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genfuncs.c

/* 
 *  gretl -- Gnu Regression, Econometrics and Time-series Library
 *  Copyright (C) 2001 Allin Cottrell and Riccardo "Jack" Lucchetti
 * 
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 * 
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 * 
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 * 
 */

/* various functions called by 'genr' */

#include "genparse.h"
#include "libset.h"
#include "monte_carlo.h"
#include "gretl_string_table.h"
#include "../../cephes/cephes.h"

#include <errno.h>

/* apparatus for saving sorted case markers */

struct val_mark {
    double x;
    char mark[OBSLEN];
};

static int compare_vms (const void *a, const void *b)
{
    const struct val_mark *va = (const struct val_mark *) a;
    const struct val_mark *vb = (const struct val_mark *) b;
     
    return (va->x > vb->x) - (va->x < vb->x);
}

static int inverse_compare_vms (const void *a, const void *b)
{
    const struct val_mark *va = (const struct val_mark *) a;
    const struct val_mark *vb = (const struct val_mark *) b;
     
    return (vb->x > va->x) - (vb->x < va->x);
}

static char **SortedS;

/* do a simple sort if there are no case markers in the dataset,
   but if there are case markers, keep a record of the sorted
   markers and attach it to the newly generated variable
*/

int sort_series (const double *x, double *y, int f, 
             const DATAINFO *pdinfo)
{
    double *z = NULL;
    struct val_mark *vm = NULL;
    int markers = 0;
    int n = sample_size(pdinfo);
    int i, t;

    if (pdinfo->S != NULL && !complex_subsampled()) {
      SortedS = strings_array_new_with_length(pdinfo->n, OBSLEN);
      markers = SortedS != NULL;
    }

    if (markers) {
      vm = malloc(n * sizeof *vm);
      if (vm == NULL) {
          free_strings_array(SortedS, pdinfo->n);
          SortedS = NULL;
          return E_ALLOC;
      }
    } else {
      z = malloc(n * sizeof *z);
      if (z == NULL) {
          return E_ALLOC;
      }
    }

    i = 0;
    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (!na(x[t])) {
          if (markers) {
            vm[i].x = x[t];
            strcpy(vm[i++].mark, pdinfo->S[t]);
          } else {
            z[i++] = x[t];
          }
      }
    }

    if (f == F_DSORT) {
      if (markers) {
          qsort(vm, i, sizeof *vm, inverse_compare_vms);
      } else {
          qsort(z, i, sizeof *z, gretl_inverse_compare_doubles);
      }
    } else {
      if (markers) {
          qsort(vm, i, sizeof *vm, compare_vms);
      } else {
          qsort(z, i, sizeof *z, gretl_compare_doubles);
      }
    }

    i = 0;
    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (na(x[t])) {
          y[t] = NADBL;
      } else if (markers) {
          y[t] = vm[i].x;
          strcpy(SortedS[t], vm[i++].mark);
      } else {
          y[t] = z[i++];
      }
    }

    free(z);
    free(vm);

    return 0;
}

struct pair_sorter {
    double x;
    double y;
};

/* sort the series y by the values of x, putting the result
   into z */

int gretl_sort_by (const double *x, const double *y, 
               double *z, const DATAINFO *pdinfo)
{
    struct pair_sorter *xy;
    int n = sample_size(pdinfo);
    int i, t;

    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (na(x[t])) {
          return E_MISSDATA;
      }
    }

    xy = malloc(n * sizeof *xy);
    if (xy == NULL) {
      return E_ALLOC;
    }

    i = 0;
    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      xy[i].x = x[t];
      xy[i].y = y[t];
      i++;
    }

    qsort(xy, n, sizeof *xy, gretl_compare_doubles);

    i = 0;
    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      z[t] = xy[i++].y;
    }

    free(xy);

    return 0;
}

static void genrank (const double *sz, int m,
                 const double *z, int n,
                 double *rz)
{
    int cases, k, i, j;
    double avg, r = 1;

    for (i=0; i<m; i++) {
      /* scan sorted z */
      cases = k = 0;

      if (i > 0 && sz[i] == sz[i-1]) {
          continue;
      }

      for (j=0; j<n; j++) {
          /* scan raw z for matches */
          if (!na(z[j])) {
            if (z[j] == sz[i]) {
                rz[k] = r;
                cases++;
            }
            k++;
          }
      }

      if (cases > 1) {
          avg = (r + r + cases - 1.0) / 2.0;
          for (j=0; j<m; j++) {
            if (rz[j] == r) {
                rz[j] = avg;
            }
          }
      } 

      r += cases;
    }
}

int rank_series (const double *x, double *y, int f, 
             const DATAINFO *pdinfo)
{
    double *sx = NULL;
    double *rx = NULL;
    int n = sample_size(pdinfo);
    int m = n;
    int i, t;

    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (na(x[t])) m--;
    }

    sx = malloc(m * sizeof *sx);
    rx = malloc(m * sizeof *rx);

    if (sx == NULL || rx == NULL) {
      free(sx);
      free(rx);
      return E_ALLOC;
    }

    i = 0;
    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (!na(x[t])) {
          sx[i] = x[t];
          rx[i] = 0.0;
          i++;
      }
    }
    
    if (f == F_DSORT) {
      qsort(sx, m, sizeof *sx, gretl_inverse_compare_doubles);
    } else {
      qsort(sx, m, sizeof *sx, gretl_compare_doubles);
    }

    genrank(sx, m, x + pdinfo->t1, n, rx);

    i = 0;
    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (!na(x[t])) {
          y[t] = rx[i++];
      }
    }    

    free(sx);
    free(rx);

    return 0;
}

/**
 * diff_series:
 * @x: array of original data.
 * @y: array into which to write the result.
 * @f: function, %F_DIFF, %F_SDIFF or %F_LDIFF.
 * @pdinfo: data set information.
 *
 * Calculates the differenced counterpart to the input 
 * series @x.  If @f = %F_SDIFF, the seasonal difference is
 * computed; if @f = %F_LDIFF, the log difference, and if
 * @f = %F_DIFF, the ordinary first difference.
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int diff_series (const double *x, double *y, int f, 
             const DATAINFO *pdinfo)
{
    int t1 = pdinfo->t1;
    int k = (f == F_SDIFF)? pdinfo->pd : 1;
    int t, err = 0;

    if (t1 < k) {
      t1 = k;
    }

    for (t=t1; t<=pdinfo->t2; t++) {

      if (dataset_is_panel(pdinfo) && t % pdinfo->pd == 0) {
          /* skip first observation in panel unit */
          continue;
      }

