
/***********************************************************************
 *
 * MODULE:       v.surf.bspline
 *
 * AUTHOR(S):    Roberto Antolin
 *
 * PURPOSE:      Spline Interpolation and cross correlation
 *
 * COPYRIGHT:    (C) 2006 by Politecnico di Milano -
 *			     Polo Regionale di Como
 *
 *               This program is free software under the
 *               GNU General Public License (>=v2).
 *               Read the file COPYING that comes with GRASS
 *               for details.
 *
 **************************************************************************/

 /*INCLUDES*/
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "bspline.h"

#define NDATA_MAX 100
#define PARAM_LAMBDA 6
#define PARAM_SPLINE 0
#define SWAP(a, b) {double t=a; a=b; b=t;}

/*-------------------------------------------------------------------------------------------*/
int cross_correlation(struct Map_info *Map, double passWE, double passNS)
    /*
       Map: Vector map from which cross-crorrelation will take values
       passWE: spline step in West-East direction
       passNS: spline step in North-South direction

       RETURN:
       TRUE on success
       FALSE on failure
     */
{
    int bilin = TRUE;		/*booleans */
    int nsplx, nsply, nparam_spl, ndata;
    double *mean, *rms, *stdev;

    /* double lambda[PARAM_LAMBDA] = { 0.0001, 0.001, 0.01, 0.1, 1.0, 10.0 }; */	/* Fixed values (by the moment) */
    double lambda[PARAM_LAMBDA] = { 0.0001, 0.001, 0.005, 0.01, 0.02, 0.05 };	/* Fixed values (by the moment) */
    /* a more exhaustive search:
    #define PARAM_LAMBDA 11
    double lambda[PARAM_LAMBDA] = { 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1.0, 5.0, 10.0 }; */

    double *TN, *Q, *parVect;	/* Interpolation and least-square vectors */
    double **N, **obsVect;	/* Interpolation and least-square matrix */

    struct Point *observ;
    struct Stats stat_vect;

    /*struct line_pnts *points; */
    /*struct line_cats *Cats; */
    struct Cell_head region;

    G_get_window(&region);

    extern int bspline_field;
    extern char *bspline_column;
    dbCatValArray cvarr;

    G_debug(5,
	    "CrossCorrelation: Some tests using different lambda_i values will be done");

    ndata = Vect_get_num_lines(Map);

    if (ndata > NDATA_MAX)
	G_warning(_("%d are too many points. "
		    "The cross validation would take too much time."), ndata);

    /*points = Vect_new_line_struct (); */
    /*Cats = Vect_new_cats_struct (); */

    /* Current region is read and points recorded into observ */
    observ = P_Read_Vector_Region_Map(Map, &region, &ndata, 1024, 1);
    G_debug(5, "CrossCorrelation: %d points read in region. ", ndata);
    G_verbose_message(_("%d points read in region"),
		      ndata);

    if (ndata > 50)
	G_warning(_("Maybe, it takes too long. "
		    "It will depend on how many points you are considering."));
    else
	G_debug(5, "CrossCorrelation: It shouldn't take too long.");

    if (ndata > 0) {		/* If at least one point is in the region */
	int i, j, lbd;		/* lbd: lambda index */
	int BW;	
	double mean_reg, *obs_mean;

	int nrec, ctype = 0, verbosity;
	struct field_info *Fi;
	dbDriver *driver_cats;

	mean = G_alloc_vector(PARAM_LAMBDA);	/* Alloc as much mean, rms and stdev values as the total */
	rms = G_alloc_vector(PARAM_LAMBDA);	/* number of parameter used used for cross validation */
	stdev = G_alloc_vector(PARAM_LAMBDA);

	verbosity = G_verbose(); /* store for later reset */

	/* Working with attributes */
	if (bspline_field > 0) {
	    db_CatValArray_init(&cvarr);

