main.c

/**
* @license Apache-2.0
*
* Copyright (c) 2020 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

#include "stdlib/stats/strided/dsmeanpn.h"
#include "stdlib/blas/ext/base/dssum.h"
#include "stdlib/blas/ext/base/dsapxsum.h"
#include "stdlib/blas/base/shared.h"
#include "stdlib/strided/base/stride2offset.h"

/**
* 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.
*
* ## Method
*
* -   This implementation uses a two-pass approach, as suggested by Neely (1966).
*
* ## 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](https://doi.org/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](https://doi.org/10.1145/3221269.3223036).
*
* @param N        number of indexed elements
* @param X        input array
* @param strideX  stride length
* @return         output value
*/
double API_SUFFIX(stdlib_strided_dsmeanpn)( const CBLAS_INT N, const float *X, const CBLAS_INT strideX ) {
	const CBLAS_INT ox = stdlib_strided_stride2offset( N, strideX );
	return API_SUFFIX(stdlib_strided_dsmeanpn_ndarray)( N, X, strideX, ox );
}

/**
* 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.
*
* @param N        number of indexed elements
* @param X        input array
* @param strideX  stride length
* @param offsetX  starting index for X
* @return         output value
*/
double API_SUFFIX(stdlib_strided_dsmeanpn_ndarray)( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX ) {
	double dN;
	double mu;
	double c;

	if ( N <= 0 ) {
		return 0.0 / 0.0; // NaN
	}
	if ( N == 1 || strideX == 0 ) {
		return X[ offsetX ];
	}
	dN = (double)N;

	// Compute an estimate for the mean:
	mu = API_SUFFIX(stdlib_strided_dssum_ndarray)( N, X, strideX, offsetX );
	mu /= dN;

	// Compute an error term:
	c = API_SUFFIX(stdlib_strided_dsapxsum_ndarray)( N, -mu, X, strideX, offsetX );
	c /= dN;

	return mu + c;
}