      if (na(x[t]) || na(x[t-k])) {
          continue;
      }

      if (f == F_DIFF || f == F_SDIFF) {
          y[t] = x[t] - x[t-k];
      } else if (f == F_LDIFF) {
          if (x[t] <= 0.0 || x[t-k] <= 0.0) {
            err = E_LOGS; /* FIXME: should be warning? */
          } else {
            y[t] = log(x[t]) - log(x[t-k]);
          }
      }
    }

    return 0; /* see FIXME above */
}

/**
 * orthdev_series:
 * @x: array of original data.
 * @y: array into which to write the result.
 * @pdinfo: data set information.
 *
 * Calculates in @y the forward orthogonal deviations of the input 
 * series @x.  That is, y[t] is the scaled difference between x[t]
 * and the mean of the subsequent observations on x.
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int orthdev_series (const double *x, double *y, const DATAINFO *pdinfo)
{
    double xbar;
    int n, s, t, Tt;

    for (t=pdinfo->t1; t<pdinfo->t2; t++) {

      if (na(x[t])) {
          continue;
      }

      if (dataset_is_panel(pdinfo)) {
          Tt = pdinfo->pd - (t % pdinfo->pd) - 1;
      } else {
          Tt = pdinfo->t2 - t;
      }

      xbar = 0.0;
      n = 0;
      for (s=1; s<=Tt; s++) {
          if (!na(x[t+s])) {
            xbar += x[t+s];
            n++;
          }
      }

      if (n > 0) {
          xbar /= n;
          /* Lead one period, for compatibility with first diffs.
             I.e. we lose the first observation rather than the
             last.  This is for arbond.  Cf. Doornik, Bond and
             Arellano, DPD documentation.
          */
          y[t+1] = sqrt(n / (n + 1.0)) * (x[t] - xbar);
      }
    }

    return 0;
}

/**
 * fracdiff_series:
 * @x: array of original data.
 * @y: array into which to write the result.
 * @d: fraction by which to difference.
 * @diff: boolean variable 1 for fracdiff, 0 for fraclag
 * @obs: used for autoreg calculation, -1 if whole series 
 *    should be calculated otherwise just the observation for
 *    obs is calculated 
 * @pdinfo: data set information.
 *
 * Calculates the fractionally differenced or lagged 
 * counterpart to the input series @x. The fractional 
 * difference operator is defined as (1-L)^d, while the
 * fractional lag operator 1-(1-L)^d.
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int fracdiff_series (const double *x, double *y, double d,
                 int diff, int obs, const DATAINFO *pdinfo)
{
    int dd, t, tmiss, T;
    const double TOL = 1.0E-12;
    int t1 = pdinfo->t1;
    int t2 = (obs >= 0)? obs : pdinfo->t2;
    double phi = (diff)? -d : d;

#if 0
    fprintf(stderr, "Doing fracdiff_series, with d = %g\n", d);
#endif

    tmiss = array_adjust_t1t2(x, &t1, &t2);

    if (tmiss > 0 && tmiss < t2) {
      t2 = tmiss;
    } 
 
    if (obs >= 0) {
      /* doing a specific observation */
      T = obs - t1 + 1;
      for (t=0; t<pdinfo->n; t++) {
          y[t] = NADBL;
      }
      if (obs != t1) {
          y[obs] = (diff)? x[obs] : 0;
          for (dd=1; dd<T && fabs(phi)>TOL; dd++) {
            y[obs] += phi * x[obs - dd];
            phi *= (dd - d)/(dd + 1);
          }
      } else if (diff) {
          y[obs] = x[obs];
      }
    } else {
      /* doing the whole series */
      T = t2 - t1 + 1;
      for (t=0; t<=t2; t++) {
          if (t >= t1 && t <= t2) {
            y[t] = (diff)? x[t] : 0;
          } else {
            y[t] = NADBL;
          } 
      }  
      for (dd=1; dd<=T && fabs(phi)>TOL; dd++) {
          for (t=t1+dd; t<=t2; t++) {
            y[t] += phi * x[t - dd];
          }
          phi *= (dd - d)/(dd + 1);
      }
    }

    return 0;
}

/**
 * boxcox_series:
 * @x: array of original data.
 * @y: array into which to write the result.
 * @d: lambda parameter.
 * @pdinfo: data set information.
 *
 * Calculates in @y the Box-Cox transformation for the 
 * input series @x.
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int boxcox_series (const double *x, double *y, double d,
               const DATAINFO *pdinfo)
{
    int t;

    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (na(x[t])) {
          y[t] = NADBL;
      } else if (d == 0) {
          y[t] = (x[t] > 0)? log(x[t]) : NADBL; 
      } else {
          y[t] = (pow(x[t], d) - 1) / d;
      }
    } 
    
    return 0;
}

int cum_series (const double *x, double *y, const DATAINFO *pdinfo)
{
    int t, s = pdinfo->t1;

    for (t=pdinfo->t1; t<=pdinfo->t2 && na(x[t]); t++) {
      s++;
    }

    if (s < pdinfo->t2) {
      y[s] = x[s];
      for (t=s+1; t<=pdinfo->t2 && !na(x[t]); t++) {
          y[t] = y[t-1] + x[t];
      }
    }

    return 0;
}

int resample_series (const double *x, double *y, const DATAINFO *pdinfo)
{
    int t1 = pdinfo->t1;
    int t2 = pdinfo->t2;
    int *z = NULL;
    int i, t, n;

    array_adjust_t1t2(x, &t1, &t2);

    n = t2 - t1 + 1;
    if (n <= 1) {
      return E_DATA;
    }

    z = malloc(n * sizeof *z);
    if (z == NULL) {
      return E_ALLOC;
    }

    /* generate n uniform drawings from [t1 .. t2] */
    gretl_rand_int_minmax(z, n, t1, t2);

    /* sample from source series x based on indices z */
    for (t=t1, i=0; t<=t2; t++, i++) {
      y[t] = x[z[i]];
    }

    free(z);

    return 0;
}

int block_resample_series (const double *x, double *y, int blocklen,
                     const DATAINFO *pdinfo)
{
    int t1 = pdinfo->t1;
    int t2 = pdinfo->t2;
    int *z = NULL;
    int m, rem, bt2, x0;
    int i, s, t, n;

    if (blocklen <= 0) {
      return E_DATA;
    }

    if (blocklen == 1) {
      return resample_series(x, y, pdinfo);
    }    

    array_adjust_t1t2(x, &t1, &t2);

    n = t2 - t1 + 1;

    m = n / blocklen;
    rem = n % blocklen;

    /* Let n now represent the number of blocks of @blocklen
       contiguous observations which we need to select; the
       last of these may not be fully used.
    */     
    n = m + (rem > 0);