	    Fi = Vect_get_field(Map, bspline_field);
	    if (Fi == NULL)
	      G_fatal_error(_("Database connection not defined for layer %d"),
			    bspline_field);

	    driver_cats =
		db_start_driver_open_database(Fi->driver, Fi->database);
	    G_debug(1, _("CrossCorrelation: driver=%s db=%s"), Fi->driver,
		    Fi->database);

	    if (driver_cats == NULL)
		G_fatal_error(_("Unable to open database <%s> by driver <%s>"),
			      Fi->database, Fi->driver);

	    nrec =
		db_select_CatValArray(driver_cats, Fi->table, Fi->key,
				      bspline_column, NULL, &cvarr);
	    G_debug(3, "nrec = %d", nrec);

	    ctype = cvarr.ctype;
	    if (ctype != DB_C_TYPE_INT && ctype != DB_C_TYPE_DOUBLE)
		G_fatal_error(_("Column type not supported"));

	    if (nrec < 0)
		G_fatal_error(_("No records selected from table <%s> "),
			      Fi->table);

	    G_debug(1, "%d records selected from table",
		    nrec);

	    db_close_database_shutdown_driver(driver_cats);
	}

	/* Setting number of splines as a function of WE and SN spline steps */
	nsplx = ceil((region.east - region.west) / passWE);
	nsply = ceil((region.north - region.south) / passNS);
	nparam_spl = nsplx * nsply;	/* Total number of splines */

	if (nparam_spl > 22900)
	    G_fatal_error(_("Too many splines (%d x %d). "
			    "Consider changing spline steps \"sie=\" \"sin=\"."),
			  nsplx, nsply);

	BW = P_get_BandWidth(bilin, nsply);
	/**/
	    /*Least Squares system */
	    N = G_alloc_matrix(nparam_spl, BW);	/* Normal matrix */
	TN = G_alloc_vector(nparam_spl);	/* vector */
	parVect = G_alloc_vector(nparam_spl);	/* Parameters vector */
	obsVect = G_alloc_matrix(ndata, 3);	/* Observation vector */
	Q = G_alloc_vector(ndata);		/* "a priori" var-cov matrix */

	obs_mean = G_alloc_vector(ndata);
	stat_vect = alloc_Stats(ndata);

	for (lbd = 0; lbd < PARAM_LAMBDA; lbd++) {	/* For each lambda value */

	    G_message(_("Beginning cross validation with "
		        "lambda_i=%.4f ... (%d of %d)"), lambda[lbd],
		      lbd+1, PARAM_LAMBDA);

	    /*
	       How the cross correlation algorithm is done:
	       For each cycle, only the first ndata-1 "observ" elements are considered for the 
	       interpolation. Within every interpolation mean is calculated to lowering edge 
	       errors. The point left out will be used for an estimation. The error between the 
	       estimation and the observation is recorded for further statistics.
	       At the end of the cycle, the last point, that is, the ndata-1 index, and the point 
	       with j index are swapped.
	     */
	    for (j = 0; j < ndata; j++) {	/* Cross Correlation will use all ndata points */
		double out_x, out_y, out_z;	/* This point is left out */

		for (i = 0; i < ndata; i++) {	/* Each time, only the first ndata-1 points */
		    double dval;		/* are considered in the interpolation */

		    /* Setting obsVect vector & Q matrix */
		    Q[i] = 1;	/* Q=I */
		    obsVect[i][0] = observ[i].coordX;
		    obsVect[i][1] = observ[i].coordY;

		    if (bspline_field > 0) {
			int cat, ival, ret;

			/*type = Vect_read_line (Map, points, Cats, observ[i].lineID); */
			/*if ( !(type & GV_POINTS ) ) continue; */

