time-to-botec

Benchmark sampling in different programming languages
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dmeanvarpn.c (3136B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2020 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 #include "stdlib/stats/base/dmeanvarpn.h"
     20 #include "stdlib/blas/ext/base/dsumpw.h"
     21 #include <stdint.h>
     22 
     23 /**
     24 * Computes the mean and variance of a double-precision floating-point strided array using a two-pass algorithm.
     25 *
     26 * ## Method
     27 *
     28 * -   This implementation uses a two-pass approach, as suggested by Neely (1966).
     29 *
     30 * ## References
     31 *
     32 * -   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).
     33 * -   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).
     34 *
     35 * @param N           number of indexed elements
     36 * @param correction  degrees of freedom adjustment
     37 * @param X           input array
     38 * @param strideX     X stride length
     39 * @param Out         output array
     40 * @param strideOut   Out stride length
     41 */
     42 void stdlib_strided_dmeanvarpn( const int64_t N, const double correction, const double *X, const int64_t strideX, double *Out, const int64_t strideOut ) {
     43 	int64_t ix;
     44 	int64_t io;
     45 	int64_t i;
     46 	double M2;
     47 	double mu;
     48 	double dN;
     49 	double M;
     50 	double d;
     51 	double c;
     52 	double n;
     53 
     54 	if ( strideX < 0 ) {
     55 		ix = (1-N) * strideX;
     56 	} else {
     57 		ix = 0;
     58 	}
     59 	if ( strideOut < 0 ) {
     60 		io = -strideOut;
     61 	} else {
     62 		io = 0;
     63 	}
     64 	if ( N <= 0 ) {
     65 		Out[ io ] = 0.0 / 0.0; // NaN
     66 		Out[ io+strideOut ] = 0.0 / 0.0; // NaN
     67 		return;
     68 	}
     69 	dN = (double)N;
     70 	n = dN - correction;
     71 	if ( N == 1 || strideX == 0 ) {
     72 		Out[ io ] = X[ ix ];
     73 		if ( n <= 0.0 ) {
     74 			Out[ io+strideOut ] = 0.0 / 0.0; // NaN
     75 		} else {
     76 			Out[ io+strideOut ] = 0.0;
     77 		}
     78 		return;
     79 	}
     80 	// Compute an estimate for the mean:
     81 	mu = stdlib_strided_dsumpw( N, X, strideX ) / dN;
     82 	if ( mu != mu ) {
     83 		Out[ io ] = 0.0 / 0.0; // NaN
     84 		Out[ io+strideOut ] = 0.0 / 0.0; // NaN
     85 		return;
     86 	}
     87 	// Compute the sum of squared differences from the mean...
     88 	M2 = 0.0;
     89 	M = 0.0;
     90 	for ( i = 0; i < N; i++ ) {
     91 		d = X[ ix ] - mu;
     92 		M2 += d * d;
     93 		M += d;
     94 		ix += strideX;
     95 	}
     96 	// Compute an error term for the mean:
     97 	c = M / dN;
     98 
     99 	Out[ io ] = mu + c;
    100 	if ( n <= 0.0 ) {
    101 		Out[ io+strideOut ] = 0.0 / 0.0; // NaN
    102 	} else {
    103 		Out[ io+strideOut ] = (M2/n) - (c*(M/n));
    104 	}
    105 	return;
    106 }