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Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.
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stdlib-js/stats-base-dsmeanpw
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Calculate thearithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.
Thearithmetic mean is defined as
npm install @stdlib/stats-base-dsmeanpw
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vardsmeanpw=require('@stdlib/stats-base-dsmeanpw');
Computes thearithmetic mean of a single-precision floating-point strided arrayx using pairwise summation with extended accumulation and returning an extended precision result.
varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([1.0,-2.0,2.0]);varv=dsmeanpw(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.
TheN andstride parameters determine which elements inx are accessed at runtime. For example, to compute thearithmetic mean of every other element inx,
varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([1.0,2.0,2.0,-7.0,-2.0,3.0,4.0,2.0]);varv=dsmeanpw(4,x,2);// returns 1.25
Note that indexing is relative to the first index. To introduce an offset, usetyped array views.
varFloat32Array=require('@stdlib/array-float32');varx0=newFloat32Array([2.0,1.0,2.0,-2.0,-2.0,2.0,3.0,4.0]);varx1=newFloat32Array(x0.buffer,x0.BYTES_PER_ELEMENT*1);// start at 2nd elementvarv=dsmeanpw(4,x1,2);// returns 1.25
Computes thearithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and alternative indexing semantics and returning an extended precision result.
varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([1.0,-2.0,2.0]);varv=dsmeanpw.ndarray(x.length,x,1,0);// returns ~0.33333
The function has the following additional parameters:
- offsetX: starting index for
x.
Whiletyped 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 thearithmetic mean for every other element inx starting from the second element
varFloat32Array=require('@stdlib/array-float32');varx=newFloat32Array([2.0,1.0,2.0,-2.0,-2.0,2.0,3.0,4.0]);varv=dsmeanpw.ndarray(4,x,2,1);// returns 1.25
- If
N <= 0, both functions returnNaN. - Accumulated intermediate values are stored as double-precision floating-point numbers.
- 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.
vardiscreteUniform=require('@stdlib/random-array-discrete-uniform');vardsmeanpw=require('@stdlib/stats-base-dsmeanpw');varx=discreteUniform(10,-50,50,{'dtype':'float32'});console.log(x);varv=dsmeanpw(x.length,x,1);console.log(v);
#include"stdlib/stats/base/dsmeanpw.h"
Computes the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.
constfloatx[]= {1.0f,2.0f,3.0f,4.0f,5.0f,6.0f,7.0f,8.0f };doublev=stdlib_strided_dsmeanpw(4,x,2 );// returns 4.0
The function accepts the following arguments:
- N:
[in] CBLAS_INTnumber of indexed elements. - X:
[in] float*input array. - strideX:
[in] CBLAS_INTstride length forX.
doublestdlib_strided_dsmeanpw(constCBLAS_INTN,constfloat*X,constCBLAS_INTstrideX );
Computes the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and alternative indexing semantics and returning an extended precision result.
constfloatx[]= {1.0f,2.0f,3.0f,4.0f,5.0f,6.0f,7.0f,8.0f };doublev=stdlib_strided_dsmeanpw_ndarray(4,x,2,0 );// returns 4.0
The function accepts the following arguments:
- N:
[in] CBLAS_INTnumber of indexed elements. - X:
[in] float*input array. - strideX:
[in] CBLAS_INTstride length forX. - offsetX:
[in] CBLAS_INTstarting index forX.
doublestdlib_strided_dsmeanpw_ndarray(constCBLAS_INTN,constfloat*X,constCBLAS_INTstrideX,constCBLAS_INToffsetX );
#include"stdlib/stats/base/dsmeanpw.h"#include<stdio.h>intmain(void ) {// Create a strided array:constfloatx[]= {1.0f,2.0f,3.0f,4.0f,5.0f,6.0f,7.0f,8.0f };// Specify the number of elements:constintN=4;// Specify the stride length:constintstrideX=2;// Compute the arithmetic mean:doublev=stdlib_strided_dsmeanpw(N,x,strideX );// Print the result:printf("mean: %lf\n",v );}
- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation."SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.
@stdlib/stats-strided/dmeanpw:calculate the arithmetic mean of a double-precision floating-point strided array using pairwise summation.@stdlib/stats-base/dsmean:calculate the arithmetic mean of a single-precision floating-point strided array using extended accumulation and returning an extended precision result.@stdlib/stats-base/meanpw:calculate the arithmetic mean of a strided array using pairwise summation.@stdlib/stats-base/smeanpw:calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation.
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Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.
