npm package: @stdlib/lapack-base-zlaswp
Description: Perform a series of row interchanges on an input matrix.
Author: The Stdlib Authors
Latest version: 0.1.1

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# zlaswp

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> Perform a series of row interchanges on an input matrix.

<section class="installation">

## Installation

```bash
npm install @stdlib/lapack-base-zlaswp
```

</section>

<section class="usage">

## Usage

```javascript
var zlaswp = require( '@stdlib/lapack-base-zlaswp' );
```

#### zlaswp( N, A, LDA, k1, k2, IPIV, incx )

Performs a series of row interchanges on an input matrix `A` using pivot indices stored in `IPIV`.

<!-- eslint-disable max-len -->

```javascript
var Int32Array = require( '@stdlib/array-int32' );
var Complex128Array = require( '@stdlib/array-complex128' );

var A = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var IPIV = new Int32Array( [ 2, 0, 1 ] );

zlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 1 );
// A => <Complex128Array>[ 5.0, 6.0, 7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 9.0, 10.0, 11.0, 12.0 ]
```

The function has the following parameters:

-   **order**: storage layout.
-   **N**: number of columns in `A`.
-   **A**: input matrix stored in linear memory as a [`Complex128Array`][@stdlib/array/complex128].
-   **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`][@stdlib/array/int32]. 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,

<!-- eslint-disable max-len -->

```javascript
var Int32Array = require( '@stdlib/array-int32' );
var Complex128Array = require( '@stdlib/array-complex128' );

var A = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var IPIV = new Int32Array( [ 2, 0, 1 ] );

zlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, -1 );
// A => <Complex128Array>[ 5.0, 6.0, 7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 9.0, 10.0, 11.0, 12.0 ]
```

To perform strided access over `IPIV`, provide an `abs(incx)` value greater than one. For example, to access every other element in `IPIV`,

<!-- eslint-disable max-len -->

```javascript
var Int32Array = require( '@stdlib/array-int32' );
var Complex128Array = require( '@stdlib/array-complex128' );

var A = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var IPIV = new Int32Array( [ 2, 999, 0, 999, 1 ] );

zlaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 2 );
// A => <Complex128Array>[ 5.0, 6.0, 7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 9.0, 10.0, 11.0, 12.0 ]
```

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, max-len -->

```javascript
var Int32Array = require( '@stdlib/array-int32' );
var Complex128Array = require( '@stdlib/array-complex128' );

// Initial arrays...
var A0 = new Complex128Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var IPIV0 = new Int32Array( [ 0, 2, 0, 1 ] );

// Create offset views...
var A1 = new Complex128Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var IPIV1 = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

zlaswp( 'row-major', 2, A1, 2, 0, 2, IPIV1, 1 );
// A0 => <Complex128Array>[ 0.0, 0.0, 5.0, 6.0, 7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 9.0, 10.0, 11.0, 12.0 ]
```

#### zlaswp.ndarray( 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.

<!-- eslint-disable max-len -->

```javascript
var Int32Array = require( '@stdlib/array-int32' );
var Complex128Array = require( '@stdlib/array-complex128' );

var A = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var IPIV = new Int32Array( [ 2, 0, 1 ] );

zlaswp.ndarray( 2, A, 2, 1, 0, 0, 2, 1, IPIV, 1, 0 );
// A => <Complex128Array>[ 5.0, 6.0, 7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 9.0, 10.0, 11.0, 12.0 ]
```

The function has the following additional parameters:

-   **N**: number of columns in `A`.
-   **A**: input matrix stored in linear memory as a [`Complex128Array`][@stdlib/array/complex128].
-   **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`][@stdlib/array/int32].
-   **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 Complex128Array = require( '@stdlib/array-complex128' );

var A = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var IPIV = new Int32Array( [ 0, 0, 2, 0, 1 ] );

zlaswp.ndarray( 2, A, 2, 1, 2, 0, 2, 1, IPIV, 1, 2 );
// A => <Complex128Array>[ 0.0, 0.0, 0.0, 0.0, 5.0, 6.0, 7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 9.0, 10.0, 11.0, 12.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Both functions access `k2-k1+1` elements from `IPIV`.
-   While `zlaswp` 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`.
-   `zlaswp()` corresponds to the [LAPACK][LAPACK] function [`zlaswp`][lapack-zlaswp].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint-disable max-len -->

<!-- eslint no-undef: "error" -->

```javascript
var Complex128Array = require( '@stdlib/array-complex128' );
var Int32Array = require( '@stdlib/array-int32' );
var ndarray2array = require( '@stdlib/ndarray-base-to-array' );
var zlaswp = require( '@stdlib/lapack-base-zlaswp' );

// 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 Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0 ] );
console.log( ndarray2array( A, shape, strides, offset, order ) );

// Define a vector of pivot indices:
var IPIV = new Int32Array( [ 2, 0, 3, 1 ] );

// Interchange rows:
zlaswp( 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 -->

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<section class="main-repo" >

* * *

## Notice

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For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/lapack-base-zlaswp/main/LICENSE

[lapack]: https://www.netlib.org/lapack/explore-html/

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