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zdrot

README.md

zdrot

Apply a plane rotation.

Usage

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

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

Applies a plane rotation.

var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zdrot( x.length, x, 1, y, 1, 0.8, 0.6 );
// x => <Complex128Array>[ ~0.8, ~1.6, ~2.4, ~3.2, 4.0, ~4.8, ~5.6, ~6.4 ]
// y => <Complex128Array>[ ~-0.6, ~-1.2, ~-1.8, ~-2.4, -3.0, ~-3.6, ~-4.2, ~-4.8 ]

The function has the following parameters:

  • N: number of indexed elements.
  • x: first input Complex128Array.
  • strideX: index increment for x.
  • y: second input Complex128Array.
  • strideY: index increment for y.

The N and stride parameters determine how values from x and y are accessed at runtime. For example, to apply a plane rotation to every other element,

var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zdrot( 2, x, 2, y, 2, 0.8, 0.6 );
// x => <Complex128Array>[ ~0.8, ~1.6, 3.0, 4.0, 4.0, ~4.8, 7.0, 8.0 ]
// y => <Complex128Array>[ ~-0.6, ~-1.2, 0.0, 0.0, -3.0, ~-3.6, 0.0, 0.0 ]

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

var Complex128Array = require( '@stdlib/array/complex128' );

// Initial arrays...
var x0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y0 = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

zdrot( 2, x1, -2, y1, 1, 0.8, 0.6 );
// x0 => <Complex128Array>[ 1.0, 2.0, ~2.4, ~3.2, 5.0, 6.0, ~5.6, ~6.4 ]
// y0 => <Complex128Array>[ 0.0, 0.0, 0.0, 0.0, ~-4.2, ~-4.8, ~-1.8, ~-2.4 ]

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

Applies a plane rotation using alternative indexing semantics.

var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zdrot.ndarray( x.length, x, 1, 0, y, 1, 0, 0.8, 0.6 );
// x => <Complex128Array>[ ~0.8, ~1.6, ~2.4, ~3.2, 4.0, ~4.8 ]
// y => <Complex128Array>[ ~-0.6, ~-1.2, ~-1.8, ~-2.4, -3.0, ~-3.6 ]

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 Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

zdrot.ndarray( 2, x, 2, 1, y, 2, 1, 0.8, 0.6 );
// x => <Complex128Array>[ 1.0, 2.0, ~2.4, ~3.2, 5.0, 6.0, ~5.6, ~6.4 ]
// y => <Complex128Array>[ 0.0, 0.0, ~-1.8, ~-2.4, 0.0, 0.0, ~-4.2, ~-4.8 ]

Notes

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

Examples

var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
var zcopy = require( '@stdlib/blas/base/zcopy' );
var zeros = require( '@stdlib/array/zeros' );
var logEach = require( '@stdlib/console/log-each' );
var zdrot = require( '@stdlib/blas/base/zdrot' );

function rand() {
    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

// Generate random input arrays:
var x = filledarrayBy( 10, 'complex128', rand );
var xc = zcopy( x.length, x, 1, zeros( x.length, 'complex128' ), 1 );

var y = filledarrayBy( 10, 'complex128', rand );
var yc = zcopy( y.length, y, 1, zeros( y.length, 'complex128' ), 1 );

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

// Print the results:
logEach( '(%s,%s) => (%s,%s)', xc, yc, x, y );

C APIs

Usage

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

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

Applies a plane rotation.

double x[] = { 1.0, 2.0, 3.0, 4.0 }; // interleaved real and imaginary components
double y[] = { 5.0, 6.0, 7.0, 8.0 };

c_zdrot( 2, (void *)x, 1, (void *)y, 1, 0.8, 0.6 );

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [inout] void* first input array.
  • strideX: [in] CBLAS_INT index increment for X.
  • Y: [inout] void* 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_zdrot( const CBLAS_INT N, void *X, const CBLAS_INT strideX, void *Y, const CBLAS_INT strideY, const double c, const double s );

c_zdrot_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 }; // interleaved real and imaginary components
double y[] = { 5.0, 6.0, 7.0, 8.0 };

c_zdrot_ndarray( 2, (void *)x, 1, 0, (void *)y, 1, 0, 0.8, 0.6 );

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [inout] void* first input array.
  • strideX: [in] CBLAS_INT index increment for X.
  • offsetX: [in] CBLAS_INT starting index for X.
  • Y: [inout] void* 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_zdrot_ndarray( const CBLAS_INT N, void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, void *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, const double c, const double s );

Examples

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

int main( void ) {
    // Create strided arrays:
    double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
    double y[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

    // Specify the number of elements:
    const int N = 4;

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

    // Copy elements:
    c_zdrot( N, (void *)x, strideX, (void *)y, strideY, 0.8, 0.6 );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "x[ %i ] = %lf + %lfj\n", i, x[ i*2 ], x[ (i*2)+1 ] );
        printf( "y[ %i ] = %lf + %lfj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }
}