feat: add lapack/base/dsptrf

lib/node_modules/@stdlib/lapack/base/dsptrf/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.
+
+-->
+
+# dsptrf
+
+> Compute the factorization of a real symmetric matrix `A` stored in packed format using the Bunch-Kaufman diagonal pivoting method.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dsptrf = require( '@stdlib/lapack/base/dsptrf' );
+```
+
+#### dsptrf( order, uplo, N, AP, IPIV )
+
+Computes the factorization of a real symmetric matrix `A` stored in packed format using the Bunch-Kaufman diagonal pivoting method.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+/*
+    A = [
+        [  4.0,  1.0, -2.0,  2.0 ],
+        [  1.0,  2.0,  0.0,  1.0 ],
+        [ -2.0,  0.0,  3.0, -2.0 ],
+        [  2.0,  1.0, -2.0, -1.0 ]
+    ]
+*/
+
+// Store the upper triangle of `A` in column-major packed form:
+var AP = new Float64Array( [ 4.0, 1.0, 2.0, -2.0, 0.0, 3.0, 2.0, 1.0, -2.0, -1.0 ] );
+var IPIV = new Int32Array( 4 );
+
+dsptrf( 'column-major', 'upper', 4, AP, IPIV );
+// IPIV => <Int32Array>[ 1, 2, 3, 1 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout. Must be either `'row-major'` or `'column-major'`.
+-   **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied. Must be either `'upper'` or `'lower'`.
+-   **N**: order of the matrix `A`.
+-   **AP**: packed form of the symmetric matrix `A` as a [`Float64Array`][mdn-float64array]. Should have `N*(N+1)/2` indexed elements. On exit, `AP` is overwritten by the block diagonal matrix `D` and the multipliers used to obtain the factor `U` or `L`.
+-   **IPIV**: vector of pivot indices as an [`Int32Array`][mdn-int32array]. Should have `N` indexed elements. On exit, `IPIV` contains details of the interchanges and the block structure of `D` (values are one-based, as in the reference LAPACK implementation).
+
+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' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+// Initial arrays...
+var AP0 = new Float64Array( [ 0.0, 4.0, 1.0, 2.0, -2.0, 0.0, 3.0, 2.0, 1.0, -2.0, -1.0 ] );
+var IPIV0 = new Int32Array( [ 0, 0, 0, 0, 0 ] );
+
+// Create offset views...
+var AP = new Float64Array( AP0.buffer, AP0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var IPIV = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dsptrf( 'column-major', 'upper', 4, AP, IPIV );
+// IPIV0 => <Int32Array>[ 0, 1, 2, 3, 1 ]
+```
+
+#### dsptrf.ndarray( order, uplo, N, AP, sap, oap, IPIV, si, oi )
+
+Computes the factorization of a real symmetric matrix `A` stored in packed format using the Bunch-Kaufman diagonal pivoting method and alternative indexing semantics.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var AP = new Float64Array( [ 4.0, 1.0, 2.0, -2.0, 0.0, 3.0, 2.0, 1.0, -2.0, -1.0 ] );
+var IPIV = new Int32Array( 4 );
+
+dsptrf.ndarray( 'column-major', 'upper', 4, AP, 1, 0, IPIV, 1, 0 );
+// IPIV => <Int32Array>[ 1, 2, 3, 1 ]
+```
+
+The function has the following additional parameters:
+
+-   **sap**: stride length for `AP`.
+-   **oap**: starting index for `AP`.
+-   **si**: stride length for `IPIV`.
+-   **oi**: starting index for `IPIV`.
+
+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 Int32Array = require( '@stdlib/array/int32' );
+
+var AP = new Float64Array( [ 0.0, 4.0, 1.0, 2.0, -2.0, 0.0, 3.0, 2.0, 1.0, -2.0, -1.0 ] );
+var IPIV = new Int32Array( [ 0, 0, 0, 0, 0 ] );
+
+dsptrf.ndarray( 'column-major', 'upper', 4, AP, 1, 1, IPIV, 1, 1 );
+// IPIV => <Int32Array>[ 0, 1, 2, 3, 1 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input arrays `AP` and `IPIV`.
+
+-   For a symmetric matrix, an upper triangle stored in row-major order is identical in memory to a lower triangle stored in column-major order (and vice versa). Accordingly, when `order` is `'row-major'`, the routine resolves `uplo` to the equivalent column-major factorization (i.e., `'row-major'` + `'upper'` is factorized as `L*D*L^T` and `'row-major'` + `'lower'` is factorized as `U*D*U^T`). The returned `AP` and `IPIV` are self-consistent for the resolved factorization.
+
+-   Both functions return a status code indicating success or failure. The status code indicates the following conditions:
+
+    -   `0`: factorization was successful.
+    -   `>0`: `D(k,k)` is exactly zero (one-based, where `k` equals the status code value). The factorization has been completed, but the block diagonal matrix `D` is exactly singular, and division by zero will occur if it is used to solve a system of equations.
+
+-   `dsptrf()` corresponds to the [LAPACK][LAPACK] routine [`dsptrf`][lapack-dsptrf].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint-disable max-len -->
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dsptrf = require( '@stdlib/lapack/base/dsptrf' );
+
+/*
+    Symmetric matrix `A` (upper triangle):
+
+    A = [
+        [  4.0,  1.0, -2.0,  2.0 ],
+        [  1.0,  2.0,  0.0,  1.0 ],
+        [ -2.0,  0.0,  3.0, -2.0 ],
+        [  2.0,  1.0, -2.0, -1.0 ]
+    ]
+*/
+
+// Store the upper triangle of `A` in column-major packed form:
+var AP = new Float64Array( [ 4.0, 1.0, 2.0, -2.0, 0.0, 3.0, 2.0, 1.0, -2.0, -1.0 ] );
+var IPIV = new Int32Array( 4 );
+
+// Compute the Bunch-Kaufman factorization `A = U*D*U^T`:
+var info = dsptrf( 'column-major', 'upper', 4, AP, IPIV );
+
+console.log( AP );
+console.log( IPIV );
+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-dsptrf]: https://www.netlib.org/lapack/explore-html/d8/d08/group__hptrf_ga9adb8a8020b104eaaf72c2aad7861a8c.html#ga9adb8a8020b104eaaf72c2aad7861a8c
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-int32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Int32Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

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

@@ -0,0 +1,104 @@
+/**
+* @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 pow = require( '@stdlib/math/base/special/pow' );
+var Int32Array = require( '@stdlib/array/int32' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dsptrf = require( './../lib/dsptrf.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - order of the matrix
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var IPIV = new Int32Array( N );
+	var AP = uniform( N*( N+1 ) / 2, -1.0, 1.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var d;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			d = dsptrf( 'column-major', 'upper', N, AP, IPIV );
+			if ( d < 0 ) {
+				b.fail( 'should return a valid status code' );
+			}
+		}
+		b.toc();
+		if ( d < 0 ) {
+			b.fail( 'should return a valid status code' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var min;
+	var max;
+	var N;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 3; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = pow( 10, i );
+		f = createBenchmark( N );
+		bench( format( '%s:N=%d', pkg, N ), f );
+	}
+}
+
+main();