditions:
+
+    -   If `=0`, then the algorithm completed successfully.
+    -   If `<0`:
+
+        -   If the i-th argument is a scalar and had an illegal value, then `INFO = -i`.
+        -   If the i-th argument is an array and the j-entry had an illegal value, then `INFO = -(i*100+j)`.
+
+    -   If `>0`, the algorithm failed:
+
+        -   `=1`, a split was marked by a positive value in `E`.
+        -   `=2`, current block of `Z` not diagonalized after `100*N` iterations (in inner while loop). On exit `Z` holds a QD array with the same eigenvalues as the given `Z`.
+        -   `=3`, termination criterion of outer while loop not met (program created more than N unreduced blocks).
+
+-   `dlasq2()` corresponds to the [LAPACK][LAPACK] routine [`dlasq2`][lapack-dlasq2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dlasq2 = require( '@stdlib/lapack/base/dlasq2' );
+
+var Z = new Float64Array( [ 144, 6, 121, 5, 100, 4, 81, 3, 64, 2, 49, 1.5, 36, 1, 25, 0.5 ] );
+
+var info = dlasq2( 4, Z );
+console.log( Z );
+console.log( info );
+```
+
+</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-dlasq2]: https://www.netlib.org/lapack/explore-html/d4/d4b/group__lasq2_gad2bd91b6a5e4dcc4614d319951f11109.html
+
+[@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/dlasq2/benchmark/benchmark.js

@@ -0,0 +1,102 @@
+/**
+* @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 format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dlasq2 = require( './../lib/dlasq2.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 Z = uniform( len*4, 0.0, 100.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			dlasq2( len, Z );
+			if ( isnan( Z[ i%Z.length ] ) ) {
+				b.fail( 'unexpected NaN value' );
+			}
+		}
+		b.toc();
+		if ( isnan( Z[ i%Z.length ] ) ) {
+			b.fail( 'unexpected NaN value' );
+		}
+		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();