src/libnetdata/statistical/statistical.c
// SPDX-License-Identifier: GPL-3.0-or-later
#include "../libnetdata.h"
NETDATA_DOUBLE default_single_exponential_smoothing_alpha = 0.1;
void log_series_to_stderr(NETDATA_DOUBLE *series, size_t entries, NETDATA_DOUBLE result, const char *msg) {
const NETDATA_DOUBLE *value, *end = &series[entries];
fprintf(stderr, "%s of %zu entries [ ", msg, entries);
for(value = series; value < end ;value++) {
if(value != series) fprintf(stderr, ", ");
fprintf(stderr, "%" NETDATA_DOUBLE_MODIFIER, *value);
}
fprintf(stderr, " ] results in " NETDATA_DOUBLE_FORMAT "\n", result);
}
// --------------------------------------------------------------------------------------------------------------------
inline NETDATA_DOUBLE sum_and_count(const NETDATA_DOUBLE *series, size_t entries, size_t *count) {
const NETDATA_DOUBLE *value, *end = &series[entries];
NETDATA_DOUBLE sum = 0;
size_t c = 0;
for(value = series; value < end ; value++) {
if(netdata_double_isnumber(*value)) {
sum += *value;
c++;
}
}
if(unlikely(!c)) sum = NAN;
if(likely(count)) *count = c;
return sum;
}
inline NETDATA_DOUBLE sum(const NETDATA_DOUBLE *series, size_t entries) {
return sum_and_count(series, entries, NULL);
}
inline NETDATA_DOUBLE average(const NETDATA_DOUBLE *series, size_t entries) {
size_t count = 0;
NETDATA_DOUBLE sum = sum_and_count(series, entries, &count);
if(unlikely(!count)) return NAN;
return sum / (NETDATA_DOUBLE)count;
}
// --------------------------------------------------------------------------------------------------------------------
NETDATA_DOUBLE moving_average(const NETDATA_DOUBLE *series, size_t entries, size_t period) {
if(unlikely(period <= 0))
return 0.0;
size_t i, count;
NETDATA_DOUBLE sum = 0, avg = 0;
NETDATA_DOUBLE p[period];
for(count = 0; count < period ; count++)
p[count] = 0.0;
for(i = 0, count = 0; i < entries; i++) {
NETDATA_DOUBLE value = series[i];
if(unlikely(!netdata_double_isnumber(value))) continue;
if(unlikely(count < period)) {
sum += value;
avg = (count == period - 1) ? sum / (NETDATA_DOUBLE)period : 0;
}
else {
sum = sum - p[count % period] + value;
avg = sum / (NETDATA_DOUBLE)period;
}
p[count % period] = value;
count++;
}
return avg;
}
// --------------------------------------------------------------------------------------------------------------------
static int qsort_compare(const void *a, const void *b) {
NETDATA_DOUBLE *p1 = (NETDATA_DOUBLE *)a, *p2 = (NETDATA_DOUBLE *)b;
NETDATA_DOUBLE n1 = *p1, n2 = *p2;
if(unlikely(isnan(n1) || isnan(n2))) {
if(isnan(n1) && !isnan(n2)) return -1;
if(!isnan(n1) && isnan(n2)) return 1;
return 0;
}
if(unlikely(isinf(n1) || isinf(n2))) {
if(!isinf(n1) && isinf(n2)) return -1;
if(isinf(n1) && !isinf(n2)) return 1;
return 0;
}
if(unlikely(n1 < n2)) return -1;
if(unlikely(n1 > n2)) return 1;
return 0;
}
inline void sort_series(NETDATA_DOUBLE *series, size_t entries) {
qsort(series, entries, sizeof(NETDATA_DOUBLE), qsort_compare);
}
inline NETDATA_DOUBLE *copy_series(const NETDATA_DOUBLE *series, size_t entries) {
NETDATA_DOUBLE *copy = mallocz(sizeof(NETDATA_DOUBLE) * entries);
memcpy(copy, series, sizeof(NETDATA_DOUBLE) * entries);
return copy;
}
NETDATA_DOUBLE median_on_sorted_series(const NETDATA_DOUBLE *series, size_t entries) {
if(unlikely(entries == 0)) return NAN;
if(unlikely(entries == 1)) return series[0];
if(unlikely(entries == 2)) return (series[0] + series[1]) / 2;
NETDATA_DOUBLE average;
if(entries % 2 == 0) {
size_t m = entries / 2;
average = (series[m] + series[m + 1]) / 2;
}
else {
average = series[entries / 2];
}
return average;
}
NETDATA_DOUBLE median(const NETDATA_DOUBLE *series, size_t entries) {
if(unlikely(entries == 0)) return NAN;
if(unlikely(entries == 1)) return series[0];
if(unlikely(entries == 2))
return (series[0] + series[1]) / 2;
NETDATA_DOUBLE *copy = copy_series(series, entries);
sort_series(copy, entries);
NETDATA_DOUBLE avg = median_on_sorted_series(copy, entries);
freez(copy);
return avg;
}
// --------------------------------------------------------------------------------------------------------------------
NETDATA_DOUBLE moving_median(const NETDATA_DOUBLE *series, size_t entries, size_t period) {
if(entries <= period)
return median(series, entries);
NETDATA_DOUBLE *data = copy_series(series, entries);
size_t i;
for(i = period; i < entries; i++) {
data[i - period] = median(&series[i - period], period);
}
NETDATA_DOUBLE avg = median(data, entries - period);
freez(data);
return avg;
}
// --------------------------------------------------------------------------------------------------------------------
// http://stackoverflow.com/a/15150143/4525767
NETDATA_DOUBLE running_median_estimate(const NETDATA_DOUBLE *series, size_t entries) {
NETDATA_DOUBLE median = 0.0f;
NETDATA_DOUBLE average = 0.0f;
size_t i;
for(i = 0; i < entries ; i++) {
NETDATA_DOUBLE value = series[i];
if(unlikely(!netdata_double_isnumber(value))) continue;
average += ( value - average ) * 0.1f; // rough running average.
