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slaswp

Perform a series of row interchanges on an input matrix.

Usage

var slaswp = require( '@stdlib/lapack-base-slaswp' );

slaswp( N, A, LDA, k1, k2, IPIV, incx )

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

var Int32Array = require( '@stdlib/array-int32' );
var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 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 ] );

slaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 1 );
// A => <Float32Array>[ 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 Float32Array.
• 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. 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,

var Int32Array = require( '@stdlib/array-int32' );
var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 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 ] );

slaswp( 'row-major', 2, A, 2, 0, 2, IPIV, -1 );
// A => <Float32Array>[ 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,

var Int32Array = require( '@stdlib/array-int32' );
var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 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 ] );

slaswp( 'row-major', 2, A, 2, 0, 2, IPIV, 2 );
// A => <Float32Array>[ 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 views.

var Int32Array = require( '@stdlib/array-int32' );
var Float32Array = require( '@stdlib/array-float32' );

// Initial arrays...
var A0 = new Float32Array( [ 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 Float32Array( 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

slaswp( 'row-major', 2, A1, 2, 0, 2, IPIV1, 1 );
// A0 => <Float32Array>[ 0.0, 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]

slaswp.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.

var Int32Array = require( '@stdlib/array-int32' );
var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 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 ] );

slaswp.ndarray( 2, A, 2, 1, 0, 0, 2, 1, IPIV, 1, 0 );
// A => <Float32Array>[ 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]

The function has the following additional parameters:

• N: number of columns in A.
• A: input matrix stored in linear memory as a Float32Array.
• 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.
• si: index increment for IPIV.
• oi: starting index for IPIV.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,

var Int32Array = require( '@stdlib/array-int32' );
var Float32Array = require( '@stdlib/array-float32' );

var A = new Float32Array( [ 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 ] );

slaswp.ndarray( 2, A, 2, 1, 4, 0, 2, 1, IPIV, 1, 2 );
// A => <Float32Array>[ 0.0, 0.0, 0.0, 0.0, 3.0, 4.0, 1.0, 2.0, 5.0, 6.0 ]

Notes

• Both functions access k2-k1+1 elements from IPIV.
• While slaswp 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.
• slaswp() corresponds to the LAPACK level 1 function slaswp.

Examples

var Float32Array = require( '@stdlib/array-float32' );
var Int32Array = require( '@stdlib/array-int32' );
var ndarray2array = require( '@stdlib/ndarray-base-to-array' );
var slaswp = require( '@stdlib/lapack-base-slaswp' );

// 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 Float32Array( [ 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:
slaswp( order, shape[ 1 ], A, strides[ 1 ], 0, shape[ 0 ]-1, IPIV, 1 );
console.log( ndarray2array( A, shape, strides, offset, order ) );

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C APIs

Installation

npm install @stdlib/lapack-base-slaswp

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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Examples

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

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

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.