main.c

/**********************************************************************
 *
 * MODULE:       v.surf.bspline
 *
 * AUTHOR(S):    Roberto Antolin & Gonzalo Moreno
 *               update for grass7 by Markus Metz
 *
 * PURPOSE:      Spline Interpolation
 *
 * 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 <sys/types.h>
#include <sys/stat.h>
#include <fcntl.h>
#include "bspline.h"
#include <grass/N_pde.h>

#define SEGSIZE 64

/* GLOBAL VARIABLES */
int bspline_field;
char *bspline_column;

/*--------------------------------------------------------------------*/
int main(int argc, char *argv[])
{
    /* Variable declarations */
    int nsply, nsplx, nrows, ncols, nsplx_adj, nsply_adj;
    int nsubregion_col, nsubregion_row, subregion_row, subregion_col;
    int subregion = 0, nsubregions = 0;
    int last_row, last_column, grid, bilin, ext, flag_auxiliar,
        cross; /* booleans */
    double stepN, stepE, lambda, mean;
    double N_extension, E_extension, edgeE, edgeN;

    const char *mapset, *drv, *db, *vector, *map;
    char table_name[GNAME_MAX + 64], title[64];
    char xname[GNAME_MAX], xmapset[GMAPSET_MAX];

    int dim_vect, nparameters, BW;
    int *lineVect;            /* Vector restoring primitive's ID */
    double *TN, *Q, *parVect; /* Interpolating and least-square vectors */
    double **N, **obsVect;    /* Interpolation and least-square matrix */

    SEGMENT out_seg, mask_seg;
    char *out_file, *mask_file;
    double seg_size;
    int seg_mb, segments_in_memory;
    int have_mask;

    /* Structs declarations */
    int raster;
    struct Map_info In, In_ext, Out;
    struct History history;

    struct GModule *module;
    struct Option *in_opt, *in_ext_opt, *out_opt, *out_map_opt, *stepE_opt,
        *stepN_opt, *lambda_f_opt, *type_opt, *dfield_opt, *col_opt, *mask_opt,
        *memory_opt, *solver, *error, *iter;
    struct Flag *cross_corr_flag, *spline_step_flag;

    struct Reg_dimens dims;
    struct Cell_head elaboration_reg, original_reg;
    struct bound_box general_box, overlap_box, original_box;

    struct Point *observ;
    struct line_cats *Cats;
    dbCatValArray cvarr;

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

    /*----------------------------------------------------------------*/
    /* Options declarations */
    module = G_define_module();
    G_add_keyword(_("vector"));
    G_add_keyword(_("surface"));
    G_add_keyword(_("interpolation"));
    G_add_keyword(_("LIDAR"));
    module->description = _("Performs bicubic or bilinear spline interpolation "
                            "with Tykhonov regularization.");

    cross_corr_flag = G_define_flag();
    cross_corr_flag->key = 'c';
    cross_corr_flag->description =
        _("Find the best Tykhonov regularizing parameter using a "
          "\"leave-one-out\" cross validation method");

    spline_step_flag = G_define_flag();
    spline_step_flag->key = 'e';
    spline_step_flag->label = _("Estimate point density and distance");
    spline_step_flag->description =
        _("Estimate point density and distance in map units for the input "
          "vector points within the current region extents and quit");

    in_opt = G_define_standard_option(G_OPT_V_INPUT);
    in_opt->label = _("Name of input vector point map");

    dfield_opt = G_define_standard_option(G_OPT_V_FIELD);
    dfield_opt->guisection = _("Settings");

    col_opt = G_define_standard_option(G_OPT_DB_COLUMN);
    col_opt->required = NO;
    col_opt->label = _("Name of the attribute column with values to be used "
                       "for approximation");
    col_opt->description = _(
        "If not given and input is 3D vector map then z-coordinates are used.");
    col_opt->guisection = _("Settings");

    in_ext_opt = G_define_standard_option(G_OPT_V_INPUT);
    in_ext_opt->key = "sparse_input";
    in_ext_opt->required = NO;
    in_ext_opt->label = _("Name of input vector map with sparse points");

    out_opt = G_define_standard_option(G_OPT_V_OUTPUT);
    out_opt->required = NO;
    out_opt->guisection = _("Outputs");