    /* the last selectable starting point for a block */
    bt2 = t2 - blocklen + 1;

    if (bt2 < t1) {
      return E_DATA;
    }

    z = malloc(n * sizeof *z);
    if (z == NULL) {
      return E_ALLOC;
    }

    /* Generate uniform random series: we want n drawings from the
       range [t1 .. t2 - blocklen + 1], each of which will be
       interpreted as the starting point of a block to be used.
    */
    gretl_rand_int_minmax(z, n, t1, bt2);

    /* Sample from the source series using blocks given by the random
       indices: note that the last block will be incomplete if rem > 0
    */
    t = t1;
    for (i=0; i<n; i++) {
      x0 = z[i];
      for (s=0; s<blocklen; s++) {
          if (t <= t2) {
            y[t++] = x[x0+s];
          } else {
            break;
          }
      }
    }

    free(z);

    return 0;
}

/**
 * filter_series:
 * @x: array of original data.
 * @y: array into which to write the result.
 * @pdinfo: data set information.
 * @A: vector for autoregressive polynomial.
 * @C: vector for moving average polynomial.
 * @y0: initial value of output series.
 *
 * Filters x according to y_t = C(L)/A(L) x_t.  If the intended
 * AR order is p, @A should be a vector of length p.  If the 
 * intended MA order is q, @C should be vector of length (q+1), 
 * the first entry giving the coefficient at lag 0.  However, if 
 * @C is %NULL this is taken to mean that the lag-0 MA coefficient 
 * is unity (and all others are zero).
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int filter_series (const double *x, double *y, const DATAINFO *pdinfo, 
               gretl_vector *A, gretl_vector *C, double y0)
{
    int t1 = pdinfo->t1;
    int t2 = pdinfo->t2;
    int t, s, i, n;
    int amax, cmax;
    double xlag, coef, *e;
    int err = 0;

    if (gretl_is_null_matrix(C)) {
      cmax = 0;
    } else {
      cmax = gretl_vector_get_length(C);
      if (cmax == 0) {
          /* if present, C must be a vector */
          return E_NONCONF;
      }
    }

    if (gretl_is_null_matrix(A)) {
      amax = 0;
    } else {
      amax = gretl_vector_get_length(A);
      if (amax == 0) {
          /* if present, A must be a vector */
          return E_NONCONF;
      }
    }

    err = array_adjust_t1t2(x, &t1, &t2);
    if (err) {
      return E_DATA;
    } 

    n = t2 - t1 + 1;
    e = malloc(n * sizeof *e);

    if (e == NULL) {
      return E_ALLOC;
    }

    s = 0;
    if (cmax) {
      for (t=t1; t<=t2; t++) {
          e[s] = 0;
          for (i=0; i<cmax; i++) {
            xlag = (t-i >= t1)? x[t-i] : 0;
            if (na(xlag)) {
                e[s] = NADBL;
                break;
            } else {
                coef = gretl_vector_get(C, i);
                e[s] += xlag * coef;
            }
          } 
          s++;
      }
    } else {
      /* implicitly MA(0) = 1 */
      for (t=t1; t<=t2; t++) {
          e[s++] = x[t];
      }
    }

    s = 0;
    if (amax) {
      for (t=t1; t<=t2; t++) {
          if (na(e[s])) {
            y[t] = NADBL;
          } else {
            y[t] = e[s];
            for (i=0; i<amax; i++) {
                xlag = (t-i>t1)? y[t-i-1] : y0;
                if (na(xlag)) {
                  y[t] = NADBL;
                  break;
                } else {
                  coef = gretl_vector_get(A, i);
                  y[t] += coef * xlag;
                }
            } 
          }
          s++;
      }
    } else {
      for (t=t1; t<=t2; t++) {
          y[t] = e[s++];
      }
    }

    free(e);

    return err;
}

int panel_statistic (const double *x, double *y, const DATAINFO *pdinfo, 
                 int k)
{
    const int *unit;
    double ret = NADBL;
    double xbar = NADBL;
    double aux = NADBL;
    int smin = 0;
    int s, t, Ti = 0;

    if (pdinfo->paninfo == NULL) {
      return E_DATA;
    }

    unit = pdinfo->paninfo->unit;

    switch (k) {
    case F_PNOBS:
      for (t=0; t<=pdinfo->n; t++) {
          if (t == pdinfo->n || (t > 0 && unit[t] != unit[t-1])) {
            for (s=smin; s<t; s++) {
                y[s] = Ti;
            }
            if (t == pdinfo->n) {
                break;
            }
            Ti = 0;
            smin = t;
          }
          if (!na(x[t])) {
            Ti++;
          }
      }
      break;
    case F_PMIN:
      for (t=0; t<=pdinfo->n; t++) {
          if (t == pdinfo->n || (t > 0 && unit[t] != unit[t-1])) {
            for (s=smin; s<t; s++) {
                y[s] = aux;
            }
            if (t == pdinfo->n) {
                break;
            }
            aux = NADBL;
            smin = t;
          }
          if (!na(x[t])) {
            if (na(aux) || x[t]<aux) {
                aux = x[t];
            }
          }
      }
      break;
    case F_PMAX:
      for (t=0; t<=pdinfo->n; t++) {
          if (t == pdinfo->n || (t > 0 && unit[t] != unit[t-1])) {
            for (s=smin; s<t; s++) {
                y[s] = aux;
            }
            if (t == pdinfo->n) {
                break;
            }
            aux = NADBL;
            smin = t;
          }
          if (!na(x[t])) {
            if (na(aux) || x[t]>aux) {
                aux = x[t];
            }
          }
      }
      break;
    case F_PMEAN:
      for (t=0; t<=pdinfo->n; t++) {
          if (t == pdinfo->n || (t > 0 && unit[t] != unit[t-1])) {
            if (!na(xbar)) {
                xbar /= Ti;
            }
            /* got a new unit (or reached the end): 
               ship out current mean */
            for (s=smin; s<t; s++) {
                y[s] = xbar;
            }
            if (t == pdinfo->n) {
                break;
            }
            Ti = 0;
            xbar = NADBL;
            smin = t;
          }
          if (!na(x[t])) {
            if (na(xbar)) {
                xbar = x[t];
            } else {
                xbar += x[t];
            }
            Ti++;
          }
      }
      break;
    case F_PSD:
      for (t=0; t<=pdinfo->n; t++) {
          if (t == pdinfo->n || (t > 0 && unit[t] != unit[t-1])) {
            if (na(xbar)) {
                ret = NADBL;
            } else if (Ti == 1) {
                ret = 0.0;
            } else {
                xbar /= Ti;
                ret = sqrt((aux/Ti - xbar*xbar) * Ti/(Ti-1));
            }
            for (s=smin; s<t; s++) {
                y[s] = ret;
            }
            if (t == pdinfo->n) {
                break;
            }
            Ti = 0;
            xbar = NADBL;
            aux = NADBL;
            smin = t;
          }
          if (!na(x[t])) {
            if (na(xbar)) {
                xbar = x[t];
                aux = x[t]*x[t];
            } else {
                xbar += x[t];
                aux += x[t]*x[t];
            }
            Ti++;
          }
      }
      break;
    default:
      break;
    }