			/*Vect_cat_get ( Cats, bspline_field, &cat ); */
			cat = observ[i].cat;

			if (cat < 0)
			    continue;

			if (ctype == DB_C_TYPE_INT) {
			    ret =
				db_CatValArray_get_value_int(&cvarr, cat,
							     &ival);
			    obsVect[i][2] = ival;
			    obs_mean[i] = ival;
			}
			else {	/* DB_C_TYPE_DOUBLE */
			    ret =
				db_CatValArray_get_value_double(&cvarr, cat,
								&dval);
			    obsVect[i][2] = dval;
			    obs_mean[i] = dval;
			}
			if (ret != DB_OK) {
			    G_warning(_("No record for point (cat = %d)"),
				      cat);
			    continue;
			}
		    }
		    else {
			obsVect[i][2] = observ[i].coordZ;
			obs_mean[i] = observ[i].coordZ;
		    }
		}		/* i index */

		/* Mean calculation for every point less the last one */
		mean_reg = calc_mean(obs_mean, ndata - 1);

		for (i = 0; i < ndata; i++)
		    obsVect[i][2] -= mean_reg;

		/* This is left out */
		out_x = observ[ndata - 1].coordX;
		out_y = observ[ndata - 1].coordY;
		out_z = obsVect[ndata - 1][2];

		if (bilin) {	/* Bilinear interpolation */
		    normalDefBilin(N, TN, Q, obsVect, passWE, passNS, nsplx,
				   nsply, region.west, region.south,
				   ndata - 1, nparam_spl, BW);
		    nCorrectGrad(N, lambda[lbd], nsplx, nsply, passWE,
				 passNS);
		}
		else {		/* Bicubic interpolation */
		    normalDefBicubic(N, TN, Q, obsVect, passWE, passNS, nsplx,
				     nsply, region.west, region.south,
				     ndata - 1, nparam_spl, BW);
		    nCorrectGrad(N, lambda[lbd], nsplx, nsply, passWE,
				 passNS);
		}

		/* 
		   if (bilin) interpolation (&interp, P_BILINEAR);
		   else interpolation (&interp, P_BICUBIC);
		 */
		G_set_verbose(G_verbose_min());
		G_math_solver_cholesky_sband(N, parVect, TN, nparam_spl, BW);
		G_set_verbose(verbosity);

		/* Estimation of j-point */
		if (bilin)
		    stat_vect.estima[j] =
			dataInterpolateBilin(out_x, out_y, passWE, passNS,
					     nsplx, nsply, region.west,
					     region.south, parVect);

		else
		    stat_vect.estima[j] =
			dataInterpolateBilin(out_x, out_y, passWE, passNS,
					     nsplx, nsply, region.west,
					     region.south, parVect);

		/* Difference between estimated and observated i-point */
		stat_vect.error[j] = out_z - stat_vect.estima[j];
		G_debug(1, "CrossCorrelation: stat_vect.error[%d]  =  %lf", j,
			stat_vect.error[j]);

		/* Once the last value is left out, it is swaped with j-value */
		observ = swap(observ, j, ndata - 1);

		G_percent(j, ndata, 2);
	    }

	    mean[lbd] = calc_mean(stat_vect.error, stat_vect.n_points);
	    rms[lbd] =
		calc_root_mean_square(stat_vect.error, stat_vect.n_points);
	    stdev[lbd] =
		calc_standard_deviation(stat_vect.error, stat_vect.n_points);

	    G_message(_("Mean = %.5lf"), mean[lbd]);
	    G_message(_("Root Mean Square (RMS) = %.5lf"),
		      rms[lbd]);
	    G_message("---");
	}			/* ENDFOR each lambda value */

	G_free_matrix(N);
	G_free_vector(TN);
	G_free_vector(Q);
	G_free_matrix(obsVect);
	G_free_vector(parVect);
#ifdef nodef
	/*TODO: if the minimum lambda is wanted, the function declaration must be changed */
	/* At this moment, consider rms only */
	rms_min = find_minimum(rms, &lbd_min);
	stdev_min = find_minimum(stdev, &lbd_min);