    out_map_opt = G_define_standard_option(G_OPT_R_OUTPUT);
    out_map_opt->key = "raster_output";
    out_map_opt->required = NO;
    out_map_opt->guisection = _("Outputs");

    mask_opt = G_define_standard_option(G_OPT_R_INPUT);
    mask_opt->key = "mask";
    mask_opt->label =
        _("Raster map to use for masking (applies to raster output only)");
    mask_opt->description =
        _("Only cells that are not NULL and not zero are interpolated");
    mask_opt->required = NO;

    stepE_opt = G_define_option();
    stepE_opt->key = "ew_step";
    stepE_opt->type = TYPE_DOUBLE;
    stepE_opt->required = NO;
    stepE_opt->label =
        _("Length of each spline step in the east-west direction");
    stepE_opt->description = _("Default: 4 * east-west resolution");
    stepE_opt->guisection = _("Settings");

    stepN_opt = G_define_option();
    stepN_opt->key = "ns_step";
    stepN_opt->type = TYPE_DOUBLE;
    stepN_opt->required = NO;
    stepN_opt->label =
        _("Length of each spline step in the north-south direction");
    stepN_opt->description = _("Default: 4 * north-south resolution");
    stepN_opt->guisection = _("Settings");

    type_opt = G_define_option();
    type_opt->key = "method";
    type_opt->description = _("Spline interpolation algorithm");
    type_opt->type = TYPE_STRING;
    type_opt->options = "bilinear,bicubic";
    type_opt->answer = "bilinear";
    type_opt->guisection = _("Settings");
    G_asprintf((char **)&(type_opt->descriptions), "bilinear;%s;bicubic;%s",
               _("Bilinear interpolation"), _("Bicubic interpolation"));

    lambda_f_opt = G_define_option();
    lambda_f_opt->key = "lambda_i";
    lambda_f_opt->type = TYPE_DOUBLE;
    lambda_f_opt->required = NO;
    lambda_f_opt->description =
        _("Tykhonov regularization parameter (affects smoothing)");
    lambda_f_opt->answer = "0.01";
    lambda_f_opt->guisection = _("Settings");

    solver = N_define_standard_option(N_OPT_SOLVER_SYMM);
    solver->options = "cholesky,cg";
    solver->answer = "cholesky";

    iter = N_define_standard_option(N_OPT_MAX_ITERATIONS);

    error = N_define_standard_option(N_OPT_ITERATION_ERROR);

    memory_opt = G_define_standard_option(G_OPT_MEMORYMB);

    /*----------------------------------------------------------------*/
    /* Parsing */
    G_gisinit(argv[0]);
    if (G_parser(argc, argv))
        exit(EXIT_FAILURE);

    vector = out_opt->answer;
    map = out_map_opt->answer;

    if (vector && map)
        G_fatal_error(_("Choose either vector or raster output, not both"));

    if (!vector && !map && !cross_corr_flag->answer)
        G_fatal_error(_("No raster or vector or cross-validation output"));

    if (!strcmp(type_opt->answer, "bilinear"))
        bilin = P_BILINEAR;
    else
        bilin = P_BICUBIC;

    G_get_set_window(&original_reg);
    stepN = 4 * original_reg.ns_res;
    if (stepN_opt->answer)
        stepN = atof(stepN_opt->answer);
    stepE = 4 * original_reg.ew_res;
    if (stepE_opt->answer)
        stepE = atof(stepE_opt->answer);
    lambda = atof(lambda_f_opt->answer);

    flag_auxiliar = FALSE;

    drv = db_get_default_driver_name();
    if (!drv) {
        if (db_set_default_connection() != DB_OK)
            G_fatal_error(_("Unable to set default DB connection"));
        drv = db_get_default_driver_name();
    }
    db = db_get_default_database_name();
    if (!db)
        G_fatal_error(_("No default DB defined"));

    /* Set auxiliary table's name */
    if (vector) {
        if (G_name_is_fully_qualified(out_opt->answer, xname, xmapset)) {
            sprintf(table_name, "%s_aux", xname);
        }
        else
            sprintf(table_name, "%s_aux", out_opt->answer);
    }