median += copysignndd( average * 0.01, value - median );
}
return median;
}
// --------------------------------------------------------------------------------------------------------------------
NETDATA_DOUBLE standard_deviation(const NETDATA_DOUBLE *series, size_t entries) {
if(unlikely(entries == 0)) return NAN;
if(unlikely(entries == 1)) return series[0];
const NETDATA_DOUBLE *value, *end = &series[entries];
size_t count;
NETDATA_DOUBLE sum;
for(count = 0, sum = 0, value = series ; value < end ;value++) {
if(likely(netdata_double_isnumber(*value))) {
count++;
sum += *value;
}
}
if(unlikely(count == 0)) return NAN;
if(unlikely(count == 1)) return sum;
NETDATA_DOUBLE average = sum / (NETDATA_DOUBLE)count;
for(count = 0, sum = 0, value = series ; value < end ;value++) {
if(netdata_double_isnumber(*value)) {
count++;
sum += powndd(*value - average, 2);
}
}
if(unlikely(count == 0)) return NAN;
if(unlikely(count == 1)) return average;
NETDATA_DOUBLE variance = sum / (NETDATA_DOUBLE)(count); // remove -1 from count to have a population stddev
NETDATA_DOUBLE stddev = sqrtndd(variance);
return stddev;
}
// --------------------------------------------------------------------------------------------------------------------
NETDATA_DOUBLE single_exponential_smoothing(const NETDATA_DOUBLE *series, size_t entries, NETDATA_DOUBLE alpha) {
if(unlikely(entries == 0))
return NAN;
if(unlikely(isnan(alpha)))
alpha = default_single_exponential_smoothing_alpha;
const NETDATA_DOUBLE *value = series, *end = &series[entries];
NETDATA_DOUBLE level = (1.0 - alpha) * (*value);
for(value++ ; value < end; value++) {
if(likely(netdata_double_isnumber(*value)))
level = alpha * (*value) + (1.0 - alpha) * level;
}
return level;
}
NETDATA_DOUBLE single_exponential_smoothing_reverse(const NETDATA_DOUBLE *series, size_t entries, NETDATA_DOUBLE alpha) {
if(unlikely(entries == 0))
return NAN;
if(unlikely(isnan(alpha)))
alpha = default_single_exponential_smoothing_alpha;
const NETDATA_DOUBLE *value = &series[entries -1];
NETDATA_DOUBLE level = (1.0 - alpha) * (*value);
for(value++ ; value >= series; value--) {
if(likely(netdata_double_isnumber(*value)))
level = alpha * (*value) + (1.0 - alpha) * level;
}
return level;
}
// --------------------------------------------------------------------------------------------------------------------
// http://grisha.org/blog/2016/02/16/triple-exponential-smoothing-forecasting-part-ii/
NETDATA_DOUBLE double_exponential_smoothing(const NETDATA_DOUBLE *series, size_t entries,
NETDATA_DOUBLE alpha,
NETDATA_DOUBLE beta,
NETDATA_DOUBLE *forecast) {
if(unlikely(entries == 0))
return NAN;
NETDATA_DOUBLE level, trend;
if(unlikely(isnan(alpha)))
alpha = 0.3;
if(unlikely(isnan(beta)))
beta = 0.05;
level = series[0];
if(likely(entries > 1))
trend = series[1] - series[0];
else
trend = 0;
const NETDATA_DOUBLE *value = series;
for(value++ ; value >= series; value--) {
if(likely(netdata_double_isnumber(*value))) {
NETDATA_DOUBLE last_level = level;
level = alpha * *value + (1.0 - alpha) * (level + trend);
trend = beta * (level - last_level) + (1.0 - beta) * trend;
}
}
if(forecast)
*forecast = level + trend;
return level;
}
// --------------------------------------------------------------------------------------------------------------------
/*
* Based on th R implementation
*
* a: level component
* b: trend component
* s: seasonal component
*
* Additive:
*
* Yhat[t+h] = a[t] + h * b[t] + s[t + 1 + (h - 1) mod p],
* a[t] = α (Y[t] - s[t-p]) + (1-α) (a[t-1] + b[t-1])
* b[t] = β (a[t] - a[t-1]) + (1-β) b[t-1]
* s[t] = γ (Y[t] - a[t]) + (1-γ) s[t-p]
*
* Multiplicative:
*
* Yhat[t+h] = (a[t] + h * b[t]) * s[t + 1 + (h - 1) mod p],
* a[t] = α (Y[t] / s[t-p]) + (1-α) (a[t-1] + b[t-1])
* b[t] = β (a[t] - a[t-1]) + (1-β) b[t-1]
* s[t] = γ (Y[t] / a[t]) + (1-γ) s[t-p]
*/
static int __HoltWinters(
const NETDATA_DOUBLE *series,
int entries, // start_time + h
NETDATA_DOUBLE alpha, // alpha parameter of Holt-Winters Filter.