    return 0;
}

/* handling sorted marker strings */

int maybe_pick_up_sorted_markers (parser *p)
{
    if (SortedS != NULL) {
      if (p->flags & P_SORT) {
          /* "genr foo = sort(baz)" */
          set_sorted_markers(p->dinfo, p->lh.v, SortedS);
      } else {
          free_strings_array(SortedS, p->dinfo->n);
      }
      SortedS = NULL;   
    } 

    return 0;
}

static double hp_lambda (const DATAINFO *pdinfo)
{
    double la = libset_get_double(HP_LAMBDA);

    if (na(la)) {
      la = 100 * pdinfo->pd * pdinfo->pd;
    }

    return la;
}

/**
 * hp_filter:
 * @x: array of original data.
 * @hp: array in which filtered series is computed.
 * @pdinfo: data set information.
 * @opt: if %OPT_T, return the trend rather than the cycle.
 *
 * Calculates the "cycle" component of the time series in
 * array @x, using the Hodrick-Prescott filter.  Adapted from the 
 * original FORTRAN code by E. Prescott. Very few changes.
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int hp_filter (const double *x, double *hp, const DATAINFO *pdinfo,
             gretlopt opt)
{
    int i, t, T, t1 = pdinfo->t1, t2 = pdinfo->t2;
    int err = 0;
    double v00 = 1.0, v11 = 1.0, v01 = 0.0;
    double det, tmp0, tmp1;
    double lambda;

    double **V = NULL;
    double m[2], tmp[2];

    int tb;
    double e0, e1, b00, b01, b11;

    for (t=t1; t<=t2; t++) {
      hp[t] = NADBL;
    }

    err = array_adjust_t1t2(x, &t1, &t2);
    if (err) {
      err = E_DATA;
      goto bailout;
    }

    T = t2 - t1 + 1;
    if (T < 4) {
      err = E_DATA;
      goto bailout;
    }

    lambda = hp_lambda(pdinfo);

    V = doubles_array_new(4, T);
    if (V == NULL) {
      return E_ALLOC;
    }

    /* adjust starting points */
    x += t1;
    hp += t1;

    /* covariance matrices for each obs */

    for (t=2; t<T; t++) {
      tmp0 = v00;
      tmp1 = v01;
      v00 = 1.0 / lambda + 4.0 * (tmp0 - tmp1) + v11;
      v01 = 2.0 * tmp0 - tmp1;
      v11 = tmp0;

      det = v00 * v11 - v01 * v01;

      V[0][t] =  v11 / det;
      V[1][t] = -v01 / det;
      V[2][t] =  v00 / det;

      tmp0 = v00 + 1.0;
      tmp1 = v00;
      
      v00 -= v00 * v00 / tmp0;
      v11 -= v01 * v01 / tmp0;
      v01 -= (tmp1 / tmp0) * v01;

    }

    m[0] = x[0];
    m[1] = x[1];

    /* forward pass */
    for (t=2; t<T; t++) {
      tmp[0] = m[1];
      m[1] = 2.0 * m[1] - m[0];
      m[0] = tmp[0];

      V[3][t-1] = V[0][t] * m[1] + V[1][t] * m[0];
      hp[t-1]   = V[1][t] * m[1] + V[2][t] * m[0];
        
      det = V[0][t] * V[2][t] - V[1][t] * V[1][t];
        
      v00 =  V[2][t] / det;
      v01 = -V[1][t] / det;
        
      tmp[1] = (x[t] - m[1]) / (v00 + 1.0);
      m[1] += v00 * tmp[1];
      m[0] += v01 * tmp[1];
    }

    V[3][T-2] = m[0];
    V[3][T-1] = m[1];
    m[0] = x[T-2];
    m[1] = x[T-1];

    /* backward pass */
    for (t=T-3; t>=0; t--) {
      t1 = t+1;
      tb = T - t - 1;
      
      tmp[0] = m[0];
      m[0] = 2.0 * m[0] - m[1];
      m[1] = tmp[0];

      if (t > 1) {
          /* combine info for y < i with info for y > i */
          e0 = V[2][tb] * m[1] + V[1][tb] * m[0] + V[3][t];
          e1 = V[1][tb] * m[1] + V[0][tb] * m[0] + hp[t];
          b00 = V[2][tb] + V[0][t1];
          b01 = V[1][tb] + V[1][t1];
          b11 = V[0][tb] + V[2][t1];
            
          det = b00 * b11 - b01 * b01;
            
          V[3][t] = (b00 * e1 - b01 * e0) / det;
      }
        
      det = V[0][tb] * V[2][tb] - V[1][tb] * V[1][tb];
      v00 =  V[2][tb] / det;
      v01 = -V[1][tb] / det;

      tmp[1] = (x[t] - m[0]) / (v00 + 1.0);
      m[1] += v01 * tmp[1];
      m[0] += v00 * tmp[1];
    }

    V[3][0] = m[0];
    V[3][1] = m[1];

    if (opt & OPT_T) {
      for (t=0; t<T; t++) {
          hp[t] = V[3][t];
      }
    } else {
      for (t=0; t<T; t++) {
          hp[t] = x[t] - V[3][t];
      }
    }

 bailout:

    for (i=0; i<4; i++) {
      free(V[i]);
    }
    free(V);

    return err;
}

/**
 * bkbp_filter:
 * @y: array of original data.
 * @bk: array into which to write the filtered series.
 * @pdinfo: data set information.
 *
 * Calculates the Baxter & King bandpass filter.
 *
 * Returns: 0 on success, non-zero error code on failure.
 */

int bkbp_filter (const double *y, double *bk, const DATAINFO *pdinfo)
{
    int t1 = pdinfo->t1, t2 = pdinfo->t2;
    int bkl, bku;

    double omubar, omlbar;
    double avg_a;
    double *a;

    int i, k, t;
    int err = 0;

    /*
      periods[0] and periods[1]: threshold periodicities for business cycle
      k: order of the approximation
    */

    /* get user settings if available (or the defaults) */
    get_bkbp_periods(pdinfo, &bkl, &bku);
    k = get_bkbp_k(pdinfo);