    /* Something went wrong in a previous v.surf.bspline execution */
    if (db_table_exists(drv, db, table_name)) {
        /* Start driver and open db */
        driver = db_start_driver_open_database(drv, db);
        if (driver == NULL)
            G_fatal_error(_("No database connection for driver <%s> is "
                            "defined. Run db.connect."),
                          drv);
        db_set_error_handler_driver(driver);

        if (P_Drop_Aux_Table(driver, table_name) != DB_OK)
            G_fatal_error(_("Old auxiliary table could not be dropped"));
        db_close_database_shutdown_driver(driver);
    }

    /* Open input vector */
    if ((mapset = G_find_vector2(in_opt->answer, "")) == NULL)
        G_fatal_error(_("Vector map <%s> not found"), in_opt->answer);

    Vect_set_open_level(1); /* WITHOUT TOPOLOGY */
    if (1 > Vect_open_old(&In, in_opt->answer, mapset))
        G_fatal_error(
            _("Unable to open vector map <%s> at the topological level"),
            in_opt->answer);

    bspline_field = 0; /* assume 3D input */
    bspline_column = col_opt->answer;

    with_z = !bspline_column && Vect_is_3d(&In);

    if (Vect_is_3d(&In)) {
        if (!with_z)
            G_verbose_message(_("Input is 3D: using attribute values instead "
                                "of z-coordinates for approximation"));
        else
            G_verbose_message(
                _("Input is 3D: using z-coordinates for approximation"));
    }
    else { /* 2D */
        if (!bspline_column)
            G_fatal_error(_("Input vector map is 2D. Parameter <%s> required."),
                          col_opt->key);
    }

    if (!with_z) {
        bspline_field = Vect_get_field_number(&In, dfield_opt->answer);
    }

    /* Estimate point density and mean distance for current region */
    if (spline_step_flag->answer) {
        double dens, dist;

        if (P_estimate_splinestep(&In, &dens, &dist) == 0) {
            fprintf(stdout, _("Estimated point density: %.4g"), dens);
            fprintf(stdout, _("Estimated mean distance between points: %.4g"),
                    dist);
        }
        else {
            fprintf(stdout, _("No points in current region"));
        }

        Vect_close(&In);
        exit(EXIT_SUCCESS);
    }

    /*----------------------------------------------------------------*/
    /* Cross-correlation begins */
    if (cross_corr_flag->answer) {
        G_debug(1, "CrossCorrelation()");
        cross = cross_correlation(&In, stepE, stepN);

        if (cross != TRUE)
            G_fatal_error(_("Cross validation didn't finish correctly"));
        else {
            G_debug(1, "Cross validation finished correctly");

            Vect_close(&In);

            G_done_msg(_("Cross validation finished for ew_step = %f and "
                         "ns_step = %f"),
                       stepE, stepN);
            exit(EXIT_SUCCESS);
        }
    }

    /* Open input ext vector */
    ext = FALSE;
    if (in_ext_opt->answer) {
        ext = TRUE;
        G_message(_("Vector map <%s> of sparse points will be interpolated"),
                  in_ext_opt->answer);

        if ((mapset = G_find_vector2(in_ext_opt->answer, "")) == NULL)
            G_fatal_error(_("Vector map <%s> not found"), in_ext_opt->answer);

        Vect_set_open_level(1); /* WITHOUT TOPOLOGY */
        if (1 > Vect_open_old(&In_ext, in_ext_opt->answer, mapset))
            G_fatal_error(
                _("Unable to open vector map <%s> at the topological level"),
                in_opt->answer);
    }

    /* Open output map */
    /* vector output */
    if (vector && !map) {
        if (strcmp(drv, "dbf") == 0)
            G_fatal_error(_("Sorry, the <%s> driver is not compatible with "
                            "the vector output of this module. "
                            "Try with raster output or another driver."),
                          drv);

        Vect_check_input_output_name(in_opt->answer, out_opt->answer,
                                     G_FATAL_EXIT);
        grid = FALSE;

        if (0 > Vect_open_new(&Out, out_opt->answer, WITH_Z))
            G_fatal_error(_("Unable to create vector map <%s>"),
                          out_opt->answer);

