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csrot

Applies a plane rotation.

Installation

npm install @stdlib/blas-base-csrot

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

csrot( N, cx, strideX, cy, strideY, c, s )

Applies a plane rotation.

var Complex64Array = require( '@stdlib/array-complex64' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 );

var z = cy.get( 0 );
// returns <Complex64>

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

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

z = cx.get( 0 );
// returns <Complex64>

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

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

The function has the following parameters:

• N: number of indexed elements.
• cx: first input Complex64Array.
• strideX: index increment for cx.
• cy: second input Complex64Array.
• strideY: index increment for cy.

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

var Complex64Array = require( '@stdlib/array-complex64' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

csrot( 2, cx, 2, cy, 2, 0.8, 0.6 );

var z = cy.get( 0 );
// returns <Complex64>

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

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

z = cx.get( 0 );
// returns <Complex64>

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

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

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

var Complex64Array = require( '@stdlib/array-complex64' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

// Initial arrays...
var cx0 = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy0 = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views...
var cx1 = new Complex64Array( cx0.buffer, cx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var cy1 = new Complex64Array( cy0.buffer, cy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

csrot( 2, cx1, -2, cy1, 1, 0.8, 0.6 );

var z = cy0.get( 2 );
// returns <Complex64>

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

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

z = cx0.get( 3 );
// returns <Complex64>

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

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

csrot.ndarray( N, cx, strideX, offsetX, cy, strideY, offsetY, c, s )

Applies a plane rotation using alternative indexing semantics.

var Complex64Array = require( '@stdlib/array-complex64' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

csrot.ndarray( cx.length, cx, 1, 0, cy, 1, 0, 0.8, 0.6 );

var z = cy.get( 0 );
// returns <Complex64>

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

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

z = cx.get( 0 );
// returns <Complex64>

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

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

The function has the following additional parameters:

• offsetX: starting index for cx.
• offsetY: starting index for cy.

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 Complex64Array = require( '@stdlib/array-complex64' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

csrot.ndarray( 2, cx, 2, 1, cy, 2, 1, 0.8, 0.6 );

var z = cy.get( 3 );
// returns <Complex64>

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

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

z = cx.get( 1 );
// returns <Complex64>

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

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

Notes

• If N <= 0, both functions leave cx and cy unchanged.
• csrot() corresponds to the BLAS level 1 function csrot.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var ccopy = require( '@stdlib/blas-base-ccopy' );
var zeros = require( '@stdlib/array-zeros' );
var logEach = require( '@stdlib/console-log-each' );
var csrot = require( '@stdlib/blas-base-csrot' );

function rand() {
    return new Complex64( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

// Generate random input arrays:
var cx = filledarrayBy( 10, 'complex64', rand );
var cxc = ccopy( cx.length, cx, 1, zeros( cx.length, 'complex64' ), 1 );

var cy = filledarrayBy( 10, 'complex64', rand );
var cyc = ccopy( cy.length, cy, 1, zeros( cy.length, 'complex64' ), 1 );

// Apply a plane rotation:
csrot( cx.length, cx, 1, cy, 1, 0.8, 0.6 );

// Print the results:
logEach( '(%s,%s) => (%s,%s)', cxc, cyc, cx, cy );

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C APIs

Usage

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

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

Applies a plane rotation.

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

c_csrot( 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.
• CX: [inout] void* first input array.
• strideX: [in] CBLAS_INT index increment for CX.
• CY: [inout] void* second input array.
• strideY: [in] CBLAS_INT index increment for CY.
• c: [in] float cosine of the angle of rotation.
• s: [in] float sine of the angle of rotation.

void c_csrot( const CBLAS_INT N, void *CX, const CBLAS_INT strideX, void *CY, const CBLAS_INT strideY, const float c, const float s );

Examples

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

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

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

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

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

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