#if BK_DEBUG
    fprintf(stderr, "lower limit = %d, upper limit = %d, \n", 
          bkl, bku);
#endif

    if (bkl >= bku) {
      strcpy(gretl_errmsg, "Error in Baxter-King frequencies");
      return 1;
    }

    err = array_adjust_t1t2(y, &t1, &t2);
    if (err) {
      return err;
    } 

    if (2 * k >= t2 - t1 + 1) {
      strcpy(gretl_errmsg, "Insufficient observations");
      return E_DATA;
    }

    a = malloc((k + 1) * sizeof *a);
    if (a == NULL) {
      return E_ALLOC;
    }
    
    omubar = M_2PI / bkl;
    omlbar = M_2PI / bku;
    
    /* first we compute the coefficients */

    avg_a = a[0] = (omubar - omlbar) / M_PI;

    for (i=1; i<=k; i++) {
      a[i] = (sin(i * omubar) - sin(i * omlbar)) / (i * M_PI);
      avg_a += 2 * a[i];
    }

    avg_a /= (2 * k + 1);

    for (i=0; i<=k; i++) {
      a[i] -= avg_a;
#if BK_DEBUG
      fprintf(stderr, "a[%d] = %#9.6g\n", i, a[i]);
#endif
    }

    /* now we filter the series, skipping the first
       and last k observations */

    for (t=0; t<pdinfo->n; t++) {
      if (t < t1 + k || t > t2 - k) {
          bk[t] = NADBL;
      } else {
          bk[t] = a[0] * y[t];
          for (i=1; i<=k; i++) {
            bk[t] += a[i] * (y[t-i] + y[t+i]);
          }
      }
    }

    free(a);

    return err;
}

static int n_new_dummies (const DATAINFO *pdinfo,
                    int nunits, int nperiods)
{
    char dname[VNAMELEN];
    int i, nnew = nunits + nperiods;

    for (i=0; i<nunits; i++) {
      sprintf(dname, "du_%d", i + 1);
      if (gretl_is_series(dname, pdinfo)) {
          nnew--;
      }
    }

    for (i=0; i<nperiods; i++) {
      sprintf(dname, "dt_%d", i + 1);
      if (gretl_is_series(dname, pdinfo)) {
          nnew--;
      }
    }

    return nnew;
}

static void 
make_dummy_name_and_label (int vi, const DATAINFO *pdinfo, int center,
                     char *vname, char *vlabel)
{
    if (center > 0) {
      sprintf(vname, "S%d", vi);
      strcpy(vlabel, "centered periodic dummy");
    } else if (center < 0) {
      sprintf(vname, "S%d", vi);
      strcpy(vlabel, "uncentered periodic dummy");
    } else if (pdinfo->pd == 4 && pdinfo->structure == TIME_SERIES) {
      sprintf(vname, "dq%d", vi);
      sprintf(vlabel, _("= 1 if quarter = %d, 0 otherwise"), vi);
    } else if (pdinfo->pd == 12 && pdinfo->structure == TIME_SERIES) {
      sprintf(vname, "dm%d", vi);
      sprintf(vlabel, _("= 1 if month = %d, 0 otherwise"), vi);
    } else {
      char dumstr[8] = "dummy_";
      char numstr[8];
      int len;

      sprintf(numstr, "%d", vi);
      len = strlen(numstr);
      dumstr[8 - len] = '\0';
      sprintf(vname, "%s%d", dumstr, vi);
      sprintf(vlabel, _("%s = 1 if period is %d, 0 otherwise"), vname, vi);
    }
}

/**
 * dummy:
 * @pZ: pointer to data matrix.
 * @pdinfo: data information struct.
 * @center: if greater than zero subtract the population mean from
 * each of the generated dummies; if less than zero, do not
 * subtract the mean but generate dummies with labels on the
 * same pattern as centered dummies (for internal use in VECMs).
 * Usually this argument is set to zero.
 *
 * Adds to the data set (if these variables are not already 
 * present) a set of periodic (usually seasonal) dummy variables.
 *
 * Returns: the ID number of the first dummy variable on success,
 * or 0 on error.
 */

int dummy (double ***pZ, DATAINFO *pdinfo, int center)
{
    char vname[VNAMELEN];
    char vlabel[MAXLABEL];
    int vi, t, pp;
    int ndums = pdinfo->pd, nnew = 0;
    int di, di0 = pdinfo->v;
    double xx, dx;

    if (ndums == 1 || ndums > 99999) {
      strcpy(gretl_errmsg, _("This command won't work with the current periodicity"));
      return 0;
    }

    for (vi=0; vi<ndums; vi++) {
      make_dummy_name_and_label(vi + 1, pdinfo, center, vname, vlabel);
      di = series_index(pdinfo, vname);
      if (di >= pdinfo->v || strcmp(vlabel, VARLABEL(pdinfo, di))) {
          nnew++;
      } else if (vi == 0) {
          di0 = di;
      } else if (di != di0 + vi) {
          /* dummies not consecutive: problem */
          di0 = pdinfo->v;
          nnew = ndums;
          break;
      }
    }

    if (nnew == 0) {
      /* all dummies already present */
      return di0;
    } else if (pZ == NULL) {
      return -1;
    }

    if (dataset_add_series(ndums, pZ, pdinfo)) {
      strcpy(gretl_errmsg, _("Out of memory!"));
      return 0;
    }

    for (vi=1, di = di0; vi<=ndums; vi++, di++) {
      make_dummy_name_and_label(vi, pdinfo, center, vname, vlabel);
      strcpy(pdinfo->varname[di], vname);
      strcpy(VARLABEL(pdinfo, di), vlabel);
    }

    if (dataset_is_daily(pdinfo)) {
      int yy, mm = 10;

      pp = pdinfo->pd;
      while ((pp = pp / 10)) {
          mm *= 10;
      }

      for (vi=1, di = di0; vi<=ndums; vi++, di++) {
          for (t=0; t<pdinfo->n; t++) {
            xx = date(t, pdinfo->pd, pdinfo->sd0) + .1;
            yy = (int) xx;
            pp = (int) (mm * (xx - yy) + 0.5);
            dx = (pp == vi)? 1.0 : 0.0;
            (*pZ)[di][t] = dx;
          }
      }
    } else {
      int p0 = get_subperiod(0, pdinfo, NULL);

      for (t=0; t<pdinfo->n; t++) {
          pp = (t + p0) % pdinfo->pd;
          for (vi=0, di = di0; vi<ndums; vi++, di++) {
            dx = (pp == vi)? 1 : 0;
            (*pZ)[di][t] = dx;
          }
      }
    }

    if (center > 0) {
      double cx = 1.0 / pdinfo->pd;
      int vimax = di0 + pdinfo->pd - 1;

      for (vi=di0; vi<=vimax; vi++) {
          for (t=0; t<pdinfo->n; t++) {
            (*pZ)[vi][t] -= cx;
          }
      }     
    }

