loess.hpp

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#ifndef LOESS_H_
#define LOESS_H_

 
typedef struct {
    size_t *items;
    size_t count;
    size_t capacity;
} Window;
 
extern bool loess_debug;
 
/*
 * This enum defines the types of weight functions available for assigning weights to data points. 
 * The choice of weight function determines how influence is assigned to observations based on their 
 * proximity to the central point at which smoothing is performed. 
 */
typedef enum {
    WEIGHT_TRICUBE, // defined as $(1 - |x|^3)^3$ for $|x| < 1$ 
    WEIGHT_BISQUARE, // defined as $(1 - |x|^2)^2$ for $|x| < 1$ 
} WEIGHT_FUNC;
 
/*
 * Enumeration of numerical methods for solving linear least squares problem:
 *   (X^T W X) beta = X^T W Y 
 */ 
typedef enum {
    // Uses complete orthogonal decomposition to compute the pseudo-inverse of the matrix (X^T W X) 
    LS_COMPLETE_ORTHOGONAL_DECOMPOSITION,
    // fastest out of variants of QR decompositions, but maybe unstable if the matrix is not rull rank 
    LS_QR_NO_PIVOTING,
    // is usually the fastest. However, if the matrix is even mildly ill-conditioned, this is not a good method. It loses roughly twice as many digits of accuracy using the normal equation, compared to the more stable methods mentioned above. 
    LS_CHOLESKY_SOLVER,
} LS_METHOD; 
 
typedef struct {
    size_t degree;   // degree of local polynomial [recommended: 2-3]
    size_t ws_min;   // minimum window size 
    double ws_step;  // window size step
    size_t ws_delay; // optional: the index at which the window is starting to increase
    size_t ws_cap;   // optional: cap on window size [not found useful in most cases] 
} Smoothing_Config;
 
extern WEIGHT_FUNC loess_weight;
 
#ifdef __cplusplus
extern "C" {
#endif // __cplusplus
 
void loess_init(double *x, double *y, size_t len);
double loess_estimate(double x, size_t window_size, size_t degree);
double *loess_create_grid(double xmin, double xmax, size_t npoints);
double *loess_apply_smoothing(Smoothing_Config *config);
void loess_free();
 
#ifdef __cplusplus
}
#endif // __cplusplus
 
#endif // LOESS_H_