        /* Copy vector Head File */
        if (ext == FALSE) {
            Vect_copy_head_data(&In, &Out);
            Vect_hist_copy(&In, &Out);
        }
        else {
            Vect_copy_head_data(&In_ext, &Out);
            Vect_hist_copy(&In_ext, &Out);
        }
        Vect_hist_command(&Out);

        G_verbose_message(
            _("Points in input vector map <%s> will be interpolated"), vector);
    }

    /* read z values from attribute table */
    if (bspline_field > 0) {
        G_message(_("Reading values from attribute table..."));
        db_CatValArray_init(&cvarr);
        Fi = Vect_get_field(&In, bspline_field);
        if (Fi == NULL)
            G_fatal_error(_("Cannot read layer info"));

        driver_cats = db_start_driver_open_database(Fi->driver, Fi->database);
        /*G_debug (0, _("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);
        db_set_error_handler_driver(driver_cats);

        nrec = db_select_CatValArray(driver_cats, Fi->table, Fi->key,
                                     col_opt->answer, 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(_("Unable to select data from table"));

        G_verbose_message(_("%d records selected from table"), nrec);

        db_close_database_shutdown_driver(driver_cats);
    }

    /*----------------------------------------------------------------*/
    /* Interpolation begins */
    G_debug(1, "Interpolation()");

    /* Open driver and database */
    driver = db_start_driver_open_database(drv, db);
    if (driver == NULL)
        G_fatal_error(_("No database connection for driver <%s> is defined. "
                        "Run db.connect."),
                      drv);
    db_set_error_handler_driver(driver);

    /* Create auxiliary table */
    if (vector) {
        if ((flag_auxiliar = P_Create_Aux4_Table(driver, table_name)) ==
            FALSE) {
            P_Drop_Aux_Table(driver, table_name);
            G_fatal_error(_("Interpolation: Creating table: "
                            "It was impossible to create table <%s>."),
                          table_name);
        }
        /* db_create_index2(driver, table_name, "ID"); */
        /* sqlite likes that ??? */
        db_close_database_shutdown_driver(driver);
        driver = db_start_driver_open_database(drv, db);
    }

    /* raster output */
    raster = -1;
    Rast_set_fp_type(DCELL_TYPE);
    if (!vector && map) {
        grid = TRUE;
        raster = Rast_open_fp_new(out_map_opt->answer);

        G_verbose_message(_("Cells for raster map <%s> will be interpolated"),
                          map);
    }

    /* Setting regions and boxes */
    G_debug(1, "Interpolation: Setting regions and boxes");
    G_get_window(&elaboration_reg);
    Vect_region_box(&original_reg, &original_box);
    Vect_region_box(&elaboration_reg, &overlap_box);
    Vect_region_box(&elaboration_reg, &general_box);

    nrows = Rast_window_rows();
    ncols = Rast_window_cols();

    /* Alloc raster matrix */
    have_mask = 0;
    out_file = mask_file = NULL;
    if (grid == TRUE) {
        int row;
        DCELL *drastbuf;

        seg_mb = atoi(memory_opt->answer);
        if (seg_mb < 3)
            G_fatal_error(_("Memory in MB must be >= 3"));

        if (mask_opt->answer)
            seg_size = sizeof(double) + sizeof(char);
        else
            seg_size = sizeof(double);

        seg_size = (seg_size * SEGSIZE * SEGSIZE) / (1 << 20);
        segments_in_memory = seg_mb / seg_size + 0.5;
        G_debug(1, "%d %dx%d segments held in memory", segments_in_memory,
                SEGSIZE, SEGSIZE);

        out_file = G_tempfile();
        if (Segment_open(&out_seg, out_file, nrows, ncols, SEGSIZE, SEGSIZE,
                         sizeof(double), segments_in_memory) != 1)
            G_fatal_error(_("Can not create temporary file"));

        /* initialize output */
        G_message(_("Initializing output..."));

        drastbuf = Rast_allocate_buf(DCELL_TYPE);
        Rast_set_d_null_value(drastbuf, ncols);
        for (row = 0; row < nrows; row++) {
            G_percent(row, nrows, 2);
            Segment_put_row(&out_seg, drastbuf, row);
        }
        G_percent(row, nrows, 2);

        if (mask_opt->answer) {
            int col, maskfd;
            DCELL dval;
            char mask_val;

