time-to-botec/squiggle/node_modules/@stdlib/stats/base/smeanpn/README.md

smeanpn

Calculate the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm.

The arithmetic mean is defined as

Usage

var smeanpn = require( '@stdlib/stats/base/smeanpn' );

smeanpn( N, x, stride )

Computes the arithmetic mean of a single-precision floating-point strided array x using a two-pass error correction algorithm.

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

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

var v = smeanpn( N, x, 1 );
// returns ~0.3333

The function has the following parameters:

• N: number of indexed elements.
• x: input Float32Array.
• stride: index increment for x.

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

var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var v = smeanpn( N, 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 floor = require( '@stdlib/math/base/special/floor' );

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 N = floor( x0.length / 2 );

var v = smeanpn( N, x1, 2 );
// returns 1.25

smeanpn.ndarray( N, x, stride, offset )

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

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

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

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

The function has the following additional parameters:

• offset: 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 value in x starting from the second value

var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

var v = smeanpn.ndarray( N, x, 2, 1 );
// returns 1.25

Notes

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float32Array = require( '@stdlib/array/float32' );
var smeanpn = require( '@stdlib/stats/base/smeanpn' );

var x;
var i;

x = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( (randu()*100.0) - 50.0 );
}
console.log( x );

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

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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.