feat: add lapack/base/dgttrf

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# dgttrf
+
+> Compute an `LU` factorization of a real tri diagonal matrix `A` using elimination with partial pivoting and row interchanges.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dgttrf = require( '@stdlib/lapack/base/dgttrf' );
+```
+
+#### dgttrf( N, DL, D, DU, DU2, IPIV )
+
+Computes an `LU` factorization of a real tri diagonal matrix `A` using elimination with partial pivoting and row interchanges.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var DL = new Float64Array( [ 1.0, 1.0 ] );
+var D = new Float64Array( [ 2.0, 3.0, 1.0 ] );
+var DU = new Float64Array( [ 1.0, 1.0 ] );
+var DU2 = new Float64Array( 1 );
+var IPIV = new Int32Array( 3 );
+
+dgttrf( 3, DL, D, DU, DU2, IPIV );
+// DL => <Float64Array>[ 0.5, 0.4 ]
+// D => <Float64Array>[ 2, 2.5, 0.6 ]
+// DU => <Float64Array>[ 1, 1 ]
+// DU2 => <Float64Array>[ 0 ]
+// IPIV => <Int32Array>[ 0, 1, 2 ]
+```
+
+The function has the following parameters:
+
+-   **N**: order of matrix `A`.
+-   **DL**: the sub diagonal elements of `A` as a [`Float64Array`][mdn-float64array]. On exit, DL is overwritten by the multipliers that define the matrix `L` from the `LU` factorization of `A`.
+-   **D**: the diagonal elements of `A` as a [`Float64Array`][mdn-float64array]. On exit, D is overwritten by the diagonal elements of the upper triangular matrix `U` from the `LU` factorization of `A`.
+-   **DU**: the super diagonal elements of `A` as a [`Float64Array`][mdn-float64array]. On exit, DU is overwritten by the elements of the first super-diagonal of `U`.
+-   **DU2**: On exit, DU2 is overwritten by the elements of the second super-diagonal of `U` as a [`Float64Array`][mdn-float64array].
+-   **IPIV**: vector of pivot indices as a [`Int32Array`][mdn-int32array].
+
+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, 1.0, 1.0 ] );
+var D0 = new Float64Array( [ 0.0, 2.0, 3.0, 1.0 ] );
+var DU0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var DU20 = new Float64Array( 2 );
+var IPIV0 = new Int32Array( 4 );
+
+// 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
+
+dgttrf( 3, DL, D, DU, DU2, IPIV );
+// DL0 => <Float64Array>[ 0, 0.5, 0.4 ]
+// D0 => <Float64Array>[ 0, 2, 2.5, 0.6 ]
+// DU0 => <Float64Array>[ 0, 1, 1 ]
+// DU20 => <Float64Array>[ 0, 0 ]
+// IPIV0 => <Int32Array>[ 0, 0, 1, 2 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dgttrf.ndarray( N, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi )
+
+Computes an `LU` factorization of a real tri diagonal matrix `A` using elimination with partial pivoting and row interchanges and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var dgttrf = require( '@stdlib/lapack/base/dgttrf' );
+
+var DL = new Float64Array( [ 1.0, 1.0 ] );
+var D = new Float64Array( [ 2.0, 3.0, 1.0 ] );
+var DU = new Float64Array( [ 1.0, 1.0 ] );
+var DU2 = new Float64Array( 1 );
+var IPIV = new Int32Array( 3 );
+
+dgttrf.ndarray( 3, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0 );
+// DL => <Float64Array>[ 0.5, 0.4 ]
+// D => <Float64Array>[ 2, 2.5, 0.6 ]
+// DU => <Float64Array>[ 1, 1 ]
+// DU2 => <Float64Array>[ 0 ]
+// IPIV => <Int32Array>[ 0, 1, 2 ]
+```
+
+The function has the following additional parameters:
+
+-   **sdl**: stride length for `DL`.
+-   **odl**:  starting index for `DL`.
+-   **sd**: stride length for `D`.
+-   **od**:  starting index for `D`.
+-   **sdu**: stride length for `DU`.
+-   **odu**:  starting index for `DU`.
+-   **sdu2**: stride length for `DU2`.
+-   **odu2**:  starting index for `DU2`.
+-   **si**: stride length for `IPIV`.
+-   **oi**:  starting index for `IPIV`.
+
+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 Int32Array = require( '@stdlib/array/int32' );
+
+var DL = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var D = new Float64Array( [ 0.0, 2.0, 3.0, 1.0 ] );
+var DU = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var DU2 = new Float64Array( 2 );
+var IPIV = new Int32Array( 4 );
+
+dgttrf.ndarray( 3, DL, 1, 1, D, 1, 1, DU, 1, 1, DU2, 1, 1, IPIV, 1, 1 );
+// DL => <Float64Array>[ 0, 0.5, 0.4 ]
+// D => <Float64Array>[ 0, 2, 2.5, 0.6 ]
+// DU => <Float64Array>[ 0, 1, 1 ]
+// DU2 => <Float64Array>[ 0, 0 ]
+// IPIV => <Int32Array>[ 0, 0, 1, 2 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input arrays `DL`, `D`, `DU`, `DU2` and `IPIV`.
+
+-   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`: `U( k, k )` is exactly zero the factorization has been completed, but the factor `U` is exactly singular, and division by zero will occur if it is used to solve a system of equations, where `k` equals the status code value.
+
+-   `dgttrf()` corresponds to the [LAPACK][LAPACK] routine [`dgttrf`][lapack-dgttrf].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dgttrf = require( '@stdlib/lapack/base/dgttrf' );
+
+var N = 9;
+
+var DL = new Float64Array( [ 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0 ] );
+
+var D = new Float64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
+
+var DU = new Float64Array( [ 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0 ] );
+
+var DU2 = new Float64Array( N-2 );
+
+var IPIV = new Int32Array( N );
+
+// Perform the `A = LU` factorization:
+var info = dgttrf( N, DL, D, DU, DU2, IPIV );
+
+console.log( DL );
+console.log( D );
+console.log( DU );
+console.log( DU2 );
+console.log( IPIV );
+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-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 -->