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zdotu

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

The dot product (or scalar product) is defined as

$$\mathbf{x}\cdot\mathbf{y} = \sum_{i=0}^{N-1} x_i y_i = x_0 y_0 + x_1 y_1 + \ldots + x_{N-1} y_{N-1}$$

Usage

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

zdotu( N, x, strideX, y, strideY )

Calculates the dot product of vectors x and y.

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

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

var z = zdotu( 3, x, 1, y, 1 );
// returns <Complex128>[ -52.0, 82.0 ]

The function has the following parameters:

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to calculate the dot product of every other element in x and the first N elements of y in reverse order,

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

var z = zdotu( 2, x, 2, y, -1 );
// returns <Complex128>[ -2.0, 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' );

// Initial arrays...
var x0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Complex128Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// 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

var z = zdotu( 1, x1, 1, y1, 1 );
// returns <Complex128>[ -15.0, 80.0 ]

zdotu.ndarray( N, x, strideX, offsetX, y, strideY, offsetY )

Calculates the dot product of x and y using alternative indexing semantics.

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

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

var z = zdotu.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns <Complex128>[ -52.0, 82.0 ]

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 calculate the dot product of every other element in x starting from the second element with the last 2 elements in y in reverse order

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( [ 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0 ] );

var z = zdotu.ndarray( 2, x, 2, 1, y, -1, y.length-1 );
// returns <Complex128>[ -40.0, 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 x = filledarrayBy( 10, 'complex128', rand );
console.log( x.toString() );

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

// Compute the dot product:
var out = zdotu( x.length, x, 1, y, -1 );
console.log( out.toString() );

// Compute the dot product using alternative indexing semantics:
out = zdotu.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( out.toString() );

C APIs

Usage

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

c_zdotu( N, *X, strideX, *Y, strideY, *dot )

Calculates the dot product of two single-precision complex floating-point vectors.

#include "stdlib/complex/float64/ctor.h"

const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 };

stdlib_complex128_t dot;
c_zdotu( 3, (void *)x, 1, (void *)y, 1, (void *)&dot );

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] void* first input array.
  • strideX: [in] CBLAS_INT index increment for X.
  • Y: [in] void* second input array.
  • strideY: [in] CBLAS_INT index increment for Y.
  • dot: [out] void* output variable.
void c_zdotu( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const void *Y, const CBLAS_INT strideY, void *dot );

c_zdotu_ndarray( N, *X, strideX, offsetX, *Y, strideY, offsetY, *dot )

Calculates the dot product of two single-precision complex floating-point vectors using alternative indexing semantics.

#include "stdlib/complex/float64/ctor.h"

const double x[] = { 4.0, 2.0, -3.0, 5.0, -1.0, 7.0 };
const double y[] = { 2.0, 6.0, -1.0, -4.0, 8.0, 9.0 };

stdlib_complex128_t dot;
c_zdotu_ndarray( 3, (void *)x, 1, 0, (void *)y, 1, 0, (void *)&dot );

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] void* first input array.
  • strideX: [in] CBLAS_INT index increment for X.
  • offsetX: [in] CBLAS_INT starting index for X.
  • Y: [in] void* second input array.
  • strideY: [in] CBLAS_INT index increment for Y.
  • offsetY: [in] CBLAS_INT starting index for Y.
  • dot: [out] void* output variable.
void c_zdotu_ndarray( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const void *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, void *dot );

Examples

#include "stdlib/blas/base/zdotu.h"
#include "stdlib/complex/float64/real.h"
#include "stdlib/complex/float64/imag.h"
#include "stdlib/complex/float64/ctor.h"
#include <stdio.h>

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

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

    // Specify strides:
    const int strideX = 1;
    const int strideY = 1;

    // Create a complex number to store the result:
    stdlib_complex128_t z;

    // Compute the dot product:
    c_zdotu( N, (const void *)x, strideX, (const void *)y, strideY, (void *)&z );

    // Print the result:
    printf( "dot: %lf + %lfi\n", stdlib_complex128_real( z ), stdlib_complex128_imag( z ) );

    // Compute the dot product:
    c_zdotu_ndarray( N, (const void *)x, strideX, 0, (const void *)y, strideY, 0, (void *)&z );

    // Print the result:
    printf( "dot: %lf + %lfi\n", stdlib_complex128_real( z ), stdlib_complex128_imag( z ) );
}