stdlib-js · iampratik13 · Jul 27, 2026
diff --git a/lib/node_modules/@stdlib/lapack/base/dptts2/README.md b/lib/node_modules/@stdlib/lapack/base/dptts2/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.
+
+-->
+
+# dptts2
+
+> Solve a tridiagonal system of the form `A * X = B` using the `L * D * L^T` factorization of `A` computed by [`dpttrf`][@stdlib/lapack/base/dpttrf].
+
+<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 the `L * D * L^T` factorization of `A` computed by [`dpttrf`][@stdlib/lapack/base/dpttrf].
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 4.0, 4.75, 5.157894736842105 ] );
+var E = new Float64Array( [ 0.25, 0.42105263157894735 ] );
+var B = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dptts2( 'column-major', 3, 1, D, E, B, 3 );
+// B => <Float64Array>[ ~0.204, ~0.184, ~0.439 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout of `B`.
+-   **N**: order of the tridiagonal matrix `A`.
+-   **nrhs**: number of right-hand sides (i.e., the number of columns of the matrix `B`).
+-   **D**: the `N` diagonal elements of the diagonal matrix `D` from the `L * D * L^T` factorization of `A` as a [`Float64Array`][mdn-float64array].
+-   **E**: the `N-1` subdiagonal elements of the unit bidiagonal factor `L` from the `L * D * L^T` factorization of `A` as a [`Float64Array`][mdn-float64array].
+-   **B**: input matrix as a [`Float64Array`][mdn-float64array]. On entry, the right-hand side vectors `B`. On exit, the solution vectors `X`.
+-   **LDB**: leading dimension of `B`.
+
+The input matrix `D` and `E` are typically computed by [`dpttrf`][@stdlib/lapack/base/dpttrf].
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dpttrf = require( '@stdlib/lapack/base/dpttrf' );
+
+var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
+var E = new Float64Array( [ 1.0, 2.0 ] );
+
+dpttrf( 3, D, E );
+
+var B = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dptts2( 'column-major', 3, 1, D, E, B, 3 );
+// B => <Float64Array>[ ~0.204, ~0.184, ~0.439 ]
+```
+
+#### 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 the `L * D * L^T` factorization of `A` computed by [`dpttrf`][@stdlib/lapack/base/dpttrf] and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 4.0, 4.75, 5.157894736842105 ] );
+var E = new Float64Array( [ 0.25, 0.42105263157894735 ] );
+var B = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+dptts2.ndarray( 3, 1, D, 1, 0, E, 1, 0, B, 1, 3, 0 );
+// B => <Float64Array>[ ~0.204, ~0.184, ~0.439 ]
+```
+
+The function has the following parameters:
+
+-   **sd**: stride length for `D`.
+-   **od**: starting index for `D`.
+-   **se**: stride length for `E`.
+-   **oe**: starting index for `E`.
+-   **sb1**: stride of the first dimension of `B`.
+-   **sb2**: stride of the 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.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var D = new Float64Array( [ 0.0, 4.0, 4.75, 5.157894736842105 ] );
+var E = new Float64Array( [ 0.0, 0.25, 0.42105263157894735 ] );
+var B = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
+
+dptts2.ndarray( 3, 1, D, 1, 1, E, 1, 1, B, 1, 3, 1 );
+// B => <Float64Array>[ 0.0, ~0.204, ~0.184, ~0.439 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dptts2()` corresponds to the [LAPACK][LAPACK] routine [`dptts2`][lapack-dptts2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var dpttrf = require( '@stdlib/lapack/base/dpttrf' );
+var dptts2 = require( '@stdlib/lapack/base/dptts2' );
+
+// Define a symmetric positive definite matrix `A` via its diagonal and subdiagonal:
+var D = new Float64Array( [ 4.0, 5.0, 6.0, 7.0 ] );
+var E = new Float64Array( [ 1.0, 2.0, 3.0 ] );
+
+// Compute the `L * D * L^T` factorization of `A` (overwrites `D` and `E`):
+dpttrf( D.length, D, E );
+
+// Define the right-hand side matrix `B` (column-major, two right-hand sides):
+var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 2.0, 1.0, 0.0, 1.0 ] );
+
+// Solve `A * X = B`, overwriting `B` with the solution `X`:
+dptts2( 'column-major', 4, 2, D, E, B, 4 );
+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/
+
+[lapack-dptts2]: https://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
+
+[@stdlib/lapack/base/dpttrf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/lapack/base/dpttrf
+
+</section>
+
+<!-- /.links -->
diff --git a/lib/node_modules/@stdlib/lapack/base/dptts2/benchmark/benchmark.js b/lib/node_modules/@stdlib/lapack/base/dptts2/benchmark/benchmark.js
@@ -0,0 +1,105 @@
+/**
+* @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 dptts2 = require( './../lib/dptts2.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var D = uniform( N, 1.0, 5.0, options );
+	var E = uniform( N-1, 0.0, 1.0, options );
+	var B = uniform( N, -1.0, 1.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var out;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			out = dptts2( 'column-major', N, 1, D, E, B, N );
+			if ( isnan( out[ 0 ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( out[ 0 ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		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 = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = pow( 10, i );
+		f = createBenchmark( N );
+		bench( format( '%s:size=%d', pkg, N ), f );
+	}
+}
+
+main();