            G_message(_("Load masking map"));

            mask_file = G_tempfile();
            if (Segment_open(&mask_seg, mask_file, nrows, ncols, SEGSIZE,
                             SEGSIZE, sizeof(char), segments_in_memory) != 1)
                G_fatal_error(_("Can not create temporary file"));

            maskfd = Rast_open_old(mask_opt->answer, "");

            for (row = 0; row < nrows; row++) {
                G_percent(row, nrows, 2);
                Rast_get_d_row(maskfd, drastbuf, row);
                for (col = 0; col < ncols; col++) {
                    dval = drastbuf[col];
                    if (Rast_is_d_null_value(&dval) || dval == 0)
                        mask_val = 0;
                    else
                        mask_val = 1;

                    Segment_put(&mask_seg, &mask_val, row, col);
                }
            }

            G_percent(row, nrows, 2);
            Rast_close(maskfd);

            have_mask = 1;
        }
        G_free(drastbuf);
    }

    /*------------------------------------------------------------------
      | Subdividing and working with tiles:
      | Each original region will be divided into several subregions.
      | Each one will be overlapped by its neighbouring subregions.
      | The overlapping is calculated as a fixed OVERLAP_SIZE times
      | the largest spline step plus 2 * edge
      ----------------------------------------------------------------*/

    /* Fixing parameters of the elaboration region */
    P_zero_dim(&dims); /* Set dim struct to zero */

    nsplx_adj = NSPLX_MAX;
    nsply_adj = NSPLY_MAX;
    if (stepN > stepE)
        dims.overlap = OVERLAP_SIZE * stepN;
    else
        dims.overlap = OVERLAP_SIZE * stepE;
    P_get_edge(bilin, &dims, stepE, stepN);
    P_set_dim(&dims, stepE, stepN, &nsplx_adj, &nsply_adj);

    G_verbose_message(_("Adjusted EW splines %d"), nsplx_adj);
    G_verbose_message(_("Adjusted NS splines %d"), nsply_adj);

    /* calculate number of subregions */
    edgeE = dims.ew_size - dims.overlap - 2 * dims.edge_v;
    edgeN = dims.sn_size - dims.overlap - 2 * dims.edge_h;

    N_extension = original_reg.north - original_reg.south;
    E_extension = original_reg.east - original_reg.west;

    nsubregion_col = ceil(E_extension / edgeE) + 0.5;
    nsubregion_row = ceil(N_extension / edgeN) + 0.5;

    if (nsubregion_col < 0)
        nsubregion_col = 0;
    if (nsubregion_row < 0)
        nsubregion_row = 0;

    nsubregions = nsubregion_row * nsubregion_col;

    /* Creating line and categories structs */
    Cats = Vect_new_cats_struct();
    Vect_cat_set(Cats, 1, 0);

    subregion_row = 0;
    elaboration_reg.south = original_reg.north;
    last_row = FALSE;

    while (last_row == FALSE) { /* For each subregion row */
        subregion_row++;
        P_set_regions(&elaboration_reg, &general_box, &overlap_box, dims,
                      GENERAL_ROW);

        if (elaboration_reg.north > original_reg.north) { /* First row */

            P_set_regions(&elaboration_reg, &general_box, &overlap_box, dims,
                          FIRST_ROW);
        }

        if (elaboration_reg.south <= original_reg.south) { /* Last row */

            P_set_regions(&elaboration_reg, &general_box, &overlap_box, dims,
                          LAST_ROW);
            last_row = TRUE;
        }

        nsply =
            ceil((elaboration_reg.north - elaboration_reg.south) / stepN) + 0.5;
        G_debug(1, "Interpolation: nsply = %d", nsply);
        /*
           if (nsply > NSPLY_MAX)
           nsply = NSPLY_MAX;
         */
        elaboration_reg.east = original_reg.west;
        last_column = FALSE;
        subregion_col = 0;

        /* TODO: process each subregion using its own thread (via OpenMP or
         * pthreads) */
        /*     I'm not sure about pthreads, but you can tell OpenMP to start all
           at the same time and it will keep num_workers supplied with the next
           job as free cpus become available */
        while (last_column == FALSE) { /* For each subregion column */
            int npoints = 0;

