zrot

Apply a plane rotation with real cosine and complex sine to a pair of double-precision complex floating-point vectors.

Installation

npm install @stdlib/lapack-base-zrot

Usage

var zrot = require( '@stdlib/lapack-base-zrot' );

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

Applies a plane rotation with real cosine and complex sine.

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

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 ] );
var s = new Complex128( 0.0, 0.75 );

zrot( zx.length, zx, 1, zy, 1, 1.25, s );

var z = zy.get( 0 );
// returns <Complex128>[ ~-1.5, ~0.75 ]

z = zx.get( 0 );
// returns <Complex128>[ ~1.25, ~2.5 ]

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 Complex128 = require( '@stdlib/complex-float64-ctor' );

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 ] );
var s = new Complex128( 0.0, 0.75 );

zrot( 2, zx, 2, zy, 2, 1.25, s );

var z = zy.get( 0 );
// returns <Complex128>[ ~-1.5, ~0.75 ]

z = zx.get( 0 );
// returns <Complex128>[ ~1.25, ~2.5 ]

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

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

// 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

var s = new Complex128( 0.0, 0.75 );

zrot( 2, zx1, -2, zy1, 1, 1.25, s );

var z = zy0.get( 2 );
// returns <Complex128>[ ~-6.0, ~5.25 ]

z = zx0.get( 3 );
// returns <Complex128>[ ~8.75, ~10.0 ]

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

Applies a plane rotation with real cosine and complex sine using alternative indexing semantics.

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

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 ] );
var s = new Complex128( 0.0, 0.75 );

zrot.ndarray( zx.length, zx, 1, 0, zy, 1, 0, 1.25, s );

var z = zy.get( 0 );
// returns <Complex128>[ ~-1.5, ~0.75 ]

z = zx.get( 0 );
// returns <Complex128>[ ~1.25, ~2.5 ]

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 Complex128 = require( '@stdlib/complex-float64-ctor' );

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 ] );
var s = new Complex128( 0.0, 0.75 );

zrot.ndarray( 2, zx, 2, 1, zy, 2, 1, 1.25, s );

var z = zy.get( 3 );
// returns <Complex128>[ ~-6.0, ~5.25 ]

z = zx.get( 1 );
// returns <Complex128>[ ~3.75, ~5.0 ]

Notes

• If N <= 0, both functions leave zx and zy unchanged.
• zrot() corresponds to the LAPACK routine zrot.

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 zrot = require( '@stdlib/lapack-base-zrot' );

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 );

var s = new Complex128( 0.0, 0.75 );

// Apply a plane rotation:
zrot( zx.length, zx, 1, zy, 1, 1.25, s );

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

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.