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Diffstat (limited to 'src/statistical.c')
| -rw-r--r-- | src/statistical.c | 459 |
1 files changed, 459 insertions, 0 deletions
diff --git a/src/statistical.c b/src/statistical.c new file mode 100644 index 000000000..807bc25ea --- /dev/null +++ b/src/statistical.c @@ -0,0 +1,459 @@ +#include "common.h" + +// -------------------------------------------------------------------------------------------------------------------- + +inline long double sum_and_count(long double *series, size_t entries, size_t *count) { + if(unlikely(entries == 0)) { + if(likely(count)) + *count = 0; + + return NAN; + } + + if(unlikely(entries == 1)) { + if(likely(count)) + *count = (isnan(series[0])?0:1); + + return series[0]; + } + + size_t i, c = 0; + long double sum = 0; + + for(i = 0; i < entries ; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + c++; + sum += value; + } + + if(likely(count)) + *count = c; + + if(unlikely(c == 0)) + return NAN; + + return sum; +} + +inline long double sum(long double *series, size_t entries) { + return sum_and_count(series, entries, NULL); +} + +inline long double average(long double *series, size_t entries) { + size_t count = 0; + long double sum = sum_and_count(series, entries, &count); + + if(unlikely(count == 0)) + return NAN; + + return sum / (long double)count; +} + +// -------------------------------------------------------------------------------------------------------------------- + +long double moving_average(long double *series, size_t entries, size_t period) { + if(unlikely(period <= 0)) + return 0.0; + + size_t i, count; + long double sum = 0, avg = 0; + long double p[period]; + + for(count = 0; count < period ; count++) + p[count] = 0.0; + + for(i = 0, count = 0; i < entries; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + + if(unlikely(count < period)) { + sum += value; + avg = (count == period - 1) ? sum / (long double)period : 0; + } + else { + sum = sum - p[count % period] + value; + avg = sum / (long double)period; + } + + p[count % period] = value; + count++; + } + + return avg; +} + +// -------------------------------------------------------------------------------------------------------------------- + +static int qsort_compare(const void *a, const void *b) { + long double *p1 = (long double *)a, *p2 = (long double *)b; + long 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(long double *series, size_t entries) { + qsort(series, entries, sizeof(long double), qsort_compare); +} + +inline long double *copy_series(long double *series, size_t entries) { + long double *copy = mallocz(sizeof(long double) * entries); + memcpy(copy, series, sizeof(long double) * entries); + return copy; +} + +long double median_on_sorted_series(long 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; + + long double avg; + if(entries % 2 == 0) { + size_t m = entries / 2; + avg = (series[m] + series[m + 1]) / 2; + } + else { + avg = series[entries / 2]; + } + + return avg; +} + +long double median(long 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; + + long double *copy = copy_series(series, entries); + sort_series(copy, entries); + + long double avg = median_on_sorted_series(copy, entries); + + freez(copy); + return avg; +} + +// -------------------------------------------------------------------------------------------------------------------- + +long double moving_median(long double *series, size_t entries, size_t period) { + if(entries <= period) + return median(series, entries); + + long double *data = copy_series(series, entries); + + size_t i; + for(i = period; i < entries; i++) { + data[i - period] = median(&series[i - period], period); + } + + long double avg = median(data, entries - period); + freez(data); + return avg; +} + +// -------------------------------------------------------------------------------------------------------------------- + +// http://stackoverflow.com/a/15150143/4525767 +long double running_median_estimate(long double *series, size_t entries) { + long double median = 0.0f; + long double average = 0.0f; + size_t i; + + for(i = 0; i < entries ; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + + average += ( value - average ) * 0.1f; // rough running average. + median += copysignl( average * 0.01, value - median ); + } + + return median; +} + +// -------------------------------------------------------------------------------------------------------------------- + +long double standard_deviation(long double *series, size_t entries) { + if(unlikely(entries < 1)) + return NAN; + + if(unlikely(entries == 1)) + return series[0]; + + size_t i, count = 0; + long double sum = 0; + + for(i = 0; i < entries ; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + + count++; + sum += value; + } + + if(unlikely(count == 0)) + return NAN; + + if(unlikely(count == 1)) + return sum; + + long double average = sum / (long double)count; + + for(i = 0, count = 0, sum = 0; i < entries ; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + + count++; + sum += powl(value - average, 2); + } + + if(unlikely(count == 0)) + return NAN; + + if(unlikely(count == 1)) + return average; + + long double variance = sum / (long double)(count - 1); // remove -1 to have a population stddev + + long double stddev = sqrtl(variance); + return stddev; +} + +// -------------------------------------------------------------------------------------------------------------------- + +long double single_exponential_smoothing(long double *series, size_t entries, long double alpha) { + size_t i, count = 0; + long double level = 0, sum = 0; + + if(unlikely(isnan(alpha))) + alpha = 0.3; + + for(i = 0; i < entries ; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + count++; + + sum += value; + + long double last_level = level; + level = alpha * value + (1.0 - alpha) * last_level; + } + + return level; +} + +// -------------------------------------------------------------------------------------------------------------------- + +// http://grisha.org/blog/2016/02/16/triple-exponential-smoothing-forecasting-part-ii/ +long double double_exponential_smoothing(long double *series, size_t entries, long double alpha, long double beta, long double *forecast) { + size_t i, count = 0; + long double level = series[0], trend, sum; + + if(unlikely(isnan(alpha))) + alpha = 0.3; + + if(unlikely(isnan(beta))) + beta = 0.05; + + if(likely(entries > 1)) + trend = series[1] - series[0]; + else + trend = 0; + + sum = series[0]; + + for(i = 1; i < entries ; i++) { + long double value = series[i]; + if(unlikely(isnan(value) || isinf(value))) continue; + count++; + + sum += value; + + long 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( + long double *series, + int entries, // start_time + h + + long double alpha, // alpha parameter of Holt-Winters Filter. + long double beta, // beta parameter of Holt-Winters Filter. If set to 0, the function will do exponential smoothing. + long double gamma, // gamma parameter used for the seasonal component. If set to 0, an non-seasonal model is fitted. + + int *seasonal, + int *period, + long double *a, // Start value for level (a[0]). + long double *b, // Start value for trend (b[0]). + long double *s, // Vector of start values for the seasonal component (s_1[0] ... s_p[0]) + + /* return values */ + long double *SSE, // The final sum of squared errors achieved in optimizing + long double *level, // Estimated values for the level component (size entries - t + 2) + long double *trend, // Estimated values for the trend component (size entries - t + 2) + long double *season // Estimated values for the seasonal component (size entries - t + 2) +) +{ + if(unlikely(entries < 4)) + return 0; + + int start_time = 2; + + long 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(long 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; +} + +long double holtwinters(long double *series, size_t entries, long double alpha, long double beta, long double gamma, long 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; + long double a0 = series[0]; + long double b0 = 0; + long double s[] = {}; + + long double errors = 0.0; + size_t nb_computations = entries; + long double *estimated_level = callocz(nb_computations, sizeof(long double)); + long double *estimated_trend = callocz(nb_computations, sizeof(long double)); + long double *estimated_season = callocz(nb_computations, sizeof(long double)); + + int ret = __HoltWinters( + series, + (int)entries, + alpha, + beta, + gamma, + &seasonal, + &period, + &a0, + &b0, + s, + &errors, + estimated_level, + estimated_trend, + estimated_season + ); + + long 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; +} |