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feat: add lapack/base/dpttrf
PR-URL: stdlib-js#2578 Ref: stdlib-js#2464 Co-authored-by: Athan Reines <[email protected]> Reviewed-by: Athan Reines <[email protected]>
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‎lib/node_modules/@stdlib/lapack/base/dpttrf/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dpttrf
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> Compute the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A`.
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<section class = "usage">
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## Usage
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```javascript
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var dpttrf = require( '@stdlib/lapack/base/dpttrf' );
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```
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#### dpttrf( N, D, E )
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Computes the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A`.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
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var E = new Float64Array( [ 1.0, 2.0 ] );
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dpttrf( 3, D, E );
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// D => <Float64Array>[ 4, 4.75, ~5.15789 ]
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// E => <Float64Array>[ 0.25, ~0.4210 ]
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```
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The function has the following parameters:
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- **N**: order of matrix `A`.
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- **D**: the `N` diagonal elements of `A` as a [`Float64Array`][mdn-float64array].
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- **E**: the N-1 subdiagonal elements of `A` as a [`Float64Array`][mdn-float64array].
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial arrays...
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var D0 = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
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var E0 = new Float64Array( [ 0.0, 1.0, 2.0 ] );
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// Create offset views...
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var D1 = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var E1 = new Float64Array( E0.buffer, E0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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dpttrf( 3, D1, E1 );
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// D0 => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
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// E0 => <Float64Array>[ 0.0, 0.25, ~0.4210 ]
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```
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#### dpttrf.ndarray( N, D, strideD, offsetD, E, strideE, offsetE )
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Computes the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A` using alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
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var E = new Float64Array( [ 1.0, 2.0 ] );
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dpttrf.ndarray( 3, D, 1, 0, E, 1, 0 );
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// D => <Float64Array>[ 4, 4.75, ~5.15789 ]
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// E => <Float64Array>[ 0.25, ~0.4210 ]
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```
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The function has the following additional parameters:
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- **strideD**: stride length for `D`.
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- **offsetD**: starting index for `D`.
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- **strideE**: stride length for `E`.
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- **offsetE**: starting index for `E`.
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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,
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<!-- eslint-disable max-len -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var D = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
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var E = new Float64Array( [ 0.0, 1.0, 2.0 ] );
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dpttrf.ndarray( 3, D, 1, 1, E, 1, 1 );
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// D => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
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// E => <Float64Array>[ 0.0, 0.25, ~0.4210 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Both functions mutate the input arrays `D` and `E`.
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- Both functions return a status code indicating success or failure. A status code indicates the following conditions:
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- `0`: factorization was successful.
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- `<0`: the k-th argument had an illegal value, where `-k` equals the status code value.
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- `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.
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- `N`: the leading principal minor of order `N` is not positive, and factorization was completed.
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- `dpttrf()` corresponds to the [LAPACK][LAPACK] routine [`dpttrf`][lapack-dpttrf].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var dpttrf = require( '@stdlib/lapack/base/dpttrf' );
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var opts = {
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'dtype': 'float64'
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};
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var D = discreteUniform( 5, 1, 5, opts );
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console.log( D );
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var E = discreteUniform( D.length-1, 1, 5, opts );
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console.log( E );
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// Perform the `L * D * L^T` factorization:
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var info = dpttrf( D.length, D, E );
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console.log( D );
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console.log( E );
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console.log( info );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[lapack-dpttrf]: https://www.netlib.org/lapack/explore-html/d4/d2c/group__pttrf_ga8f112041da2b9b443f8761a1eaaf15b6.html#ga8f112041da2b9b443f8761a1eaaf15b6
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

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

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var pkg = require( './../package.json' ).name;
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var dpttrf = require( './../lib/dpttrf.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var D = uniform( len, 0.0, 100.0, options );
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var E = uniform( len, 0.0, 100.0, options );
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return benchmark;
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function benchmark( b ) {
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var d;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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d = dpttrf( len, D, E );
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if ( isnan( d ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( d ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

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