feat: add lapack/base/dpttrf

PR-URL: #2578
Ref: #2464
Co-authored-by: Athan Reines <kgryte@gmail.com>
Reviewed-by: Athan Reines <kgryte@gmail.com>

lib/node_modules/@stdlib/lapack/base/dpttrf/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.
+
+-->
+
+# dpttrf
+
+> Compute the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dpttrf = require( '@stdlib/lapack/base/dpttrf' );
+```
+
+#### dpttrf( N, D, E )
+
+Computes the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
+var E = new Float64Array( [ 1.0, 2.0 ] );
+
+dpttrf( 3, D, E );
+// D => <Float64Array>[ 4, 4.75, ~5.15789 ]
+// E => <Float64Array>[ 0.25, ~0.4210 ]
+```
+
+The function has the following parameters:
+
+-   **N**: order of matrix `A`.
+-   **D**: the `N` diagonal elements of `A` as a [`Float64Array`][mdn-float64array].
+-   **E**: the N-1 subdiagonal elements of `A` as a [`Float64Array`][mdn-float64array].
+
+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 D0 = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
+var E0 = new Float64Array( [ 0.0, 1.0, 2.0 ] );
+
+// Create offset views...
+var D1 = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var E1 = new Float64Array( E0.buffer, E0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dpttrf( 3, D1, E1 );
+// D0 => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
+// E0 => <Float64Array>[ 0.0, 0.25, ~0.4210 ]
+```
+
+#### dpttrf.ndarray( N, D, strideD, offsetD, E, strideE, offsetE )
+
+Computes the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A` using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
+var E = new Float64Array( [ 1.0, 2.0 ] );
+
+dpttrf.ndarray( 3, D, 1, 0, E, 1, 0 );
+// D => <Float64Array>[ 4, 4.75, ~5.15789 ]
+// E => <Float64Array>[ 0.25, ~0.4210 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideD**: stride length for `D`.
+-   **offsetD**:  starting index for `D`.
+-   **strideE**: stride length for `E`.
+-   **offsetE**:  starting index for `E`.
+
+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 D = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
+var E = new Float64Array( [ 0.0, 1.0, 2.0 ] );
+
+dpttrf.ndarray( 3, D, 1, 1, E, 1, 1 );
+// D => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
+// E => <Float64Array>[ 0.0, 0.25, ~0.4210 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input arrays `D` and `E`.
+
+-   Both functions return a status code indicating success or failure. A status code indicates the following conditions:
+
+    -   `0`: factorization was successful.
+    -   `<0`: the k-th argument had an illegal value, where `-k` equals the status code value.
+    -   `0 < k < N`: the leading principal minor of order `k` is not positive and factorization could not be completed, where `k` equals the status code value.
+    -   `N`: the leading principal minor of order `N` is not positive, and factorization was completed.
+
+-   `dpttrf()` corresponds to the [LAPACK][LAPACK] routine [`dpttrf`][lapack-dpttrf].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var dpttrf = require( '@stdlib/lapack/base/dpttrf' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var D = discreteUniform( 5, 1, 5, opts );
+console.log( D );
+
+var E = discreteUniform( D.length-1, 1, 5, opts );
+console.log( E );
+
+// Perform the `L * D * L^T` factorization:
+var info = dpttrf( D.length, D, E );
+console.log( D );
+console.log( E );
+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-dpttrf]: https://www.netlib.org/lapack/explore-html/d4/d2c/group__pttrf_ga8f112041da2b9b443f8761a1eaaf15b6.html#ga8f112041da2b9b443f8761a1eaaf15b6
+
+[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/dpttrf/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 dpttrf = require( './../lib/dpttrf.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 D = uniform( len, 0.0, 100.0, options );
+	var E = uniform( len, 0.0, 100.0, options );
+	return benchmark;
+
+	function benchmark( b ) {
+		var d;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			d = dpttrf( len, D, E );
+			if ( isnan( d ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( d ) ) {
+			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();