feat: add lapack/base/dlaswp

PR-URL: #2483
Ref: #2464
Co-authored-by: Athan Reines <[email protected]>
Reviewed-by: Athan Reines <[email protected]> 
Signed-off-by: Pranav Goswami <[email protected]>

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

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+<!--
+
+@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.
+
+-->
+
+# dlaswp
+
+> Perform a series of row interchanges on an input matrix.
+
+<section class = "usage">
+
+## Usage
+
+```javascript
+var dlaswp = require( '@stdlib/lapack/base/dlaswp' );
+```
+
+#### dlaswp( N, A, LDA, k1, k2, IPIV, incx )
+
+Perform a series of row interchanges on an input matrix `A` using pivot indices stored in `IPIV`.
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
+var IPIV = new Int32Array( [ 2, 0, 1 ] );
+
+dlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 1 );
+// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **N**: number of columns in `A`.
+-   **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **k1**: index of first row to interchange when `incx` is positive and the index of the last row to interchange when `incx` is negative.
+-   **k2**: index of last row to interchange when `incx` is positive and the index of the first row to interchange when `incx` is negative.
+-   **IPIV**: vector of pivot indices as an [`Int32Array`][mdn-int32array]. Must contain at least `k1+(k2-k1)*abs(incx)` elements. Only the elements in positions `k1` through `k1+(k2-k1)*abs(incx)` are accessed.
+-   **incx**: increment between successive values of `IPIV`. Elements from `IPIV` are accessed according to `IPIV[k1+(k-k1)*abs(incx)] = j`, thus implying that rows `k` and `j` should be interchanged. If `incx` is negative, the pivots are applied in reverse order.
+
+The sign of the increment parameter `incx` determines the order in which pivots are applied. For example, to apply pivots in reverse order,
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
+var IPIV = new Int32Array( [ 2, 0, 1 ] );
+
+dlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, -1 );
+// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
+```
+
+To perform strided access over `IPIV`, provide an `abs(incx)` value greater than one. For example, to access every other element in `IPIV`,
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
+var IPIV = new Int32Array( [ 2, 999, 0, 999, 1 ] );
+
+dlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 2 );
+// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
+```
+
+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 Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays...
+var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var IPIV0 = new Int32Array( [ 0, 2, 0, 1] );
+
+// Create offset views...
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 1st element
+var IPIV1 = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 1st element
+
+dlaswp( 'row-major', 2, A1, 2, 0, 2, IPIV1, 1 );
+// A0 => <Float64Array>[ 0.0, 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
+```
+
+#### dlaswp.ndarray( order, N, A, sa1, sa2, oa, k1, k2, inck, IPIV, si, oi )
+
+Performs a series of row interchanges on the matrix `A` using pivot indices stored in `IPIV` and alternative indexing semantics.
+
+```javascript
+var Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); // => [ [ 1.0, 2.0 ], [ 3.0, 4.0 ], [ 5.0, 6.0 ] ]
+var IPIV = new Int32Array( [ 2, 0, 1 ] );
+
+dlaswp.ndarray( 'row-major', 2, A, 2, 1, 0, 0, 2, 1, IPIV, 1, 0 );
+// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **order**: storage layout.
+-   **N**: number of columns in `A`.
+-   **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: starting index for `A`.
+-   **k1**: index of first row to interchange when `inck` is positive and the index of the last row to interchange when `inck` is negative.
+-   **k2**: index of last row to interchange when `inck` is positive and the index of the first row to interchange when `inck` is negative.
+-   **inck**: direction in which to apply pivots (-1 to apply pivots in reverse order; otherwise, apply in provided order).
+-   **IPIV**: vector of pivot indices as an [`Int32Array`][mdn-int32array].
+-   **si**: index increment 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 Int32Array = require( '@stdlib/array/int32' );
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var IPIV = new Int32Array( [ 0, 0, 2, 0, 1 ] );
+
+dlaswp.ndarray( 'row-major', 2, A, 2, 1, 4, 0, 2, 1, IPIV, 1, 2 );
+// A => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions access `k2-k1+1` elements from `IPIV`.
+-   While `dlaswp` conflates the order in which pivots are applied with the order in which elements in `IPIV` are accessed, the `ndarray` method delineates control of those behaviors with separate parameters `inck` and `si`.
+-   `dlaswp()` corresponds to the [LAPACK][LAPACK] level 1 function [`dlaswp`][dlaswp].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var dlaswp = require( '@stdlib/lapack/base/dlaswp' );
+
+// Specify matrix meta data:
+var shape = [ 4, 2 ];
+var strides = [ 1, 4 ];
+var offset = 0;
+var order = 'column-major';
+
+// Create a matrix stored in linear memory:
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
+console.log( ndarray2array( A, shape, strides, offset, order ) );
+
+// Define a vector of pivot indices:
+var IPIV = new Int32Array( [ 2, 0, 3, 1 ] );
+
+// Interchange rows:
+dlaswp( order, shape[ 1 ], A, strides[ 1 ], 0, shape[ 0 ]-1, IPIV, 1 );
+console.log( ndarray2array( A, shape, strides, offset, 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/
+
+[dlaswp]: https://www.netlib.org/lapack/explore-html/d7/d6b/dlaswp_8f_source.html
+
+[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 -->