dnanvarianceyc.c (2386B)
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/dnanvarianceyc.h" 20 #include <stdint.h> 21 22 /** 23 * Computes the variance of a double-precision floating-point strided array ignoring `NaN` values and 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_dnanvarianceyc( const int64_t N, const double correction, const double *X, const int64_t stride ) { 40 double sum; 41 int64_t ix; 42 double nc; 43 double n; 44 double S; 45 double v; 46 double d; 47 double i; 48 49 if ( N <= 0 ) { 50 return 0.0 / 0.0; // NaN 51 } 52 if ( N == 1 || stride == 0 ) { 53 v = X[ 0 ]; 54 if ( v == v && (double)N-correction > 0.0 ) { 55 return 0.0; 56 } 57 return 0.0 / 0.0; // NaN 58 } 59 if ( stride < 0 ) { 60 ix = (1-N) * stride; 61 } else { 62 ix = 0; 63 } 64 // Find the first non-NaN element... 65 for ( i = 0; i < N; i++ ) { 66 v = X[ ix ]; 67 if ( v == v ) { 68 break; 69 } 70 ix += stride; 71 } 72 if ( i == N ) { 73 return 0.0 / 0.0; // NaN 74 } 75 ix += stride; 76 sum = v; 77 S = 0.0; 78 n = 1.0; 79 i += 1; 80 for (; i < N; i++ ) { 81 v = X[ ix ]; 82 if ( v == v ) { 83 n += 1.0; 84 sum += v; 85 d = (n*v) - sum; 86 S += (1.0/(n*(n-1.0))) * d * d; 87 } 88 ix += stride; 89 } 90 nc = n - correction; 91 if ( nc <= 0.0 ) { 92 return 0.0 / 0.0; // NaN 93 } 94 return S / nc; 95 }