@stdlib/lapack-base-dlaswp

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dlaswp

Perform a series of row interchanges on an input matrix.

Usage

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.

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.
• 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 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,

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 views.

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 2nd element
var IPIV1 = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 2nd 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( 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 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( 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:

• N: number of columns in A.
• A: input matrix stored in linear memory as a 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.
• 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 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( 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 ]

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 level 1 function dlaswp.

Examples

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 ) );

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C APIs

Installation

npm install @stdlib/lapack-base-dlaswp

Usage

TODO

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Examples

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Notice

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

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License

See LICENSE.

Copyright

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