feat: add lapack/base/dptts2

lib/node_modules/@stdlib/lapack/base/dptts2/README.md

@@ -0,0 +1,252 @@
+<!--
+
+@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.
+
+-->
+
+# dptts2
+
+> Solve a tridiagonal system of the form `A * X = B` using `L * D * L^T` factorization of `A`.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dptts2 = require( '@stdlib/lapack/base/dptts2' );
+```
+
+#### dptts2( order, N, NRHS, D, E, B, LDB )
+
+Solves a tridiagonal system of the form `A * X = B` using `L * D * L^T` factorization of `A`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 1.0, 1.0, 1.0 ] );
+var E = new Float64Array( [ 2.0, 3.0 ] );
+var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+dptts2( 'row-major', 3, 2, D, E, B, 2 );
+// B => <Float64Array>[ 11.0, 38.0, -5.0, -18.0, 2.0, 6.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **N**: order of the tridiagonal matrix `A`.
+-   **NRHS**: number of right-hand sides i.e. the number of columns in `B`.
+-   **D**: array containing the diagonal elements of `A`.
+-   **E**: array containing the subdiagonal elements of `A`.
+-   **B**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
+-   **LDB**: stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`).
+
+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, 1.0, 1.0, 1.0 ] );
+var E0 = new Float64Array( [ 0.0, 2.0, 3.0 ] );
+var B0 = new Float64Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+// 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
+var B1 = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*2 ); // start at 2nd element
+
+dptts2( 'row-major', 3, 2, D1, E1, B1, 2 );
+// B0 => <Float64Array>[ 0.0, 0.0, 11.0, 38.0, -5.0, -18.0, 2.0, 6.0 ]
+```
+
+#### dptts2.ndarray( N, NRHS, D, sd, od, E, se, oe, B, sb1, sb2, ob )
+
+Solves a tridiagonal system of the form `A * X = B` using `L * D * L^T` factorization of `A` using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 1.0, 1.0, 1.0 ] );
+var E = new Float64Array( [ 2.0, 3.0 ] );
+var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+dptts2.ndarray( 3, 2, D, 1, 0, E, 1, 0, B, 2, 1, 0 );
+// B => <Float64Array>[ 11.0, 38.0, -5.0, -18.0, 2.0, 6.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: order of the tridiagonal matrix `A`.
+-   **NRHS**: number of right-hand sides i.e. the number of columns in `B`.
+-   **D**: array containing the diagonal elements of `A`.
+-   **sd**: stride length for `D`.
+-   **od**: starting index for `D`.
+-   **E**: array containing the subdiagonal elements of `A`.
+-   **se**: stride length for `E`.
+-   **oe**: starting index for `E`.
+-   **B**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
+-   **sb1**: stride of first dimension of `B`.
+-   **sb2**: stride of second dimension of `B`.
+-   **ob**: starting index for `B`.
+
+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( [ 1.0, 1.0, 1.0 ] );
+var E = new Float64Array( [ 2.0, 3.0 ] );
+var B = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+dptts2.ndarray( 3, 2, D, 1, 0, E, 1, 0, B, 2, 1, 1 );
+// B => <Float64Array>[ 0.0, 11.0, 38.0, -5.0, -18.0, 2.0, 6.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dptts2()` corresponds to [LAPACK][LAPACK] routine [`dptts2`][dptts2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dptts2 = require( '@stdlib/lapack/base/dptts2' );
+
+var D = new Float64Array( [ 1.0, 1.0, 1.0 ] );
+var E = new Float64Array( [ 2.0, 3.0 ] );
+var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+
+dptts2.ndarray( 3, 2, D, 1, 0, E, 1, 0, B, 2, 1, 0 );
+console.log( B );
+```
+
+</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/
+
+[dptts2]: https://www.netlib.org/lapack/explore-html/d5/d5d/group__ptts2_ga35fdfa6109e8f9cbfbde271814bf0b27.html#ga35fdfa6109e8f9cbfbde271814bf0b27
+
+[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/dptts2/benchmark/benchmark.js

@@ -0,0 +1,107 @@
+/**
+* @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 floor = require( '@stdlib/math/base/special/floor' );
+var pkg = require( './../package.json' ).name;
+var dptts2 = require( './../lib/dptts2.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 B;
+	var D = uniform( len, -10.0, 10.0, options );
+	var E = uniform( len-1, -10.0, 10.0, options );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			B = uniform( len * len, -10.0, 10.0, options );
+			z = dptts2( 'row-major', len, len, D, E, B, len );
+			if ( isnan( z[ i%z.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z[ i%z.length ] ) ) {
+			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 = 5; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( len );
+		bench( pkg+':order=row-major:size='+(len*len), f );
+	}
+}
+
+main();