            /* needed for sparse points interpolation */
            int npoints_ext, *lineVect_ext = NULL;
            double **obsVect_ext; /*, mean_ext = .0; */
            struct Point *observ_ext;

            subregion_col++;
            subregion++;
            if (nsubregions > 1)
                G_message(_("Processing subregion %d of %d..."), subregion,
                          nsubregions);

            P_set_regions(&elaboration_reg, &general_box, &overlap_box, dims,
                          GENERAL_COLUMN);

            if (elaboration_reg.west < original_reg.west) { /* First column */

                P_set_regions(&elaboration_reg, &general_box, &overlap_box,
                              dims, FIRST_COLUMN);
            }

            if (elaboration_reg.east >= original_reg.east) { /* Last column */

                P_set_regions(&elaboration_reg, &general_box, &overlap_box,
                              dims, LAST_COLUMN);
                last_column = TRUE;
            }
            nsplx =
                ceil((elaboration_reg.east - elaboration_reg.west) / stepE) +
                0.5;
            G_debug(1, "Interpolation: nsplx = %d", nsplx);
            /*
               if (nsplx > NSPLX_MAX)
               nsplx = NSPLX_MAX;
             */
            G_debug(1, "Interpolation: (%d,%d): subregion bounds",
                    subregion_row, subregion_col);
            G_debug(1, "Interpolation: \t\tNORTH:%.2f\t",
                    elaboration_reg.north);
            G_debug(1, "Interpolation: WEST:%.2f\t\tEAST:%.2f",
                    elaboration_reg.west, elaboration_reg.east);
            G_debug(1, "Interpolation: \t\tSOUTH:%.2f", elaboration_reg.south);

#ifdef DEBUG_SUBREGIONS
            fprintf(stdout, "B 5\n");
            fprintf(stdout, " %.11g %.11g\n", elaboration_reg.east,
                    elaboration_reg.north);
            fprintf(stdout, " %.11g %.11g\n", elaboration_reg.west,
                    elaboration_reg.north);
            fprintf(stdout, " %.11g %.11g\n", elaboration_reg.west,
                    elaboration_reg.south);
            fprintf(stdout, " %.11g %.11g\n", elaboration_reg.east,
                    elaboration_reg.south);
            fprintf(stdout, " %.11g %.11g\n", elaboration_reg.east,
                    elaboration_reg.north);
            fprintf(stdout, "C 1 1\n");
            fprintf(stdout, " %.11g %.11g\n",
                    (elaboration_reg.west + elaboration_reg.east) / 2,
                    (elaboration_reg.south + elaboration_reg.north) / 2);
            fprintf(stdout, " 1 %d\n", subregion);
#endif

            /* reading points in interpolation region */
            dim_vect = nsplx * nsply;
            observ_ext = NULL;
            if (grid == FALSE && ext == TRUE) {
                observ_ext = P_Read_Vector_Region_Map(
                    &In_ext, &elaboration_reg, &npoints_ext, dim_vect, 1);
            }
            else
                npoints_ext = 1;

            if (grid == TRUE && have_mask) {
                /* any unmasked cells in general region ? */
                mean = 0;
                observ_ext = P_Read_Raster_Region_masked(
                    &mask_seg, &original_reg, original_box, general_box,
                    &npoints_ext, dim_vect, mean);
            }

            observ = NULL;
            if (npoints_ext > 0) {
                observ = P_Read_Vector_Region_Map(
                    &In, &elaboration_reg, &npoints, dim_vect, bspline_field);
            }
            else
                npoints = 1;

            G_debug(1,
                    "Interpolation: (%d,%d): Number of points in "
                    "<elaboration_box> is %d",
                    subregion_row, subregion_col, npoints);
            if (npoints > 0)
                G_verbose_message(_("%d points found in this subregion"),
                                  npoints);
            /* only interpolate if there are any points in current subregion */
            if (npoints > 0 && npoints_ext > 0) {
                int i;

                nparameters = nsplx * nsply;
                BW = P_get_BandWidth(bilin, nsply);

