feat: add lapack/base/dgtts2

lib/node_modules/@stdlib/lapack/base/dgtts2/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.
+
+-->
+
+<!-- lint disable max-len -->
+
+# dgtts2
+
+> Solve a system of linear equations with a tridiagonal matrix using the LU factorization computed by [dgttrf][lapack-dgttrf].
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dgtts2 = require( '@stdlib/lapack/base/dgtts2' );
+```
+
+#### dgtts2( order, itrans, N, nrhs, DL, D, DU, DU2, IPIV, B, LDB )
+
+Solves a system of linear equations with a tri diagonal matrix using the LU factorization computed by [dgttrf][lapack-dgttrf].
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var DL = new Float64Array( [ 0.25, 0.26666667 ] );
+var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
+var DU = new Float64Array( [ 1.0, 0.73333333 ] );
+var DU2 = new Float64Array( [ 0.0 ] );
+var IPIV = new Int32Array( [ 0, 1, 2 ] );
+var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
+
+var out = dgtts2( 'column-major', 1, 3, 1, DL, D, DU, DU2, IPIV, B, 3 );
+// out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **itrans**: specifies the form of the system of equations.
+-   **N**: order of the matrix `A`.
+-   **nrhs**: number of right-hand sides, i.e., the number of columns of the matrix `B`.
+-   **DL**:  multipliers that define the matrix `L` as a [`Float64Array`][mdn-float64array].
+-   **D**: diagonal elements of the upper triangular matrix `U` as a [`Float64Array`][mdn-float64array].
+-   **DU**: elements of the first super-diagonal of `U` as a [`Float64Array`][mdn-float64array].
+-   **DU2**: elements of the second super-diagonal of `U` as a [`Float64Array`][mdn-float64array].
+-   **IPIV**: vector of pivot indices as an [`Int32Array`][mdn-int32array].
+-   **B**: right-hand side matrix B, overwritten by the solution matrix `X` 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' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+// Initial arrays...
+var DL0 = new Float64Array( [ 0.0, 0.25, 0.26666667 ] );
+var D0 = new Float64Array( [ 0.0, 4.0, 3.75, 3.73333333 ] );
+var DU0 = new Float64Array( [ 0.0, 1.0, 0.73333333 ] );
+var DU20 = new Float64Array( [ 0.0, 0.0 ] );
+var IPIV0 = new Int32Array( [ 0, 0, 1, 2 ] );
+var B0 = new Float64Array( [ 0.0, 7.0, 8.0, 7.0 ] );
+
+// Create offset views...
+var DL = new Float64Array( DL0.buffer, DL0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var D = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var DU = new Float64Array( DU0.buffer, DU0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var DU2 = new Float64Array( DU20.buffer, DU20.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var IPIV = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var B = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dgtts2( 'column-major', 1, 3, 1, DL, D, DU, DU2, IPIV, B, 3 );
+// B0 => <Float64Array>[ 0.0, ~1.44, ~1.25, ~1.55 ]
+```
+
+#### dgtts2.ndarray( itrans, N, nrhs, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi, B, sb1, sb2, ob )
+
+Solves a system of linear equations with a tri diagonal matrix using the LU factorization computed by [dgttrf][lapack-dgttrf] and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var DL = new Float64Array( [ 0.25, 0.26666667 ] );
+var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
+var DU = new Float64Array( [ 1.0, 0.73333333 ] );
+var DU2 = new Float64Array( [ 0.0 ] );
+var IPIV = new Int32Array( [ 0, 1, 2 ] );
+var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
+
+var out = dgtts2.ndarray( 1, 3, 1, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, 1, 1, 0 );
+// out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
+```
+
+The function has the following parameters:
+
+-   **itrans**: specifies the form of the system of equations.
+-   **N**: order of the matrix `A`.
+-   **nrhs**: number of right-hand sides, i.e., the number of columns of the matrix `B`.
+-   **DL**:  multipliers that define the matrix `L` as a [`Float64Array`][mdn-float64array].
+-   **sdl**: stride length for `DL`.
+-   **odl**: starting index for `DL`.
+-   **D**: diagonal elements of the upper triangular matrix `U` as a [`Float64Array`][mdn-float64array].
+-   **sd**: stride length for `D`.
+-   **od**: starting index for `D`.
+-   **DU**: elements of the first super-diagonal of `U` as a [`Float64Array`][mdn-float64array].
+-   **sdu**: stride length for `DU`.
+-   **odu**: starting index for `DU`.
+-   **DU2**: elements of the second super-diagonal of `U` as a [`Float64Array`][mdn-float64array].
+-   **sdu2**: stride length for `DU2`.
+-   **odu2**: starting index for `DU2`.
+-   **IPIV**: vector of pivot indices as an [`Int32Array`][mdn-int32array].
+-   **si**: stride length for `IPIV`.
+-   **oi**: starting index for `IPIV`.
+-   **B**: right-hand side matrix B, overwritten by the solution matrix `X` as a [`Float64Array`][mdn-float64array].
+-   **sb1**: stride length for first dimension of `B`.
+-   **sb2**: stride length for 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,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var DL = new Float64Array( [ 0.0, 0.25, 0.26666667 ] );
+var D = new Float64Array( [ 0.0, 4.0, 3.75, 3.73333333 ] );
+var DU = new Float64Array( [ 0.0, 1.0, 0.73333333 ] );
+var DU2 = new Float64Array( [ 0.0, 0.0 ] );
+var IPIV = new Int32Array( [ 0, 0, 1, 2 ] );
+var B = new Float64Array( [ 0.0, 7.0, 8.0, 7.0 ] );
+
+var out = dgtts2.ndarray( 1, 3, 1, DL, 1, 1, D, 1, 1, DU, 1, 1, DU2, 1, 1, IPIV, 1, 1, B, 1, 1, 1 );
+// out => <Float64Array>[ 0.0, ~1.44, ~1.25, ~1.55 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `dgtts2()` corresponds to the [LAPACK][lapack] routine [`dgtts2`][lapack-dgtts2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var dgtts2 = require( '@stdlib/lapack/base/dgtts2' );
+
+var shape = [ 3, 3 ];
+var order = 'row-major';
+var strides = shape2strides( shape, order );
+
+var B = new Float64Array( [ 7.0, 8.0, 7.0, 2.0, 3.0, 4.0, 1.0, 1.5, 2.0 ] );
+console.log( ndarray2array( B, shape, strides, 0, order ) );
+
+var DL = new Float64Array( [ 0.25, 0.26666667 ] );
+var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
+var DU = new Float64Array( [ 1.0, 0.73333333 ] );
+var DU2 = new Float64Array( [ 0.0 ] );
+var IPIV = new Int32Array( [ 0, 1, 2 ] );
+
+var X = dgtts2( 'row-major', 1, 3, 3, DL, D, DU, DU2, IPIV, B, 3 );
+console.log( ndarray2array( X, shape, strides, 0, order ) );
+```
+
+</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-dgtts2]: https://www.netlib.org/lapack/explore-html/d2/dea/group__gtts2_gae123fb2b13f2398457e4c47f5c7f7fcd.html#gae123fb2b13f2398457e4c47f5c7f7fcd
+
+[lapack-dgttrf]: https://www.netlib.org/lapack/explore-html/d6/d46/group__gttrf_ga8d1e46216e6c861c89bd4328b8be52a1.html#ga8d1e46216e6c861c89bd4328b8be52a1
+
+[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 -->
+