    return di0;
}

/**
 * panel_dummies:
 * @pZ: pointer to data matrix.
 * @pdinfo: data information struct.
 * @opt: %OPT_T for time dummies, otherwise unit dummies.
 *
 * Adds to the data set a set of dummy variables corresponding
 * to either the cross-sectional units in a panel, or the
 * time periods.
 *
 * Returns: 0 on successful completion, error code on error.
 */

int panel_dummies (double ***pZ, DATAINFO *pdinfo, gretlopt opt)
{
    char vname[16];
    int vi, t, yy, pp, mm;
    int orig_v = pdinfo->v;
    int ndum, nnew;
    int n_unitdum = 0;
    int n_timedum = 0;
    int newvnum;
    double xx;

    if (opt & OPT_T) {
      ndum = n_timedum = pdinfo->pd;
    } else {      
      n_unitdum = pdinfo->n / pdinfo->pd;
      if (pdinfo->n % pdinfo->pd) {
          n_unitdum++;
      }
      ndum = n_unitdum;
    }
    
    if (ndum == 1) {
      return E_PDWRONG;
    }

    nnew = n_new_dummies(pdinfo, n_unitdum, n_timedum);

    if (nnew > 0 && dataset_add_series(nnew, pZ, pdinfo)) {
      return E_ALLOC;
    }

    pp = pdinfo->pd;
    mm = 10;
    while ((pp = pp / 10)) {
      mm *= 10;
    }

    newvnum = orig_v;

    /* generate time-based dummies, if wanted */

    for (vi=1; vi<=n_timedum; vi++) {
      int dnum;

      sprintf(vname, "dt_%d", vi);

      dnum = series_index(pdinfo, vname);
      if (dnum >= orig_v) {
          dnum = newvnum++;
      }

      strcpy(pdinfo->varname[dnum], vname);
      sprintf(VARLABEL(pdinfo, dnum), 
            _("%s = 1 if %s is %d, 0 otherwise"), vname, 
            _("period"), vi);

      for (t=0; t<pdinfo->n; t++) {
          xx = date(t, pdinfo->pd, pdinfo->sd0);
          yy = (int) xx;
          pp = (int) (mm * (xx - yy) + 0.5);
          (*pZ)[dnum][t] = (pp == vi)? 1.0 : 0.0;
      }
    }

    /* generate unit-based dummies, if wanted */

    for (vi=1; vi<=n_unitdum; vi++) {
      int dmin = (vi - 1) * pdinfo->pd;
      int dmax = vi * pdinfo->pd;
      int dnum;

      sprintf(vname, "du_%d", vi);

      dnum = series_index(pdinfo, vname);
      if (dnum >= orig_v) {
          dnum = newvnum++;
      }     

      strcpy(pdinfo->varname[dnum], vname);
      sprintf(VARLABEL(pdinfo, dnum), 
            _("%s = 1 if %s is %d, 0 otherwise"), vname, 
            _("unit"), vi);

      for (t=0; t<pdinfo->n; t++) {
          (*pZ)[dnum][t] = (t >= dmin && t < dmax)? 1 : 0;
      }
    }

    return 0;
}

/**
 * gen_unit:
 * @pZ: pointer to data matrix.
 * @pdinfo: data information struct.
 *
 * (For panel data only) adds to the data set an index variable 
 * that uniquely identifies the cross-sectional units.
 *
 * Returns: 0 on successful completion, error code on error.
 */

int gen_unit (double ***pZ, DATAINFO *pdinfo)
{
    int xt = 0;
    int i, t;

    if (pdinfo->structure != STACKED_TIME_SERIES) {
      strcpy(gretl_errmsg, "'genr unit' can be used only with "
             "panel data");
      return 1;
    }

    i = series_index(pdinfo, "unit");

    if (i == pdinfo->v && dataset_add_series(1, pZ, pdinfo)) {
      return E_ALLOC;
    }

    strcpy(pdinfo->varname[i], "unit");
    strcpy(VARLABEL(pdinfo, i), _("cross-sectional unit index"));

    for (t=0; t<pdinfo->n; t++) {
      if (t % pdinfo->pd == 0) {
          xt++;
      }
      (*pZ)[i][t] = (double) xt;
    }

    return 0;
}

/**
 * panel_unit_first_obs:
 * @t: zero-based observation number.
 * @pdinfo: data information struct.
 *
 * Returns: 1 if observation @t is the first time-series
 * observation on a given cross-sectional unit in a
 * panel dataset, else 0.
 */

int panel_unit_first_obs (int t, const DATAINFO *pdinfo)
{
    char *p, obs[OBSLEN];
    int ret = 0;

    ntodate(obs, t, pdinfo);
    p = strchr(obs, ':');
    if (p != NULL && atoi(p + 1) == 1) {
      ret = 1;
    }

    return ret;
}

/* make special time variable for panel data */

static void 
make_panel_time_var (double *x, const DATAINFO *pdinfo)
{
    int t, xt = 0;

    for (t=0; t<pdinfo->n; t++) {
      if (t % pdinfo->pd == 0) {
          xt = 1;
      }
      x[t] = (double) xt++;
    }
}

/**
 * gen_time:
 * @pZ: pointer to data array.
 * @pdinfo: data information struct.
 * @tm: if non-zero, an actual time trend is wanted,
 * otherwise just an index of observations.
 *
 * Generates (and adds to the dataset, if it's not already
 * present) a time-trend or index variable.  This function
 * is panel-data aware: if the dataset is a panel and
 * @tm is non-zero, the trend will not simply run
 * consecutively over the entire range of the data, but
 * will correctly represent the location in time of
 * each observation.  The index is 1-based.
 *
 * Returns: 0 on success, non-zero on error.
 */

int gen_time (double ***pZ, DATAINFO *pdinfo, int tm)
{
    int i, t;

    i = series_index(pdinfo, (tm)? "time" : "index");

    if (i == pdinfo->v && dataset_add_series(1, pZ, pdinfo)) {
      return E_ALLOC;
    }

    if (tm) {
      strcpy(pdinfo->varname[i], "time");
      strcpy(VARLABEL(pdinfo, i), _("time trend variable"));
    } else {
      strcpy(pdinfo->varname[i], "index");
      strcpy(VARLABEL(pdinfo, i), _("data index variable"));
    }
    
    if (tm && pdinfo->structure == STACKED_TIME_SERIES) {
      make_panel_time_var((*pZ)[i], pdinfo);
    } else {
      for (t=0; t<pdinfo->n; t++) {
          (*pZ)[i][t] = (double) (t + 1);
      }
    }