                /* Least Squares system */
                N = G_alloc_matrix(nparameters, BW);   /* Normal matrix */
                TN = G_alloc_vector(nparameters);      /* vector */
                parVect = G_alloc_vector(nparameters); /* Parameters vector */
                obsVect = G_alloc_matrix(npoints, 3);  /* Observation vector */
                Q = G_alloc_vector(npoints); /* "a priori" var-cov matrix */
                lineVect = G_alloc_ivector(npoints); /*  */

                for (i = 0; i < npoints;
                     i++) { /* Setting obsVect vector & Q matrix */
                    double dval;

                    Q[i] = 1; /* Q=I */
                    lineVect[i] = observ[i].lineID;
                    obsVect[i][0] = observ[i].coordX;
                    obsVect[i][1] = observ[i].coordY;

                    /* read z coordinates from attribute table */
                    if (bspline_field > 0) {
                        int cat, ival, ret;

                        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;
                            observ[i].coordZ = ival;
                        }
                        else { /* DB_C_TYPE_DOUBLE */
                            ret = db_CatValArray_get_value_double(&cvarr, cat,
                                                                  &dval);
                            obsVect[i][2] = dval;
                            observ[i].coordZ = dval;
                        }
                        if (ret != DB_OK) {
                            G_warning(_("Interpolation: (%d,%d): No record for "
                                        "point (cat = %d)"),
                                      subregion_row, subregion_col, cat);
                            continue;
                        }
                    }
                    /* use z coordinates of 3D vector */
                    else {
                        obsVect[i][2] = observ[i].coordZ;
                    }
                }

                /* Mean calculation for every point */
                mean = P_Mean_Calc(&elaboration_reg, observ, npoints);

                G_debug(1, "Interpolation: (%d,%d): mean=%lf", subregion_row,
                        subregion_col, mean);

                G_free(observ);

                for (i = 0; i < npoints; i++)
                    obsVect[i][2] -= mean;

                /* Bilinear interpolation */
                if (bilin) {
                    G_debug(1,
                            "Interpolation: (%d,%d): Bilinear interpolation...",
                            subregion_row, subregion_col);
                    normalDefBilin(N, TN, Q, obsVect, stepE, stepN, nsplx,
                                   nsply, elaboration_reg.west,
                                   elaboration_reg.south, npoints, nparameters,
                                   BW);
                    nCorrectGrad(N, lambda, nsplx, nsply, stepE, stepN);
                }
                /* Bicubic interpolation */
                else {
                    G_debug(1,
                            "Interpolation: (%d,%d): Bicubic interpolation...",
                            subregion_row, subregion_col);
                    normalDefBicubic(N, TN, Q, obsVect, stepE, stepN, nsplx,
                                     nsply, elaboration_reg.west,
                                     elaboration_reg.south, npoints,
                                     nparameters, BW);
                    nCorrectGrad(N, lambda, nsplx, nsply, stepE, stepN);
                }

                if (G_strncasecmp(solver->answer, "cg", 2) == 0)
                    G_math_solver_cg_sband(N, parVect, TN, nparameters, BW,
                                           atoi(iter->answer),
                                           atof(error->answer));
                else
                    G_math_solver_cholesky_sband(N, parVect, TN, nparameters,
                                                 BW);

                G_free_matrix(N);
                G_free_vector(TN);
                G_free_vector(Q);

                if (grid == TRUE) { /* GRID INTERPOLATION ==> INTERPOLATION INTO
                                       A RASTER */
                    G_debug(1, "Interpolation: (%d,%d): Regular_Points...",
                            subregion_row, subregion_col);

                    if (!have_mask) {
                        P_Regular_Points(&elaboration_reg, &original_reg,
                                         general_box, overlap_box, &out_seg,
                                         parVect, stepN, stepE, dims.overlap,
                                         mean, nsplx, nsply, nrows, ncols,
                                         bilin);
                    }
                    else {
                        P_Sparse_Raster_Points(
                            &out_seg, &elaboration_reg, &original_reg,
                            general_box, overlap_box, observ_ext, parVect,
                            stepE, stepN, dims.overlap, nsplx, nsply,
                            npoints_ext, bilin, mean);
                    }
                }
                else { /* OBSERVATION POINTS INTERPOLATION */
                    if (ext == FALSE) {
                        G_debug(1, "Interpolation: (%d,%d): Sparse_Points...",
                                subregion_row, subregion_col);
                        P_Sparse_Points(&Out, &elaboration_reg, general_box,
                                        overlap_box, obsVect, parVect, lineVect,
                                        stepE, stepN, dims.overlap, nsplx,
                                        nsply, npoints, bilin, Cats, driver,
                                        mean, table_name);
                    }
                    else { /* FLAG_EXT == TRUE */

