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cdotc

Calculate the dot product x^H * y of x and y.

The dot product (or scalar product) is defined as

Usage

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

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

Calculates the dot product x^H * y of x and y.

var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ 7.0, -8.0, -1.0, -9.0 ] );
var y = new Complex64Array( [ 6.0, -6.0, -9.0, 5.0 ] );

var out = cdotc( x.length, x, 1, y, 1 );
// returns <Complex64>[ 54.0, -80.0 ]

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Complex64Array.
  • strideX: index increment for x.
  • y: input Complex64Array.
  • strideY: index increment for y.

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 value in x and the first N elements of y in reverse order,

var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ -1.0, -9.0, 2.0, -8.0 ] );
var y = new Complex64Array( [ -5.0, 1.0, -6.0, 7.0 ] );

var out = cdotc( x.length, x, 1, y, -1 );
// returns <Complex64>[ -75.0, -99.0 ]

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

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

var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ 7.0, -8.0, -1.0, -9.0 ] );
var y = new Complex64Array( [ 6.0, -6.0, -9.0, 5.0 ] );

var out = cdotc.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns <Complex64>[ 54.0, -80.0 ]

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 value in x starting from the second value with the last 2 elements in y in reverse order

var Complex64Array = require( '@stdlib/array/complex64' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );

var x = new Complex64Array( [ 7.0, -8.0, -1.0, -9.0 ] );
var y = new Complex64Array( [ 6.0, -6.0, -9.0, 5.0 ] );

var out = cdotc.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
// returns <Complex64>[ -55.0, 23.0 ]

Notes

  • If N <= 0, both functions return complex64 with real and imaginary as 0.0.
  • cdotc() corresponds to the BLAS level 1 function cdotc.

Examples

var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var Complex64 = require( '@stdlib/complex/float32/ctor' );
var cdotc = require( '@stdlib/blas/base/cdotc' );

function rand() {
    return new Complex64( discreteUniform( 0, 10 ), discreteUniform( 1, 5 ) );
}

var x = filledarrayBy( 10, 'complex64', rand );
console.log( x.toString() );

var y = filledarrayBy( 10, 'complex64', rand );
console.log( y.toString() );

// Perform dot product of x and y
var out = cdotc.ndarray( x.length, x, 1, 0, y, -1, y.length-1 );
console.log( out );

C APIs

Usage

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

c_cdotc( N, *X, strideX, *Y, strideY )

Calculates the dot product x^H * y of x and y.

#include "stdlib/complex/float32/ctor.h"

float x[] = { 7.0f, -8.0f, -1.0f, -9.0f };
float y[] = { 6.0f, -6.0f, -9.0f, 5.0f };

stdlib_complex64_t out = c_cdotc( 2, (void *)x, 1, (void *)y, 1 );

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.
stdlib_complex64_t c_cdotc( const CBLAS_INT N, const void *X, const CBLAS_INT strideX, const void *Y, const CBLAS_INT strideY );

c_cdotc_ndarray( N, *X, strideX, offsetX, *Y, strideY, offsetY )

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

#include "stdlib/complex/float32/ctor.h"

float x[] = { 7.0f, -8.0f, -1.0f, -9.0f };
float y[] = { 6.0f, -6.0f, -9.0f, 5.0f };

stdlib_complex64_t out = c_cdotc_ndarray( 2, (void *)x, 1, 0, (void *)y, 1, 0 );

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.
stdlib_complex64_t c_cdotc_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 );

Examples

#include "stdlib/blas/base/cdotc.h"
#include "stdlib/complex/float32/ctor.h"
#include "stdlib/complex/float32/reim.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays of interleaved real and imaginary components:
    float x[] = { 7.0f, -8.0f, -1.0f, -9.0f };
    float y[] = { 6.0f, -6.0f, -9.0f, 5.0f };

    // Specify the number of elements:
    const int N = 2;

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

    // Compute the dot product:
    stdlib_complex64_t dot = c_cdotc( N, (void *)x, strideX, (void *)y, strideY );

    // Print the result:
    float re;
    float im;
    stdlib_complex64_reim( dot, &re, &im );
    printf( "cdotc( x, y ) = %f + %fi\n", re, im );

    // Compute the dot product using alternative indexing semantics:
    dot = c_cdotc_ndarray( N, (void *)x, -strideX, 1, (void *)y, strideY, 0 );

    // Print the result:
    stdlib_complex64_reim( dot, &re, &im );
    printf( "cdotc( x, y ) = %f + %fi\n", re, im );
}

See Also

  • @stdlib/blas/base/cdotu: calculate the dot product of two single-precision complex floating-point vectors.
  • @stdlib/blas/base/zdotc: calculate the dot product of two double-precision complex floating-point vectors, conjugating the first vector.