time-to-botec

Benchmark sampling in different programming languages
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dvarianceyc.c (2026B)

      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/dvarianceyc.h"
     20 #include <stdint.h>
     21 
     22 /**
     23 * Computes the variance of a double-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.
     24 *
     25 * ## Method
     26 *
     27 * -   This implementation uses a one-pass algorithm, as proposed by Youngs and Cramer (1971).
     28 *
     29 * ## References
     30 *
     31 * -   Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." _Technometrics_ 13 (3): 657–65. doi:[10.1080/00401706.1971.10488826](https://doi.org/10.1080/00401706.1971.10488826).
     32 *
     33 * @param N           number of indexed elements
     34 * @param correction  degrees of freedom adjustment
     35 * @param X           input array
     36 * @param stride      stride length
     37 * @return            output value
     38 */
     39 double stdlib_strided_dvarianceyc( const int64_t N, const double correction, const double *X, const int64_t stride ) {
     40 	double sum;
     41 	int64_t ix;
     42 	int64_t i;
     43 	double di;
     44 	double S;
     45 	double v;
     46 	double n;
     47 	double d;
     48 
     49 	n = (double)N - correction;
     50 	if ( N <= 0 || n <= 0.0 ) {
     51 		return 0.0 / 0.0; // NaN
     52 	}
     53 	if ( N == 1 || stride == 0 ) {
     54 		return 0.0;
     55 	}
     56 	if ( stride < 0 ) {
     57 		ix = (1-N) * stride;
     58 	} else {
     59 		ix = 0;
     60 	}
     61 	sum = X[ ix ];
     62 	ix += stride;
     63 	S = 0.0;
     64 	for ( i = 2; i <= N; i++ ) {
     65 		di = (double)i;
     66 		v = X[ ix ];
     67 		sum += v;
     68 		d = (di*v) - sum;
     69 		S += (1.0/(di*(di-1.0))) * d * d;
     70 		ix += stride;
     71 	}
     72 	return S / n;
     73 }