    return 0;
}

/**
 * genr_wkday:
 * @pZ: pointer to data array.
 * @pdinfo: data information struct.
 *
 * Generates (and adds to the dataset, if it's not already
 * present) an index representing the day of the week for
 * each observation (for dated daily data only).
 * The index has value 0 for Sunday, 1 for Monday, and
 * so on.
 *
 * Returns: 0 on success, non-zero code on error.
 */

int gen_wkday (double ***pZ, DATAINFO *pdinfo)
{
    char datestr[OBSLEN];
    int i, t;

    if (!dated_daily_data(pdinfo)) {
      return E_PDWRONG;
    }

    i = series_index(pdinfo, "weekday");

    if (i == pdinfo->v && dataset_add_series(1, pZ, pdinfo)) {
      return E_ALLOC;
    }

    strcpy(pdinfo->varname[i], "weekday");
    strcpy(VARLABEL(pdinfo, i), _("day of week (1 = Monday)"));
    
    for (t=0; t<pdinfo->n; t++) {
      ntodate_full(datestr, t, pdinfo);
      (*pZ)[i][t] = get_day_of_week(datestr);
    }

    return 0;
}

typedef enum {
    PLOTVAR_INDEX,
    PLOTVAR_TIME,
    PLOTVAR_ANNUAL,
    PLOTVAR_QUARTERS,
    PLOTVAR_MONTHS,
    PLOTVAR_CALENDAR,
    PLOTVAR_DECADES,
    PLOTVAR_HOURLY,
    PLOTVAR_MAX
} plotvar_type; 

int plotvar_code (const DATAINFO *pdinfo)
{
    if (!dataset_is_time_series(pdinfo)) {
      return PLOTVAR_INDEX;
    } else if (pdinfo->pd == 1) {
      return PLOTVAR_ANNUAL;
    } else if (pdinfo->pd == 4) {
      return PLOTVAR_QUARTERS;
    } else if (pdinfo->pd == 12) {
      return PLOTVAR_MONTHS;
    } else if (pdinfo->pd == 24) {
      return PLOTVAR_HOURLY;
    } else if (calendar_data(pdinfo)) {
      return PLOTVAR_CALENDAR;
    } else if (dataset_is_decennial(pdinfo)) {
      return PLOTVAR_DECADES;
    } else {
      return PLOTVAR_TIME;
    }
}

/**
 * gretl_plotx:
 * @pdinfo: data information struct.
 *
 * Finds or creates a special dummy variable for use on the
 * x-axis in plotting; this will have the full length of the
 * data series as given in @pdinfo, and will be appropriately
 * configured for the data frequency.  Do not try to free this
 * variable.
 *
 * Returns: pointer to plot x-variable, or %NULL on failure.
 */

const double *gretl_plotx (const DATAINFO *pdinfo)
{
    static double *x;
    static int ptype;
    static int Tbak;
    static double sd0bak;

    int t, y1, T;
    int new_ptype;
    double sd0;
    float rm;

    if (pdinfo == NULL) {
      /* cleanup signal */
      free(x);
      x = NULL;
      ptype = 0;
      T = 0;
      sd0 = 0;
      return NULL;
    }

    new_ptype = plotvar_code(pdinfo);
    T = pdinfo->n;
    sd0 = pdinfo->sd0;

    if (x != NULL && new_ptype == ptype && Tbak == T && sd0 == sd0bak) {
      /* a suitable array is already at hand */
      return x;
    }

    if (x != NULL) {
      free(x);
    }

    x = malloc(T * sizeof *x);
    if (x == NULL) {
      return NULL;
    }

    Tbak = T;
    ptype = new_ptype;
    sd0bak = sd0;

    y1 = (int) sd0;
    rm = sd0 - y1;

    switch (ptype) {
    case PLOTVAR_ANNUAL: 
      for (t=0; t<T; t++) {
          x[t] = (double) (t + atoi(pdinfo->stobs));
      }
      break;
    case PLOTVAR_QUARTERS:
      x[0] = y1 + (10.0 * rm - 1.0) / 4.0;
      for (t=1; t<T; t++) {
          x[t] = x[t-1] + .25;
      }
      break;
    case PLOTVAR_MONTHS:
      x[0] = y1 + (100.0 * rm - 1.0) / 12.0;
      for (t=1; t<T; t++) {
          x[t] = x[t-1] + (1.0 / 12.0);
      }
      break;
    case PLOTVAR_HOURLY:
      x[0] = y1 + (100.0 * rm - 1.0) / 24.0;
      for (t=1; t<T; t++) {
          x[t] = x[t-1] + (1.0 / 24.0);
      }
      break;
    case PLOTVAR_CALENDAR:
      for (t=0; t<T; t++) {
          if (pdinfo->S != NULL) {
            x[t] = get_dec_date(pdinfo->S[t]);
          } else {
            char datestr[OBSLEN];
                
            calendar_date_string(datestr, t, pdinfo);
            x[t] = get_dec_date(datestr);
          }
      }
      break;
    case PLOTVAR_DECADES:
      for (t=0; t<T; t++) {
          x[t] = pdinfo->sd0 + 10 * t;
      }
      break;
    case PLOTVAR_INDEX:
      for (t=0; t<T; t++) {
          x[t] = (double) (t + 1);
      }
      break;
    case PLOTVAR_TIME:
      for (t=0; t<T; t++) {
          x[t] = (double) (t + 1);
      }
      break;
    default:
      break;
    }

    return x;
}

/**
 * genr_fit_resid:
 * @pmod: pointer to model to be tested.
 * @pZ: pointer to data matrix.
 * @pdinfo: information on the data set.
 * @code: GENR_RESID or GENR_FITTED or GENR_RESID2.
 * @undo: if non-zero, don't bother labeling the variables
 *
 * Adds residuals or fitted values or squared residuals from a
 * given model to the data set.
 * 
 * Returns: 0 on successful completion, error code on error.
 */

int genr_fit_resid (const MODEL *pmod, double ***pZ, DATAINFO *pdinfo,
                int code, int undo)
{
    char vname[VNAMELEN], vlabel[MAXLABEL];
    const double *x = NULL;
    int i, t;

    if (code == M_H) {
      x = gretl_model_get_data(pmod, "garch_h");
      if (x == NULL) return E_BADSTAT;
    } else if (code == M_AHAT) {
      x = gretl_model_get_data(pmod, "ahat");
      if (x == NULL) return E_BADSTAT;
    } else if (code == M_UHAT || code == M_UHAT2) {
      if (pmod->uhat == NULL) return E_BADSTAT;
    } else if (code == M_YHAT) {
      if (pmod->yhat == NULL) return E_BADSTAT;
    }

