81 lines
2.3 KiB
C
81 lines
2.3 KiB
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/base/dnanmeanwd.h"
|
|||
|
#include <stdint.h>
|
|||
|
|
|||
|
/**
|
|||
|
* Computes the arithmetic mean of a double-precision floating-point strided array, using Welford's algorithm and ignoring `NaN` values.
|
|||
|
*
|
|||
|
* ## Method
|
|||
|
*
|
|||
|
* - This implementation uses Welford's algorithm for efficient computation, which can be derived as follows
|
|||
|
*
|
|||
|
* ```tex
|
|||
|
* \begin{align*}
|
|||
|
* \mu_n &= \frac{1}{n} \sum_{i=0}^{n-1} x_i \\
|
|||
|
* &= \frac{1}{n} \biggl(x_{n-1} + \sum_{i=0}^{n-2} x_i \biggr) \\
|
|||
|
* &= \frac{1}{n} (x_{n-1} + (n-1)\mu_{n-1}) \\
|
|||
|
* &= \mu_{n-1} + \frac{1}{n} (x_{n-1} - \mu_{n-1})
|
|||
|
* \end{align*}
|
|||
|
* ```
|
|||
|
*
|
|||
|
* ## References
|
|||
|
*
|
|||
|
* - Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022](https://doi.org/10.1080/00401706.1962.10490022).
|
|||
|
* - van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961](https://doi.org/10.1145/362929.362961).
|
|||
|
*
|
|||
|
* @param N number of indexed elements
|
|||
|
* @param X input array
|
|||
|
* @param stride stride length
|
|||
|
* @return output value
|
|||
|
*/
|
|||
|
double stdlib_strided_dnanmeanwd( const int64_t N, const double *X, const int64_t stride ) {
|
|||
|
int64_t ix;
|
|||
|
int64_t i;
|
|||
|
int64_t n;
|
|||
|
double mu;
|
|||
|
double v;
|
|||
|
|
|||
|
if ( N <= 0 ) {
|
|||
|
return 0.0 / 0.0; // NaN
|
|||
|
}
|
|||
|
if ( N == 1 || stride == 0 ) {
|
|||
|
return X[ 0 ];
|
|||
|
}
|
|||
|
if ( stride < 0 ) {
|
|||
|
ix = (1-N) * stride;
|
|||
|
} else {
|
|||
|
ix = 0;
|
|||
|
}
|
|||
|
mu = 0.0;
|
|||
|
n = 0;
|
|||
|
for ( i = 0; i < N; i++ ) {
|
|||
|
v = X[ ix ];
|
|||
|
if ( v == v ) {
|
|||
|
n += 1;
|
|||
|
mu += ( v-mu ) / (double)n;
|
|||
|
}
|
|||
|
ix += stride;
|
|||
|
}
|
|||
|
if ( n == 0 ) {
|
|||
|
return 0.0 / 0.0; // NaN;
|
|||
|
}
|
|||
|
return mu;
|
|||
|
}
|