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:

StartBinomialOrMatrix x Subscript i Baseline Choose y Subscript i Baseline EndBinomialOrMatrix equals Start 2 By 2 Matrix 1st Row 1st Column c 2nd Column s 2nd Row 1st Column negative s 2nd Column c EndMatrix StartBinomialOrMatrix x Subscript i Baseline Choose y Subscript i EndBinomialOrMatrix

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

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 );

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* second 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 );

c_drot_ndarray( N, *X, strideX, offsetX, *Y, strideY, offsetY, c, s )

Applies a plane rotation using alternative indexing semantics.

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_ndarray( 5, x, 1, 0, y, 1, 0, 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.
  • offsetX: [in] CBLAS_INT starting index for X.
  • Y: [inout] double* second input array.
  • strideY: [in] CBLAS_INT index increment for Y.
  • offsetY: [in] CBLAS_INT starting index for Y.
  • c: [in] double cosine of the angle of rotation.
  • s: [in] double sine of the angle of rotation.
void c_drot_ndarray( const CBLAS_INT N, double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, 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 = 3;

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // 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 ] );
    }

    // Apply plane rotation:
    c_drot_ndarray( N, x, strideX, 0, y, strideY, 4, 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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