dcusumkbn2

Calculate the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.

Usage

var dcusumkbn2 = require( '@stdlib/blas/ext/base/dcusumkbn2' );

dcusumkbn2( N, sum, x, strideX, y, strideY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var y = new Float64Array( x.length );

dcusumkbn2( x.length, 0.0, x, 1, y, 1 );
// y => <Float64Array>[ 1.0, -1.0, 1.0 ]

x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
y = new Float64Array( x.length );

dcusumkbn2( x.length, 10.0, x, 1, y, 1 );
// y => <Float64Array>[ 11.0, 9.0, 11.0 ]

The function has the following parameters:

  • N: number of indexed elements.
  • sum: initial sum.
  • x: input Float64Array.
  • strideX: index increment for x.
  • y: output Float64Array.
  • strideY: index increment for y.

The N and stride parameters determine which elements in x and y are accessed at runtime. For example, to compute the cumulative sum of every other element in x,

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var y = new Float64Array( x.length );

var N = 4;

var v = dcusumkbn2( N, 0.0, x, 2, y, 1 );
// y => <Float64Array>[ 1.0, 3.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]

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

var Float64Array = require( '@stdlib/array/float64' );

// Initial arrays...
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float64Array( x0.length );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

var N = 4;

dcusumkbn2( N, 0.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]

dcusumkbn2.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var y = new Float64Array( x.length );

dcusumkbn2.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
// y => <Float64Array>[ 1.0, -1.0, 1.0 ]

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, offsetX and offsetY parameters support indexing semantics based on a starting indices. For example, to calculate the cumulative sum of every other value in x starting from the second value and to store in the last N elements of y starting from the last element

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y = new Float64Array( x.length );

var N = 4;

dcusumkbn2.ndarray( N, 0.0, x, 2, 1, y, -1, y.length-1 );
// y => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]

Notes

  • If N <= 0, both functions return y unchanged.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var Float64Array = require( '@stdlib/array/float64' );
var dcusumkbn2 = require( '@stdlib/blas/ext/base/dcusumkbn2' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
var y = new Float64Array( x.length );

console.log( x );
console.log( y );

dcusumkbn2( x.length, 0.0, x, 1, y, -1 );
console.log( y );

C APIs

Usage

#include "stdlib/blas/ext/base/dcusumkbn2.h"

stdlib_strided_dcusumkbn2( N, sum, *X, strideX, *Y, strideY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.

const double x[] = { 1.0, 2.0, 3.0, 4.0 }
double y[] = { 0.0, 0.0, 0.0, 0.0 }

stdlib_strided_dcusumkbn2( 4, 0.0, x, 1, y, 1 );

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • sum: [in] double initial sum.
  • X: [in] double* input array.
  • strideX: [in] CBLAS_INT index increment for X.
  • Y: [out] double* output array.
  • strideY: [in] CBLAS_INT index increment for Y.
void stdlib_strided_dcusumkbn2( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY );

stdlib_strided_dcusumkbn2_ndarray( N, sum, *X, strideX, offsetX, *Y, strideY, offsetY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.

const double x[] = { 1.0, 2.0, 3.0, 4.0 }
double y[] = { 0.0, 0.0, 0.0, 0.0 }

stdlib_strided_dcusumkbn2_ndarray( 4, 0.0, x, 1, 0, y, 1, 0 );

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • sum: [in] double initial sum.
  • X: [in] double* input array.
  • strideX: [in] CBLAS_INT index increment for X.
  • offsetX: [in] CBLAS_INT starting index for X.
  • Y: [out] double* output array.
  • strideY: [in] CBLAS_INT index increment for Y.
  • offsetY: [in] CBLAS_INT starting index for Y.
void stdlib_strided_dcusumkbn2_ndarray( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );

Examples

#include "stdlib/blas/ext/base/dcusumkbn2.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 };
    double y[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

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

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute the cumulative sum:
    stdlib_strided_dcusumkbn2( N, 0.0, x, strideX, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %d ] = %lf\n", i, y[ i ] );
    }
}

References

  • Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." Computing 76 (3): 279–93. doi:10.1007/s00607-005-0139-x.
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