                        /* done that earlier */
                        /*
                           int npoints_ext, *lineVect_ext = NULL;
                           double **obsVect_ext;
                           struct Point *observ_ext;

                           observ_ext =
                           P_Read_Vector_Region_Map(&In_ext,
                           &elaboration_reg,
                           &npoints_ext, dim_vect,
                           1);
                         */

                        obsVect_ext = G_alloc_matrix(
                            npoints_ext, 3); /* Observation vector_ext */
                        lineVect_ext = G_alloc_ivector(npoints_ext);

                        for (i = 0; i < npoints_ext;
                             i++) { /* Setting obsVect_ext vector & Q matrix */
                            obsVect_ext[i][0] = observ_ext[i].coordX;
                            obsVect_ext[i][1] = observ_ext[i].coordY;
                            obsVect_ext[i][2] = observ_ext[i].coordZ - mean;
                            lineVect_ext[i] = observ_ext[i].lineID;
                        }

                        G_free(observ_ext);

                        G_debug(1, "Interpolation: (%d,%d): Sparse_Points...",
                                subregion_row, subregion_col);
                        P_Sparse_Points(&Out, &elaboration_reg, general_box,
                                        overlap_box, obsVect_ext, parVect,
                                        lineVect_ext, stepE, stepN,
                                        dims.overlap, nsplx, nsply, npoints_ext,
                                        bilin, Cats, driver, mean, table_name);

                        G_free_matrix(obsVect_ext);
                        G_free_ivector(lineVect_ext);
                    } /* END FLAG_EXT == TRUE */
                }     /* END GRID == FALSE */
                G_free_vector(parVect);
                G_free_matrix(obsVect);
                G_free_ivector(lineVect);
            }
            else {
                if (observ)
                    G_free(observ);
                if (observ_ext)
                    G_free(observ_ext);
                if (npoints == 0)
                    G_warning(_("No data within this subregion. "
                                "Consider increasing spline step values."));
            }
        } /*! END WHILE; last_column = TRUE */
    }     /*! END WHILE; last_row = TRUE */

    G_verbose_message(_("Writing output..."));
    /* Writing the output raster map */
    if (grid == TRUE) {
        int row, col;
        DCELL *drastbuf, dval;

        if (have_mask) {
            Segment_close(&mask_seg); /* close segment structure  */
        }

        drastbuf = Rast_allocate_buf(DCELL_TYPE);
        for (row = 0; row < nrows; row++) {
            G_percent(row, nrows, 2);
            for (col = 0; col < ncols; col++) {
                Segment_get(&out_seg, &dval, row, col);
                drastbuf[col] = dval;
            }
            Rast_put_d_row(raster, drastbuf);
        }

        Rast_close(raster);

        Segment_close(&out_seg); /* close segment structure  */
        /* set map title */
        sprintf(title, "%s interpolation with Tykhonov regularization",
                type_opt->answer);
        Rast_put_cell_title(out_map_opt->answer, title);
        /* write map history */
        Rast_short_history(out_map_opt->answer, "raster", &history);
        Rast_command_history(&history);
        Rast_write_history(out_map_opt->answer, &history);
    }
    /* Writing to the output vector map the points from the overlapping zones */
    else if (flag_auxiliar == TRUE) {
        if (ext == FALSE)
            P_Aux_to_Vector(&In, &Out, driver, table_name);
        else
            P_Aux_to_Vector(&In_ext, &Out, driver, table_name);

        /* Drop auxiliary table */
        G_debug(1, "%s: Dropping <%s>", argv[0], table_name);
        if (P_Drop_Aux_Table(driver, table_name) != DB_OK)
            G_fatal_error(_("Auxiliary table could not be dropped"));
    }

    db_close_database_shutdown_driver(driver);

    Vect_close(&In);
    if (ext != FALSE)
        Vect_close(&In_ext);
    if (vector)
        Vect_close(&Out);

    G_done_msg(" ");

    exit(EXIT_SUCCESS);
} /*END MAIN */