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

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dlaswp
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> Perform a series of row interchanges on an input matrix.
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<section class = "usage">
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## Usage
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```javascript
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var dlaswp = require( '@stdlib/lapack/base/dlaswp' );
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```
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#### dlaswp( N, A, LDA, k1, k2, IPIV, incx )
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Perform a series of row interchanges on an input matrix `A` using pivot indices stored in `IPIV`.
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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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 ] ]
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var IPIV = new Int32Array( [ 2, 0, 1 ] );
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dlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 1 );
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// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **N**: number of columns in `A`.
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- **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
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- **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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- **k1**: index of first row to interchange when `incx` is positive and the index of the last row to interchange when `incx` is negative.
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- **k2**: index of last row to interchange when `incx` is positive and the index of the first row to interchange when `incx` is negative.
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- **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.
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- **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.
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The sign of the increment parameter `incx` determines the order in which pivots are applied. For example, to apply pivots in reverse order,
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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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 ] ]
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var IPIV = new Int32Array( [ 2, 0, 1 ] );
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dlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, -1 );
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// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
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```
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To perform strided access over `IPIV`, provide an `abs(incx)` value greater than one. For example, to access every other element in `IPIV`,
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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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 ] ]
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var IPIV = new Int32Array( [ 2, 999, 0, 999, 1 ] );
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dlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 2 );
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// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial arrays...
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var A0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var IPIV0 = new Int32Array( [ 0, 2, 0, 1] );
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// Create offset views...
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var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 1st element
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var IPIV1 = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 1st element
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dlaswp( 'row-major', 2, A1, 2, 0, 2, IPIV1, 1 );
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// A0 => <Float64Array>[ 0.0, 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
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```
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#### dlaswp.ndarray( order, N, A, sa1, sa2, oa, k1, k2, inck, IPIV, si, oi )
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Performs a series of row interchanges on the matrix `A` using pivot indices stored in `IPIV` and alternative indexing semantics.
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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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 ] ]
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var IPIV = new Int32Array( [ 2, 0, 1 ] );
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dlaswp.ndarray( 'row-major', 2, A, 2, 1, 0, 0, 2, 1, IPIV, 1, 0 );
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// A => <Float64Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
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```
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The function has the following additional parameters:
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- **order**: storage layout.
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- **N**: number of columns in `A`.
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- **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
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- **sa1**: stride of the first dimension of `A`.
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- **sa2**: stride of the second dimension of `A`.
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- **oa**: starting index for `A`.
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- **k1**: index of first row to interchange when `inck` is positive and the index of the last row to interchange when `inck` is negative.
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- **k2**: index of last row to interchange when `inck` is positive and the index of the first row to interchange when `inck` is negative.
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- **inck**: direction in which to apply pivots (-1 to apply pivots in reverse order; otherwise, apply in provided order).
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- **IPIV**: vector of pivot indices as an [`Int32Array`][mdn-int32array].
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- **si**: index increment for `IPIV`.
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- **oi**: starting index for `IPIV`.
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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,
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<!-- eslint-disable max-len -->
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```javascript
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var Int32Array = require( '@stdlib/array/int32' );
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
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var IPIV = new Int32Array( [ 0, 0, 2, 0, 1 ] );
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dlaswp.ndarray( 'row-major', 2, A, 2, 1, 4, 0, 2, 1, IPIV, 1, 2 );
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// A => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Both functions access `k2-k1+1` elements from `IPIV`.
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- 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`.
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- `dlaswp()` corresponds to the [LAPACK][LAPACK] level 1 function [`dlaswp`][dlaswp].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var Int32Array = require( '@stdlib/array/int32' );
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var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
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var dlaswp = require( '@stdlib/lapack/base/dlaswp' );
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// Specify matrix meta data:
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var shape = [ 4, 2 ];
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var strides = [ 1, 4 ];
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var offset = 0;
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var order = 'column-major';
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// Create a matrix stored in linear memory:
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var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
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console.log( ndarray2array( A, shape, strides, offset, order ) );
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// Define a vector of pivot indices:
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var IPIV = new Int32Array( [ 2, 0, 3, 1 ] );
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// Interchange rows:
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dlaswp( order, shape[ 1 ], A, strides[ 1 ], 0, shape[ 0 ]-1, IPIV, 1 );
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console.log( ndarray2array( A, shape, strides, offset, order ) );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[lapack]: https://www.netlib.org/lapack/explore-html/
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[dlaswp]: https://www.netlib.org/lapack/explore-html/d7/d6b/dlaswp_8f_source.html
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-int32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Int32Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

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