dcusumpw
Calculate the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
Usage
var dcusumpw = require( '@stdlib/blas/ext/base/dcusumpw' );
dcusumpw( N, sum, x, strideX, y, strideY )
Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
var Float64Array = require( '@stdlib/array/float64' );
var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var y = new Float64Array( x.length );
dcusumpw( 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 );
dcusumpw( 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 the strided arrays are accessed at runtime. For example, to compute the cumulative sum of every other element in the strided input array,
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 v = dcusumpw( 4, 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
dcusumpw( 4, 0.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]
dcusumpw.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )
Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation 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 );
dcusumpw.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, offset parameters support indexing semantics based on starting indices. For example, to calculate the cumulative sum of every other value in the strided input array starting from the second value and to store in the last N
elements of the strided output array 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 );
dcusumpw.ndarray( 4, 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 returny
unchanged. - In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
Examples
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var Float64Array = require( '@stdlib/array/float64' );
var dcusumpw = require( '@stdlib/blas/ext/base/dcusumpw' );
var x = discreteUniform( 10, -100, 100, {
'dtype': 'float64'
});
var y = new Float64Array( x.length );
console.log( x );
console.log( y );
dcusumpw( x.length, 0.0, x, 1, y, -1 );
console.log( y );
C APIs
Usage
#include "stdlib/blas/ext/base/dcusumpw.h"
stdlib_strided_dcusumpw( N, sum, *X, strideX, *Y, strideY )
Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
const double x[] = { 1.0, 2.0, 3.0, 4.0 };
double y[] = { 0.0, 0.0, 0.0, 0.0 };
stdlib_strided_dcusumpw( 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 forX
. - Y:
[out] double*
output array. - strideY:
[in] CBLAS_INT
index increment forY
.
void stdlib_strided_dcusumpw( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY );
stdlib_strided_dcusumpw_ndarray( N, sum, *X, strideX, offsetX, *Y, strideY, offsetY )
Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation 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_dcusumpw_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 forX
. - offsetX:
[in] CBLAS_INT
starting index forX
. - Y:
[out] double*
output array. - strideY:
[in] CBLAS_INT
index increment forY
. - offsetY:
[in] CBLAS_INT
starting index forY
.
void stdlib_strided_dcusumpw_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/dcusumpw.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 };
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_dcusumpw( 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
- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.