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drotm

Apply a modified Givens plane rotation.

Installation

npm install @stdlib/blas-base-drotm

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

var drotm = require( '@stdlib/blas-base-drotm' );

drotm( N, x, strideX, y, strideY, param )

Applies a modified Givens plane rotation.

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );

drotm( 2, x, 2, y, 1, param );
// x => <Float64Array>[ ~-17.0, 2.0, ~-18.0, 4.0, 5.0 ]
// y => <Float64Array>[ ~8.0, ~13.0, 8.0, 9.0, 10.0 ]

The function has the following parameters:

• N: number of indexed elements.
• x: first input Float64Array.
• strideX: index increment for x.
• y: second input Float64Array.
• strideY: index increment for y.
• param: parameters for the modified Givens transformation

The N and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a modified Givens plane rotation to every other element,

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );

drotm( 3, x, 2, y, 2, param );
// x => <Float64Array>[ ~-20.0, 2.0, ~-24.0, 4.0, ~-28.0, 6.0 ]
// y => <Float64Array>[ ~9.0, 8.0, ~15.0, 10.0, ~21.0, 12.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y0 = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
var param = new Float64Array( [ 1.0, 0.0, 2.0, 3.0, 0.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

drotm( 2, x1, 1, y1, 1, param );
// x0 => <Float64Array>[ 1.0, ~9.0, ~10.0, 4.0, 5.0 ]
// y0 => <Float64Array>[ 6.0, 7.0, 8.0, ~-2.0, ~-3.0 ]

drotm.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, param )

Applies a modified Givens plane rotation using alternative indexing semantics.

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float64Array( [ 6.0, 7.0, 8.0, 9.0, 10.0 ] );
var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );

drotm.ndarray( 2, x, 1, 0, y, 2, 1, param );
// x => <Float64Array>[ ~-20.0, ~-25.0, 3.0, 4.0, 5.0 ]
// y => <Float64Array>[ 6.0, ~9.0, 8.0, ~13.0, 10.0 ]

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

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, to apply a modified Givens plane rotation to every other element starting from the second element,

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
var param = new Float64Array( [ 0.0, 0.0, 2.0, -3.0, 0.0 ] );

drotm.ndarray( 3, x, 2, 1, y, 2, 1, param );
// x => <Float64Array>[ 1.0, ~-22.0, 3.0, ~-26.0, 5.0, ~-30.0 ]
// y => <Float64Array>[ 7.0, ~12.0, 9.0, ~18.0, 11.0, ~24.0 ]

Notes

• If N <= 0, both functions leave x and y unchanged.
• drotm() corresponds to the BLAS level 1 function drotm.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var drotm = require( '@stdlib/blas-base-drotm' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 500, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 255, opts );
console.log( y );

var param = discreteUniform( 5, -5, 5, opts );
console.log( param );

// Apply a plane rotation:
drotm( x.length, x, 1, y, 1, param );
console.log( x );
console.log( y );

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C APIs

Usage

#include "stdlib/blas/base/drotm.h"

c_drotm( N, *X, strideX, *Y, strideY, param )

Applies a modified Givens plane rotation.

double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };
const double param[5] = { 0.0, 0.0, 2.0, -3.0, 0.0 };

c_drotm( 5, x, 1, y, 1, param );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [inout] double* first input array.
• strideX: [in] CBLAS_INT index increment for X.
• Y: [inout] double* second input array.
• strideY: [in] CBLAS_INT index increment for Y.
• param: [in] double parameters for the modified Givens transformation.

void c_drotm( const CBLAS_INT N, double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY, const double *param );

Examples

#include "stdlib/blas/base/drotm.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
    double y[] = { 6.0, 7.0, 8.0, 9.0, 10.0 };

    // Specify the number of elements:
    const int N = 5;

    // Specify stride lengths:
    const int strideX = 1;
    const int strideY = 1;

    // Specify parameters for the modified Givens transformation:
    const double param[5] = { 0.0, 0.0, 2.0, -3.0, 0.0 };

    // Apply plane rotation:
    c_drotm( N, x, strideX, y, strideY, param );

    // Print the result:
    for ( int i = 0; i < 5; i++ ) {
        printf( "x[ %i ] = %lf, y[ %i ] = %lf\n", i, x[ i ], i, y[ i ] );
    }
}

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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.