NETDATA_DOUBLE
beta, // beta parameter of Holt-Winters Filter. If set to 0, the function will do exponential smoothing.
NETDATA_DOUBLE
gamma, // gamma parameter used for the seasonal component. If set to 0, an non-seasonal model is fitted.
const int *seasonal,
const int *period,
const NETDATA_DOUBLE *a, // Start value for level (a[0]).
const NETDATA_DOUBLE *b, // Start value for trend (b[0]).
NETDATA_DOUBLE *s, // Vector of start values for the seasonal component (s_1[0] ... s_p[0])
/* return values */
NETDATA_DOUBLE *SSE, // The final sum of squared errors achieved in optimizing
NETDATA_DOUBLE *level, // Estimated values for the level component (size entries - t + 2)
NETDATA_DOUBLE *trend, // Estimated values for the trend component (size entries - t + 2)
NETDATA_DOUBLE *season // Estimated values for the seasonal component (size entries - t + 2)
)
{
if(unlikely(entries < 4))
return 0;
int start_time = 2;
NETDATA_DOUBLE res = 0, xhat = 0, stmp = 0;
int i, i0, s0;
/* copy start values to the beginning of the vectors */
level[0] = *a;
if(beta > 0) trend[0] = *b;
if(gamma > 0) memcpy(season, s, *period * sizeof(NETDATA_DOUBLE));
for(i = start_time - 1; i < entries; i++) {
/* indices for period i */
i0 = i - start_time + 2;
s0 = i0 + *period - 1;
/* forecast *for* period i */
xhat = level[i0 - 1] + (beta > 0 ? trend[i0 - 1] : 0);
stmp = gamma > 0 ? season[s0 - *period] : (*seasonal != 1);
if (*seasonal == 1)
xhat += stmp;
else
xhat *= stmp;
/* Sum of Squared Errors */
res = series[i] - xhat;
*SSE += res * res;
/* estimate of level *in* period i */
if (*seasonal == 1)
level[i0] = alpha * (series[i] - stmp)
+ (1 - alpha) * (level[i0 - 1] + trend[i0 - 1]);
else
level[i0] = alpha * (series[i] / stmp)
+ (1 - alpha) * (level[i0 - 1] + trend[i0 - 1]);
/* estimate of trend *in* period i */
if (beta > 0)
trend[i0] = beta * (level[i0] - level[i0 - 1])
+ (1 - beta) * trend[i0 - 1];
/* estimate of seasonal component *in* period i */
if (gamma > 0) {
if (*seasonal == 1)
season[s0] = gamma * (series[i] - level[i0])
+ (1 - gamma) * stmp;
else
season[s0] = gamma * (series[i] / level[i0])
+ (1 - gamma) * stmp;
}
}
return 1;
}
NETDATA_DOUBLE holtwinters(const NETDATA_DOUBLE *series, size_t entries,
NETDATA_DOUBLE alpha,
NETDATA_DOUBLE beta,
NETDATA_DOUBLE gamma,
NETDATA_DOUBLE *forecast) {
if(unlikely(isnan(alpha)))
alpha = 0.3;
if(unlikely(isnan(beta)))
beta = 0.05;
if(unlikely(isnan(gamma)))
gamma = 0;
int seasonal = 0;
int period = 0;
NETDATA_DOUBLE a0 = series[0];
NETDATA_DOUBLE b0 = 0;
NETDATA_DOUBLE s[] = {};
NETDATA_DOUBLE errors = 0.0;
size_t nb_computations = entries;
NETDATA_DOUBLE *estimated_level = callocz(nb_computations, sizeof(NETDATA_DOUBLE));
NETDATA_DOUBLE *estimated_trend = callocz(nb_computations, sizeof(NETDATA_DOUBLE));
NETDATA_DOUBLE *estimated_season = callocz(nb_computations, sizeof(NETDATA_DOUBLE));
int ret = __HoltWinters(
series,
(int)entries,
alpha,
beta,
gamma,
&seasonal,
&period,
&a0,
&b0,
s,
&errors,
estimated_level,
estimated_trend,
estimated_season
);
NETDATA_DOUBLE value = estimated_level[nb_computations - 1];
if(forecast)
*forecast = 0.0;
freez(estimated_level);
freez(estimated_trend);
freez(estimated_season);
if(!ret)
return 0.0;
return value;
}