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drot

Apply a plane rotation.

This BLAS level 1 routine applies a real plane rotation to real double-precision floating-point vectors. The plane rotation is applied to N points, where the points to be rotated are contained in vectors x and y and where the cosine and sine of the angle of rotation are c and s, respectively. The operation is as follows:

where x_i and y_i are the individual elements on which the rotation is applied.

Installation

npm install @stdlib/blas-base-drot

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

drot( N, x, strideX, y, strideY, c, s )

Applies a 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 ] );

drot( x.length, x, 1, y, 1, 0.8, 0.6 );
// x => <Float64Array>[ ~4.4, ~5.8, 7.2, 8.6, 10.0 ]
// y => <Float64Array>[ ~4.2, 4.4, 4.6, 4.8, 5.0 ]

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.
• c: cosine of the angle of rotation.
• s: sine of the angle of rotation.

The N and stride parameters determine how values in the strided arrays are accessed at runtime. For example, to apply a 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 ] );

drot( 3, x, 2, y, 2, 0.8, 0.6 );
// x => <Float64Array>[ 5.0, 2.0, 7.8, 4.0, 10.6, 6.0 ]
// y => <Float64Array>[ ~5.0, 8.0, 5.4, 10.0, ~5.8, 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, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// 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

drot( 3, x1, -2, y1, 1, 0.8, 0.6 );
// x0 => <Float64Array>[ 1.0, ~8.8, 3.0, 9.8, 5.0, 10.8 ]
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 4.4, 6.4, ~8.4 ]

drot.ndarray( N, x, strideX, offsetX, y, strideY, offsetY, c, s )

Applies a 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 ] );

drot.ndarray( 4, x, 1, 1, y, 1, 1, 0.8, 0.6 );
// x => <Float64Array>[ 1.0, ~5.8, 7.2, 8.6, 10.0 ]
// y => <Float64Array>[ 6.0, 4.4, ~4.6, ~4.8, 5.0 ]

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 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 ] );

drot.ndarray( 3, x, 2, 1, y, 2, 1, 0.8, 0.6 );
// x => <Float64Array>[ 1.0, 6.4, 3.0, 9.2, 5.0, 12.0 ]
// y => <Float64Array>[ 7.0, 5.2, 9.0, 5.6, 11.0, ~6.0 ]

Notes

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

Examples

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

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 );

// Apply a plane rotation:
drot( x.length, x, 1, y, 1, 0.8, 0.6 );
console.log( x );
console.log( y );

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C APIs

Usage

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

c_drot( N, *X, strideX, *Y, strideY, c, s )

Applies a 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 };

c_drot( 5, x, 1, y, 1, 0.8, 0.6 );

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* first input array.
• strideY: [in] CBLAS_INT index increment for Y.
• c: [in] double cosine of the angle of rotation.
• s: [in] double sine of the angle of rotation.

void c_drot( const CBLAS_INT N, double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY, const double c, const double s );

Examples

#include "stdlib/blas/base/drot.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 angle of rotation:
    const double c = 0.8;
    const double s = 0.6;

    // Apply plane rotation:
    c_drot( N, x, strideX, y, strideY, c, s );

    // 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.