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dsmeanpn

README.md

dsmeanpn

Calculate the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and returning an extended precision result.

The arithmetic mean is defined as

$$\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i$$

Usage

var dsmeanpn = require( '@stdlib/stats/strided/dsmeanpn' );

dsmeanpn( N, x, strideX )

Computes the arithmetic mean of a single-precision floating-point strided array x using a two-pass error correction algorithm with extended accumulation and returning an extended precision result.

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = dsmeanpn( x.length, x, 1 );
// returns ~0.3333

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Float32Array.
  • strideX: stride length for x.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the arithmetic mean of every other element in x,

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = dsmeanpn( 4, x, 2 );
// returns 1.25

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

var Float32Array = require( '@stdlib/array/float32' );

var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = dsmeanpn( 4, x1, 2 );
// returns 1.25

dsmeanpn.ndarray( N, x, strideX, offsetX )

Computes the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and alternative indexing semantics and returning an extended precision result.

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = dsmeanpn.ndarray( x.length, x, 1, 0 );
// returns ~0.33333

The function has the following additional parameters:

  • offsetX: starting index for x.

While typed array views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the arithmetic mean for every other element in x starting from the second element

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = dsmeanpn.ndarray( 4, x, 2, 1 );
// returns 1.25

Notes

  • If N <= 0, both functions return NaN.
  • Accumulated intermediate values are stored as double-precision floating-point numbers.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var dsmeanpn = require( '@stdlib/stats/strided/dsmeanpn' );

var x = discreteUniform( 10, -50, 50, {
    'dtype': 'float32'
});
console.log( x );

var v = dsmeanpn( x.length, x, 1 );
console.log( v );

C APIs

Usage

#include "stdlib/stats/strided/dsmeanpn.h"

stdlib_strided_dsmeanpn( N, *X, strideX )

Computes the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and returning an extended precision result.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

double v = stdlib_strided_dsmeanpn( 4, x, 2 );
// returns 4.0

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] float* input array.
  • strideX: [in] CBLAS_INT stride length for X.
double stdlib_strided_dsmeanpn( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );

stdlib_strided_dsmeanpn_ndarray( N, *X, strideX, offsetX )

Computes the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm with extended accumulation and alternative indexing semantics and returning an extended precision result.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

double v = stdlib_strided_dsmeanpn_ndarray( 4, x, 2, 0 );
// returns 4.0

The function accepts the following arguments:

  • N: [in] CBLAS_INT number of indexed elements.
  • X: [in] float* input array.
  • strideX: [in] CBLAS_INT stride length for X.
  • offsetX: [in] CBLAS_INT starting index for X.
double stdlib_strided_dsmeanpn_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/stats/strided/dsmeanpn.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

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

    // Specify the stride length:
    const int strideX = 2;

    // Compute the arithmetic mean:
    double v = stdlib_strided_dsmeanpn( N, x, strideX );

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

References

  • Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." Communications of the ACM 9 (7). Association for Computing Machinery: 496–99. doi:10.1145/365719.365958.
  • Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In Proceedings of the 30th International Conference on Scientific and Statistical Database Management. New York, NY, USA: Association for Computing Machinery. doi:10.1145/3221269.3223036.

See Also

  • @stdlib/stats/strided/dmeanpn: calculate the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm.
  • @stdlib/stats/strided/dsmean: calculate the arithmetic mean of a single-precision floating-point strided array using extended accumulation and returning an extended precision result.
  • @stdlib/stats/strided/dsnanmeanpn: calculate the arithmetic mean of a single-precision floating-point strided array, ignoring NaN values, using a two-pass error correction algorithm with extended accumulation, and returning an extended precision result.
  • @stdlib/stats/strided/meanpn: calculate the arithmetic mean of a strided array using a two-pass error correction algorithm.
  • @stdlib/stats/strided/smeanpn: calculate the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm.