// Hurst Exponent
//
// hurst_exponent
//
// Hurst exponent via R/S analysis
//
// H = slope of linear regression of log(R/S) vs log(n)
//
// Inputs:    1
// Outputs:   1
// Constants: 1


#include <math.h>
#include "ts.h"

typedef struct {
    uint_t k;
} ts_hurst_exponent_params_t;

ts_parameter_t const ts_hurst_exponent_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 1, .params_size = sizeof(ts_hurst_exponent_params_t) };

uint_t ts_hurst_exponent_offset( ts_constant_t const *c )
{
	( void )c;
	return ( 0 );
}

int ts_hurst_exponent(
	fp_t * const *y, uint_t y_n,
	fp_t const * const *x, uint_t x_n,
	uint_t n, ts_constant_t const *c
)
{
	TS_PROLOGUE( ts_hurst_exponent_p );
	if ( !c ) return -1;
    uint_t k = ((ts_hurst_exponent_params_t *)c)->k;
    if (k == 0 || k > n) return -1;

    for ( uint_t i = 0; i < n; ++i )
    {
        if (i + 1 < k) {
            y[0][i] = 0;
            continue;
        }

        uint_t data_len = i + 1;
        uint_t num_lags = 0;
        fp_t sum_log_s = 0;
        fp_t sum_log_rs = 0;
        fp_t sum_log_s2 = 0;
        fp_t sum_log_s_log_rs = 0;

        for ( uint_t s = 2; s <= k && s <= data_len / 2; ++s )
        {
            uint_t ns = data_len / s;
            if (ns == 0) continue;

            fp_t total_log_rs = 0;
            uint_t valid_segs = 0;

            for ( uint_t seg = 0; seg < ns; ++seg )
            {
                uint_t start = seg * s;
                uint_t end = start + s;
                if (end > data_len) break;

                fp_t mean = 0;
                for ( uint_t p = start; p < end; ++p )
                    mean += x[0][p];
                mean /= (fp_t)s;

                fp_t cumsum = 0;
                fp_t max_dev = 0, min_dev = 0;
                for ( uint_t p = start; p < end; ++p )
                {
                    cumsum += x[0][p] - mean;
                    if (cumsum > max_dev) max_dev = cumsum;
                    if (cumsum < min_dev) min_dev = cumsum;
                }

                fp_t r = max_dev - min_dev;
                fp_t std = 0;
                for ( uint_t p = start; p < end; ++p )
                {
                    fp_t d = x[0][p] - mean;
                    std += d * d;
                }
                std = sqrt(std / (fp_t)s);

                if (std > 0 && r > 0) {
                    total_log_rs += log(r / std);
                    valid_segs++;
                }
            }

            if (valid_segs > 0) {
                fp_t log_s = log((fp_t)s);
                fp_t mean_log_rs = total_log_rs / (fp_t)valid_segs;
                sum_log_s += log_s;
                sum_log_rs += mean_log_rs;
                sum_log_s2 += log_s * log_s;
                sum_log_s_log_rs += log_s * mean_log_rs;
                num_lags++;
            }
        }

        if (num_lags >= 2) {
            fp_t denom = (fp_t)num_lags * sum_log_s2 - sum_log_s * sum_log_s;
            if (fabs(denom) > 1e-300) {
                fp_t h = ((fp_t)num_lags * sum_log_s_log_rs - sum_log_s * sum_log_rs) / denom;
                y[0][i] = h;
            } else {
                y[0][i] = 0;
            }
        } else {
            y[0][i] = 0;
        }
    }
	return 0;
}