	/* Writing some output */
	G_message(_("Different number of splines and lambda_i values have "
		    "been taken for the cross correlation"));
	G_message(_("The minimum value for the test (rms=%lf) was "
		    "obtained with: lambda_i = %.3f"),
		  rms_min,
		  lambda[lbd_min]);

	*lambda_min = lambda[lbd_min];
#endif

	G_message(_("Table of results:"));
	fprintf(stdout, _("    lambda |       mean |        rms |\n"));
	for (lbd = 0; lbd < PARAM_LAMBDA; lbd++) {
	    fprintf(stdout, " %9.5f | %10.4f | %10.4f |\n", lambda[lbd],
		    mean[lbd], rms[lbd]);
	}
	
	G_free_vector(mean);
	G_free_vector(rms);
    }				/* ENDIF (ndata > 0) */
    else
	G_warning(_("No point lies into the current region"));

    G_free(observ);
    return TRUE;
}

#ifdef nodef
void interpolation(struct ParamInterp *interp, boolean bilin)
{
    if (bilin == P_BILINEAR) {	/* Bilinear interpolation */
	normalDefBilin(interp->N, interp->TN, interp->Q, interp->obsVect,
		       interp->stepE, interp->stepN, interp->nsplx,
		       interp->nsply, interp->region.west,
		       interp->region.south, interp->ndata,
		       interp->nparam_spl, interp->BW);

	nCorrectGrad(interp->N, interp->lambda[lbd], interp->nsplx,
		     interp->nsply, interp->stepE, interp->stepN);
    }
    else {			/* Bicubic interpolation */
	normalDefBicubic(interp->N, interp->TN, interp->Q, interp->obsVect,
			 interp->stepE, interp->stepN, interp->nsplx,
			 interp->nsply, interp->region.west,
			 interp->region.south, interp->ndata,
			 interp->nparam_spl, interp->BW);

	nCorrectGrad(interp->N, interp->lambda[lbd], interp->nsplx,
		     interp->nsply, interp->stepE, interp->stepN);
    }
    return TRUE;
}
#endif

double calc_mean(double *values, int nvalues)
{
    int i;
    double sum = .0;

    if (nvalues == 0)
	return .0;
    for (i = 0; i < nvalues; i++)
	sum += values[i];
    return sum / nvalues;
}


double calc_root_mean_square(double *values, int nvalues)
{
    int i;
    double rms, sum = .0;

    if (nvalues == 0)
	return .0;

    for (i = 0; i < nvalues; i++)
	sum += pow(values[i], 2) / nvalues;

    rms = sqrt(sum);
    return rms;

}

double calc_standard_deviation(double *values, int nvalues)
{
    double mean, rms, stdev;

    if (nvalues == 0)
	return .0;

    rms = calc_root_mean_square(values, nvalues);
    mean = calc_mean(values, nvalues);

    stdev = sqrt(pow(rms, 2) - pow(mean, 2));
    return stdev;
}

struct Stats alloc_Stats(int n)
{
    double *err, *stm;
    struct Stats stat;

    stat.n_points = n;
    err = (double *)G_calloc(n, sizeof(double));
    stm = (double *)G_calloc(n, sizeof(double));

    stat.error = err;
    stat.estima = stm;

    return stat;
}

double find_minimum(double *values, int *l_min)
{
    int l;
    double min;

    min = values[0];

    for (l = 0; l < PARAM_LAMBDA; l++) {
	if (min > values[l]) {
	    min = values[l];
	    *l_min = l;
	}
    }
    return min;
}

struct Point *swap(struct Point *point, int a, int b)
{
    /* Once the last value is left out, it is swaped with j-value */
    SWAP(point[a].coordX, point[b].coordX);
    SWAP(point[a].coordY, point[b].coordY);
    SWAP(point[a].coordZ, point[b].coordZ);
    SWAP(point[a].cat, point[b].cat);

    return point;
}
