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zdrot

Applies a plane rotation.

Installation

npm install @stdlib/blas-base-zdrot

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

zdrot( N, zx, strideX, zy, strideY, c, s )

Applies a plane rotation.

var Complex128Array = require( '@stdlib/array-complex128' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

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

zdrot( zx.length, zx, 1, zy, 1, 0.8, 0.6 );

var z = zy.get( 0 );
// returns <Complex128>

var re = real( z );
// returns ~-0.6

var im = imag( z );
// returns ~-1.2

z = zx.get( 0 );
// returns <Complex128>

re = real( z );
// returns ~0.8

im = imag( z );
// returns ~1.6

The function has the following parameters:

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

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

var Complex128Array = require( '@stdlib/array-complex128' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

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

zdrot( 2, zx, 2, zy, 2, 0.8, 0.6 );

var z = zy.get( 0 );
// returns <Complex128>

var re = real( z );
// returns ~-0.6

var im = imag( z );
// returns ~-1.2

z = zx.get( 0 );
// returns <Complex128>

re = real( z );
// returns ~0.8

im = imag( z );
// returns ~1.6

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

var Complex128Array = require( '@stdlib/array-complex128' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

// Initial arrays...
var zx0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var zy0 = new Complex128Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var zx1 = new Complex128Array( zx0.buffer, zx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var zy1 = new Complex128Array( zy0.buffer, zy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

zdrot( 2, zx1, -2, zy1, 1, 0.8, 0.6 );

var z = zy0.get( 2 );
// returns <Complex128>

var re = real( z );
// returns ~-4.2

var im = imag( z );
// returns ~-4.8

z = zx0.get( 3 );
// returns <Complex128>

re = real( z );
// returns ~5.6

im = imag( z );
// returns ~6.4

zdrot.ndarray( N, zx, strideX, offsetX, zy, strideY, offsetY, c, s )

Applies a plane rotation using alternative indexing semantics.

var Complex128Array = require( '@stdlib/array-complex128' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

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

zdrot.ndarray( zx.length, zx, 1, 0, zy, 1, 0, 0.8, 0.6 );

var z = zy.get( 0 );
// returns <Complex128>

var re = real( z );
// returns ~-0.6

var im = imag( z );
// returns ~-1.2

z = zx.get( 0 );
// returns <Complex128>

re = real( z );
// returns ~0.8

im = imag( z );
// returns ~1.6

The function has the following additional parameters:

• offsetX: starting index for zx.
• offsetY: starting index for zy.

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 real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

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

zdrot.ndarray( 2, zx, 2, 1, zy, 2, 1, 0.8, 0.6 );

var z = zy.get( 3 );
// returns <Complex128>

var re = real( z );
// returns ~-4.2

var im = imag( z );
// returns ~-4.8

z = zx.get( 1 );
// returns <Complex128>

re = real( z );
// returns ~2.4

im = imag( z );
// returns ~3.2

Notes

• If N <= 0, both functions leave zx and zy 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 zx = filledarrayBy( 10, 'complex128', rand );
var zxc = zcopy( zx.length, zx, 1, zeros( zx.length, 'complex128' ), 1 );

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

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

// Print the results:
logEach( '(%s,%s) => (%s,%s)', zxc, zyc, zx, zy );

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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.
• zx: [inout] void* first input array.
• strideX: [in] CBLAS_INT index increment for zx.
• zy: [inout] void* second input array.
• strideY: [in] CBLAS_INT index increment for zy.
• 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.
• zx: [inout] void* first input array.
• strideX: [in] CBLAS_INT index increment for zx.
• offsetX: [in] CBLAS_INT starting index for zx.
• zy: [inout] void* second input array.
• strideY: [in] CBLAS_INT index increment for zy.
• offsetY: [in] CBLAS_INT starting index for zy.
• 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 zx[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
    double zy[] = { 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 *)zx, strideX, (void *)zy, strideY, 0.8, 0.6 );

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

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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.