feat: add lapack/base/dlagtf

lib/node_modules/@stdlib/lapack/base/dlagtf/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.
+
+-->
+
+# dlagtf
+
+> Compute an `LU` factorization of a matrix `T - lambda*I`, where `T` is a general real tridiagonal matrix and `lambda` is a scalar, using partial pivoting with row interchanges.
+
+<section class="intro">
+
+The `dlagtf` routine factorizes the matrix `T - lambda*I`, where `T` is an N-by-N real tridiagonal matrix and `lambda` is a scalar, as:
+
+```math
+T - \lambda I = P L U
+```
+
+where `P` is a permutation matrix, `L` is a unit lower tridiagonal matrix with at most one non-zero sub-diagonal element per column, and `U` is an upper triangular matrix with at most two non-zero super-diagonal elements per column.
+
+The factorization is obtained by Gaussian elimination with partial pivoting and implicit row scaling.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlagtf = require( '@stdlib/lapack/base/dlagtf' );
+```
+
+#### dlagtf( N, A, lambda, B, C, tol, D, IN )
+
+Computes an `LU` factorization of a matrix `T - lambda*I`, where `T` is a general real tridiagonal matrix and `lambda` is a scalar, using partial pivoting with row interchanges.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var dlagtf = require( '@stdlib/lapack/base/dlagtf' );
+
+var A = new Float64Array( [ 2.0, 3.0, 1.0 ] );
+var B = new Float64Array( [ 1.0, 1.0 ] );
+var C = new Float64Array( [ 1.0, 1.0 ] );
+var D = new Float64Array( [ 0.0 ] );
+var IN = new Int32Array( [ 0, 0, 0 ] );
+
+dlagtf( 3, A, 0.0, B, C, 0.0, D, IN );
+// A => <Float64Array>[ 2.0, 2.5, 0.6 ]
+// B => <Float64Array>[ 1.0, 1.0 ]
+// C => <Float64Array>[ 0.5, 0.4 ]
+// D => <Float64Array>[ 0.0 ]
+// IN => <Int32Array>[ 0, 0, 0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: order of the matrix `T`.
+-   **A**: diagonal elements of `T` as a [`Float64Array`][mdn-float64array]. Should have `N` indexed elements. Overwritten by the diagonal elements of `U`.
+-   **lambda**: scalar constant.
+-   **B**: first super-diagonal elements of `T` as a [`Float64Array`][mdn-float64array]. Should have `N-1` indexed elements. Overwritten by the first super-diagonal elements of `U`.
+-   **C**: first sub-diagonal elements of `T` as a [`Float64Array`][mdn-float64array]. Should have `N-1` indexed elements. Overwritten by the multipliers that define `L`.
+-   **tol**: relative tolerance constant used to indicate whether `T - lambda*I` is nearly singular.
+-   **D**: second super-diagonal elements of `U` as a [`Float64Array`][mdn-float64array]. Should have `N-2` indexed elements. Overwritten by the second super-diagonal elements of `U`.
+-   **IN**: pivot indicators and singularity details as an [`Int32Array`][mdn-int32array]. Should have `N` indexed elements.
+
+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' );
+var dlagtf = require( '@stdlib/lapack/base/dlagtf' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 2.0, 3.0, 1.0 ] );
+var B0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var C0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var D0 = new Float64Array( [ 0.0, 0.0 ] );
+var IN0 = new Int32Array( [ 0, 0, 0, 0 ] );
+
+// Create offset views...
+var A = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var B = new Float64Array( B0.buffer, B0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var C = new Float64Array( C0.buffer, C0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var D = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var IN = new Int32Array( IN0.buffer, IN0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlagtf( 3, A, 0.0, B, C, 0.0, D, IN );
+// A0 => <Float64Array>[ 0.0, 2.0, 2.5, 0.6 ]
+// C0 => <Float64Array>[ 0.0, 0.5, 0.4 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dlagtf.ndarray( N, A, strideA, offsetA, lambda, B, strideB, offsetB, C, strideC, offsetC, tol, D, strideD, offsetD, IN, strideIN, offsetIN )
+
+Computes an `LU` factorization of a matrix `T - lambda*I`, where `T` is a general real tridiagonal matrix and `lambda` is a scalar, using partial pivoting with row interchanges and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var dlagtf = require( '@stdlib/lapack/base/dlagtf' );
+
+var A = new Float64Array( [ 2.0, 3.0, 1.0 ] );
+var B = new Float64Array( [ 1.0, 1.0 ] );
+var C = new Float64Array( [ 1.0, 1.0 ] );
+var D = new Float64Array( [ 0.0 ] );
+var IN = new Int32Array( [ 0, 0, 0 ] );
+
+dlagtf.ndarray( 3, A, 1, 0, 0.0, B, 1, 0, C, 1, 0, 0.0, D, 1, 0, IN, 1, 0 );
+// A => <Float64Array>[ 2.0, 2.5, 0.6 ]
+// B => <Float64Array>[ 1.0, 1.0 ]
+// C => <Float64Array>[ 0.5, 0.4 ]
+// D => <Float64Array>[ 0.0 ]
+// IN => <Int32Array>[ 0, 0, 0 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideA**: stride length for `A`.
+-   **offsetA**: starting index for `A`.
+-   **strideB**: stride length for `B`.
+-   **offsetB**: starting index for `B`.
+-   **strideC**: stride length for `C`.
+-   **offsetC**: starting index for `C`.
+-   **strideD**: stride length for `D`.
+-   **offsetD**: starting index for `D`.
+-   **strideIN**: stride length for `IN`.
+-   **offsetIN**: starting index for `IN`.
+
+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 dlagtf = require( '@stdlib/lapack/base/dlagtf' );
+
+var A = new Float64Array( [ 0.0, 2.0, 3.0, 1.0 ] );
+var B = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var C = new Float64Array( [ 0.0, 1.0, 1.0 ] );
+var D = new Float64Array( [ 0.0, 0.0 ] );
+var IN = new Int32Array( [ 0, 0, 0, 0 ] );
+
+dlagtf.ndarray( 3, A, 1, 1, 0.0, B, 1, 1, C, 1, 1, 0.0, D, 1, 1, IN, 1, 1 );
+// A => <Float64Array>[ 0.0, 2.0, 2.5, 0.6 ]
+// C => <Float64Array>[ 0.0, 0.5, 0.4 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input arrays `A`, `B`, `C`, `D`, and `IN`.
+-   `dlagtf()` corresponds to the [LAPACK][lapack] routine [`dlagtf`][lapack-dlagtf].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dlagtf = require( '@stdlib/lapack/base/dlagtf' );
+
+var N = 5;
+
+var A = new Float64Array( [ 2.0, 3.0, 1.0, 2.0, 1.0 ] );
+var B = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] );
+var C = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] );
+var D = new Float64Array( N-2 );
+var IN = new Int32Array( N );
+
+var info = dlagtf( N, A, 0.0, B, C, 0.0, D, IN );
+
+console.log( A );
+console.log( B );
+console.log( C );
+console.log( D );
+console.log( IN );
+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-dlagtf]: https://netlib.org/lapack/explore-html/d1/d90/group__lagtf_ga10cc4eb3c789fad38b52a86698d5a24a.html#ga10cc4eb3c789fad38b52a86698d5a24a
+
+[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 -->