drsskbn

Calculate the residual sum of squares of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm.

The residual sum of squares (also referred to as the sum of squared residuals (SSR) and the sum of squared errors (SSE)) is defined as

Installation

npm install @stdlib/blas-ext-base-drsskbn

Usage

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

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

Computes the residual sum of squares of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm.

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

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

var z = drsskbn( x.length, x, 1, y, 1 );
// returns 45.0

The function has the following parameters:

• N: number of indexed elements.
• x: first input Float64Array.
• strideX: stride length for x.
• y: second input Float64Array.
• strideY: stride length for y.

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

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( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );

var z = drsskbn( x.length, x, 1, y, 1 );
// returns 72.0

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

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

var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float64Array( [ 8.0, -2.0, 3.0, -2.0, 7.0, -2.0, 0.0, -1.0 ] );

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*1 ); // start at 2nd element

var z = drsskbn( 4, x1, 2, y1, 2 );
// returns 50.0

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

Computes the residual sum of squares of two double-precision floating-point strided arrays using an improved 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( [ 1.0, 1.0, -4.0 ] );

var z = drsskbn.ndarray( x.length, x, 1, 0, y, 1, 0 );
// returns 45.0

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 residual sum of squares for every other element in x and y starting from the second 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, 6.0 ] );
var y = new Float64Array( [ 8.0, -2.0, 3.0, -2.0, 7.0, -2.0, 0.0, -1.0, 4.0 ] );

var z = drsskbn.ndarray( 4, x, 2, 1, y, 2, 1 );
// returns 50.0

Notes

• If N <= 0, both functions return 0.0.

Examples

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, -50, 50, opts );
console.log( x );

var y = discreteUniform( 10, -50, 50, opts );
console.log( y );

var d = drsskbn( x.length, x, 1, y, 1 );
console.log( d );

C APIs

Usage

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

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

Computes the residual sum of squares of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm.

const double x[] = { 1.0, -2.0, 2.0 };
const double y[] = { 1.0, 1.0, -4.0 };

double z = stdlib_strided_drsskbn( 3, x, 1, y, 1 );
// returns 45.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* first input array.
• strideX: [in] CBLAS_INT stride length for X.
• Y: [in] double* second input array.
• strideY: [in] CBLAS_INT stride length for Y.

double stdlib_strided_drsskbn( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY );

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

Computes the residual sum of squares of two double-precision floating-point strided arrays using an improved Kahan–Babuška algorithm and alternative indexing semantics.

const double x[] = { 1.0, -2.0, 2.0 };
const double y[] = { 1.0, 1.0, -4.0 };

double v = stdlib_strided_drsskbn_ndarray( 3, x, 1, 0, y, 1, 0 );
// returns 45.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* first input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [in] double* second input array.
• strideY: [in] CBLAS_INT stride length for Y.
• offsetY: [in] CBLAS_INT starting index for Y.

double stdlib_strided_drsskbn_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );

Examples

#include "stdlib/blas/ext/base/drsskbn.h"
#include <stdio.h>

int main( void ) {
    // Create two strided arrays:
    const double x[] = { 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 };
    const double y[] = { 5.0, 12.0, -8.0, 15.0, 9.0, 0.0 };

    // Specify the number of elements:
    const int N = 5;

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

    // Compute the residual sum of squares of `x` and `y`:
    double d = stdlib_strided_drsskbn( N, x, strideX, y, strideY );

    // Print the result:
    printf( "rss: %lf\n", d );

    // Specify index offsets:
    const int offsetX = 1;
    const int offsetY = 1;

    // Compute the residual sum of squares of `x` and `y` with offsets:
    d = stdlib_strided_drsskbn_ndarray( N, x, strideX, offsetX, y, strideY, offsetY );

    // Print the result:
    printf( "rss: %lf\n", d );
}

References

• Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." Zeitschrift Für Angewandte Mathematik Und Mechanik 54 (1): 39–51. doi:10.1002/zamm.19740540106.

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For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

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