README.md

dmeanpw

Compute the arithmetic mean of a one-dimensional double-precision floating-point ndarray using pairwise summation.

The arithmetic mean is defined as

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

Usage

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

dmeanpw( arrays )

Computes the arithmetic mean of a one-dimensional double-precision floating-point ndarray using pairwise summation.

var Float64Array = require( '@stdlib/array/float64' );
var ndarray = require( '@stdlib/ndarray/base/ctor' );

var xbuf = new Float64Array( [ 1.0, 3.0, 4.0, 2.0 ] );
var x = new ndarray( 'float64', xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var v = dmeanpw( [ x ] );
// returns 2.5

The function has the following parameters:

• arrays: array-like object containing a one-dimensional input ndarray.

Notes

• If provided an empty one-dimensional ndarray, the function returns NaN.
• 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 ndarray = require( '@stdlib/ndarray/base/ctor' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var dmeanpw = require( '@stdlib/stats/base/ndarray/dmeanpw' );

var xbuf = discreteUniform( 10, -50, 50, {
    'dtype': 'float64'
});
var x = new ndarray( 'float64', xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

var v = dmeanpw( [ x ] );
console.log( v );

---

C APIs

Usage

#include "stdlib/stats/base/ndarray/dmeanpw.h"

stdlib_stats_dmeanpw( arrays )

Computes the arithmetic mean of a one-dimensional double-precision floating-point ndarray using pairwise summation.

#include "stdlib/ndarray/ctor.h"
#include "stdlib/ndarray/dtypes.h"
#include "stdlib/ndarray/index_modes.h"
#include "stdlib/ndarray/orders.h"
#include "stdlib/ndarray/base/bytes_per_element.h"
#include <stdint.h>

// Create an ndarray:
const double data[] = { 1.0, 2.0, 3.0, 4.0 };
int64_t shape[] = { 4 };
int64_t strides[] = { STDLIB_NDARRAY_FLOAT64_BYTES_PER_ELEMENT };
int8_t submodes[] = { STDLIB_NDARRAY_INDEX_ERROR };

struct ndarray *x = stdlib_ndarray_allocate( STDLIB_NDARRAY_FLOAT64, (uint8_t *)data, 1, shape, strides, 0, STDLIB_NDARRAY_ROW_MAJOR, STDLIB_NDARRAY_INDEX_ERROR, 1, submodes );

// Compute the arithmetic mean:
const struct ndarray *arrays[] = { x };
double v = stdlib_stats_dmeanpw( arrays );
// returns ~2.5

// Free allocated memory:
stdlib_ndarray_free( x );

The function accepts the following arguments:

• arrays: [in] struct ndarray** list containing a one-dimensional input ndarray.

double stdlib_stats_dmeanpw( const struct ndarray *arrays[] );

Examples

#include "stdlib/stats/base/ndarray/dmeanpw.h"
#include "stdlib/ndarray/ctor.h"
#include "stdlib/ndarray/dtypes.h"
#include "stdlib/ndarray/index_modes.h"
#include "stdlib/ndarray/orders.h"
#include "stdlib/ndarray/base/bytes_per_element.h"
#include <stdint.h>
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
   // Create a data buffer:
   const double data[] = { 1.0, -2.0, 3.0, -4.0, 5.0, -6.0, 7.0, -8.0 };

   // Specify the number of array dimensions:
   const int64_t ndims = 1;

   // Specify the array shape:
   int64_t shape[] = { 4 };

   // Specify the array strides:
   int64_t strides[] = { 2*STDLIB_NDARRAY_FLOAT64_BYTES_PER_ELEMENT };

   // Specify the byte offset:
   const int64_t offset = 0;

   // Specify the array order:
   const enum STDLIB_NDARRAY_ORDER order = STDLIB_NDARRAY_ROW_MAJOR;

   // Specify the index mode:
   const enum STDLIB_NDARRAY_INDEX_MODE imode = STDLIB_NDARRAY_INDEX_ERROR;

   // Specify the subscript index modes:
   int8_t submodes[] = { STDLIB_NDARRAY_INDEX_ERROR };
   const int64_t nsubmodes = 1;

   // Create an ndarray:
   struct ndarray *x = stdlib_ndarray_allocate( STDLIB_NDARRAY_FLOAT64, (uint8_t *)data, ndims, shape, strides, offset, order, imode, nsubmodes, submodes );
   if ( x == NULL ) {
      fprintf( stderr, "Error allocating memory.\n" );
      exit( 1 );
   }

   // Define a list of ndarrays:
   const struct ndarray *arrays[] = { x };

   // Compute the arithmetic mean:
   double v = stdlib_stats_dmeanpw( arrays );

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

   // Free allocated memory:
   stdlib_ndarray_free( x );
}

References

• Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.