From a133c9c3b637b1dbe7b5b053f7e2572c1950cead Mon Sep 17 00:00:00 2001
From: Lennart Weller <lhw@ring0.de>
Date: Thu, 27 Jul 2017 11:55:47 +0200
Subject: New upstream version 1.7.0+dfsg

---
 src/statistical.c | 459 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 459 insertions(+)
 create mode 100644 src/statistical.c

(limited to 'src/statistical.c')

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;
+}
-- 
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