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// Hull Ma
//
// hull_ma
//
// Hull Moving Average
//
// HMA = WMA(2*WMA(n/2) - WMA(n), √n)
//
// Inputs: 1
// Outputs: 1
// Constants: 1
#include <math.h>
#include <stdlib.h>
#include "ts.h"
typedef struct {
uint_t k;
} ts_hull_ma_params_t;
ts_parameter_t const ts_hull_ma_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 1, .params_size = sizeof(ts_hull_ma_params_t) };
uint_t ts_hull_ma_offset( ts_constant_t const *c )
{
( void )c;
return ( c ? ((ts_hull_ma_params_t *)c)->k + (uint_t)sqrt((fp_t)((ts_hull_ma_params_t *)c)->k) - 2 : 0 );
}
int ts_hull_ma(
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_hull_ma_p );
if ( !c ) return -1;
TS_CHECK_INPUT(x, x_n, n);
uint_t k = ((ts_hull_ma_params_t *)c)->k;
if (k < 2) return -1;
uint_t half_k = k / 2;
uint_t sqrt_k = (uint_t)sqrt((fp_t)k);
if (sqrt_k < 1) sqrt_k = 1;
fp_t *wma_half = calloc( n, sizeof( fp_t ) );
fp_t *wma_full = calloc( n, sizeof( fp_t ) );
if ( !wma_half || !wma_full ) { free( wma_half ); free( wma_full ); return -1; }
/* WMA(n/2) */
fp_t wt_half = (fp_t)half_k * ((fp_t)half_k + 1.0) / 2.0;
for ( uint_t i = half_k - 1; i < n; ++i )
{
fp_t s = 0;
for ( uint_t j = 0; j < half_k; ++j )
s += x[0][i - j] * (fp_t)(half_k - j);
wma_half[i] = s / wt_half;
}
/* WMA(n) */
fp_t wt_full = (fp_t)k * ((fp_t)k + 1.0) / 2.0;
for ( uint_t i = k - 1; i < n; ++i )
{
fp_t s = 0;
for ( uint_t j = 0; j < k; ++j )
s += x[0][i - j] * (fp_t)(k - j);
wma_full[i] = s / wt_full;
}
/* HMA = WMA(sqrt(n), 2*WMA(n/2) - WMA(n)) */
fp_t wt_sqrt = (fp_t)sqrt_k * ((fp_t)sqrt_k + 1.0) / 2.0;
uint_t offset = k + sqrt_k - 2;
for (uint_t j = 0; j < n && j < offset; ++j) y[0][j] = NAN;
for ( uint_t i = offset; i < n; ++i )
{
fp_t s = 0;
for ( uint_t j = 0; j < sqrt_k; ++j )
{
fp_t diff = 2.0 * wma_half[i - j] - wma_full[i - j];
s += diff * (fp_t)(sqrt_k - j);
}
y[0][i] = s / wt_sqrt;
}
free( wma_half );
free( wma_full );
return 0;
}
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