README.md

zdotu

Calculate the dot product of two double-precision complex floating-point vectors.

The dot product (or scalar product) is defined as

$$\mathbf{zx}\cdot\mathbf{zy} = \sum_{i=0}^{N-1} zx_i zy_i = zx_0 zy_0 + zx_1 zy_1 + \ldots + zx_{N-1} zy_{N-1}$$

Usage

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

zdotu( N, zx, strideX, zy, strideY )

Calculates the dot product of vectors zx and zy.

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

var zx = new Complex128Array( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
var zy = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );

var z = zdotu( 3, zx, 1, zy, 1 );
// returns <Complex128>

var re = real( z );
// returns -52.0

var im = imag( z );
// returns 82.0

The function has the following parameters:

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

The N and strides parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the dot product of every other value in zx and the first N elements of zy in reverse order,

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( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var z = zdotu( 2, zx, 2, zy, -1 );
// returns <Complex128>

var re = real( z );
// returns -2.0

var im = imag( z );
// returns 14.0

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 ] );
var zy0 = new Complex128Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// 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 3th element

var z = zdotu( 1, zx1, 1, zy1, 1 );
// returns <Complex128>

var re = real( z );
// returns -15.0

var im = imag( z );
// returns 80.0

zdotu.ndarray( N, zx, strideX, offsetX, zy, strideY, offsetY )

Calculates the dot product of zx and zy 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( [ 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 ] );
var zy = new Complex128Array( [ 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 ] );

var z = zdotu.ndarray( zx.length, zx, 1, 0, zy, 1, 0 );
// returns <Complex128>

var re = real( z );
// returns -52.0

var im = imag( z );
// returns 82.0

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 calculate the dot product of every other value in zx starting from the second value with the last 2 elements in zy in reverse order

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( [ 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0 ] ); // eslint-disable-line max-len

var z = zdotu.ndarray( 2, zx, 2, 1, zy, -1, zy.length-1 );
// returns <Complex128>

var re = real( z );
// returns -40.0

var im = imag( z );
// returns 310.0

Notes

• If N <= 0, both functions return 0.0 + 0.0i.
• zdotu() corresponds to the BLAS level 1 function zdotu.

Examples

var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var zdotu = require( '@stdlib/blas/base/zdotu' );

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

var zx = filledarrayBy( 10, 'complex128', rand );
console.log( zx.toString() );

var zy = filledarrayBy( 10, 'complex128', rand );
console.log( zy.toString() );

var out = zdotu.ndarray( zx.length, zx, 1, 0, zy, -1, zy.length-1 );
console.log( out.toString() );