    if (dataset_add_series(1, pZ, pdinfo)) {
      return E_ALLOC;
    }

    i = pdinfo->v - 1;

    for (t=0; t<pdinfo->n; t++) {
      (*pZ)[i][t] = NADBL;
    }

    if (code == M_UHAT) {
      sprintf(vname, "uhat%d", pmod->ID);
      if (pmod->ci == GARCH && (pmod->opt & OPT_U)) {
          sprintf(vlabel, _("standardized residual from model %d"), pmod->ID);
      } else {
          sprintf(vlabel, _("residual from model %d"), pmod->ID);
      }
      for (t=pmod->t1; t<=pmod->t2; t++) {
          (*pZ)[i][t] = pmod->uhat[t];
      }
    } else if (code == M_YHAT) {
      sprintf(vname, "yhat%d", pmod->ID);
      sprintf(vlabel, _("fitted value from model %d"), pmod->ID);
      for (t=pmod->t1; t<=pmod->t2; t++) {
          (*pZ)[i][t] = pmod->yhat[t];
      }
    } else if (code == M_UHAT2) { 
      /* squared residuals */
      sprintf(vname, "usq%d", pmod->ID);
      if (pmod->ci == GARCH && (pmod->opt & OPT_U)) {
          sprintf(vlabel, _("squared standardized residual from model %d"), pmod->ID);
      } else {
          sprintf(vlabel, _("squared residual from model %d"), pmod->ID);
      }
      for (t=pmod->t1; t<=pmod->t2; t++) {
          if (na(pmod->uhat[t])) {
            (*pZ)[i][t] = NADBL;
          } else {
            (*pZ)[i][t] = pmod->uhat[t] * pmod->uhat[t];
          }
      }
    } else if (code == M_H) { 
      /* garch variance */
      sprintf(vname, "h%d", pmod->ID);
      sprintf(vlabel, _("fitted variance from model %d"), pmod->ID);
      for (t=pmod->t1; t<=pmod->t2; t++) {
          (*pZ)[i][t] = x[t];
      }
    } else if (code == M_AHAT) { 
      /* fixed-effects constants */
      sprintf(vname, "ahat%d", pmod->ID);
      sprintf(vlabel, _("per-unit constants from model %d"), pmod->ID);
      for (t=pmod->t1; t<=pmod->t2; t++) {
          (*pZ)[i][t] = x[t];
      }
    } 

    strcpy(pdinfo->varname[i], vname);

    if (!undo) {
      strcpy(VARLABEL(pdinfo, i), vlabel);
    }

    return 0;
}

int get_observation_number (const char *s, const DATAINFO *pdinfo)
{
    char test[OBSLEN];
    size_t n;
    int t;

    *test = 0;
    strncat(test, (*s == '"')? s + 1 : s, OBSLEN - 1);

    n = strlen(test);
    if (test[n-1] == '"') {
      test[n-1] = '\0';
    }

    if (pdinfo->markers && pdinfo->S != NULL) {
      for (t=0; t<pdinfo->n; t++) {
          if (!strcmp(test, pdinfo->S[t])) {
            return t + 1;
          }
      }
      if (calendar_data(pdinfo)) {
          for (t=0; t<pdinfo->n; t++) {
            if (!strcmp(test, pdinfo->S[t]) ||
                !strcmp(test, pdinfo->S[t] + 2)) {
                return t + 1;
            }
          }
      }
    }

    if (pdinfo->structure == TIME_SERIES) {
      t = dateton(test, pdinfo);
      if (t >= 0) {
          return t + 1;
      }
    }

    if (calendar_data(pdinfo)) {
      char datestr[OBSLEN];

      for (t=0; t<pdinfo->n; t++) {
          calendar_date_string(datestr, t, pdinfo);
          if (!strcmp(test, datestr) ||
            !strcmp(test, datestr + 2)) {
            return t + 1;
          }
      }
    }

    return 0;
}

#define OBS_DEBUG 0

static int plain_obs_number (const char *obs, const DATAINFO *pdinfo)
{
    char *test;
    int t = -1;

    errno = 0;

    strtol(obs, &test, 10);

    if (errno == 0 && *test == '\0') {
      t = atoi(obs) - 1; /* convert from 1-based to 0-based */
      if (t >= pdinfo->n) {
          t = -1;
      }
    }

    return t;
}

/* Given what looks like an observation number or date within "[" and
   "]", try to determine the observation number.  This is quite tricky
   since we try to handle both dates and plain observation numbers
   (and in addition, variables representing the latter); and we may
   have to deal with the translation from 1-based indexing in user
   space to 0-based indexing for internal purposes.
*/

int get_t_from_obs_string (const char *s, const double **Z, 
                     const DATAINFO *pdinfo)
{
    int t = dateton(s, pdinfo);

#if OBS_DEBUG
    fprintf(stderr, "\nget_t_from_obs_string: s ='%s', dateton gives t = %d\n", 
          s, t);
#endif

    if (t < 0) {
      if (isdigit((unsigned char) *s)) {
          t = plain_obs_number(s, pdinfo);
#if OBS_DEBUG
          fprintf(stderr, " plain_obs_number gives t = %d\n", t);
#endif
      } else {
          if (gretl_is_scalar(s)) {
            t = gretl_scalar_get_value(s);
          } 

          if (t > pdinfo->n) {
            char try[16];

            sprintf(try, "%d", t);
            t = dateton(try, pdinfo);
#if OBS_DEBUG
            fprintf(stderr, " revised via dateton: t = %d\n", t);
#endif
          } else {
            /* convert to 0-based */
            t--;
          }
      }
    }

    if (t < 0) {
      sprintf(gretl_errmsg, _("Observation number out of bounds"));
    }

#if OBS_DEBUG
    fprintf(stderr, " return value: t = %d\n", t);
#endif

    return t;
}

int check_declarations (char ***pS, parser *p)
{
    char **S;
    const char *s;
    int i, n = 1;

    gretl_error_clear();

    if (p->lh.substr == NULL) {
      p->err = E_ALLOC;
      return 0;
    }

    s = p->lh.substr;
    s += strspn(s, " ");

    while (*s) {
      if (*s == ',' || *s == ' ') {
          n++;
          s++;
          s += strspn(s, " ");
      } else {
          s++;
      }
    }

    S = strings_array_new(n);
    if (S == NULL) {
      p->err = E_ALLOC;
      return 0;
    }

    s = p->lh.substr;
    for (i=0; i<n; i++) {
      S[i] = gretl_word_strdup(s, &s);
      if (S[i] == NULL) {
          p->err = E_DATA;
          break;
      }
    }

    if (*s != '\0') {
      p->err = E_DATA;
    }

    for (i=0; i<n && !p->err; i++) {
      if (gretl_is_series(S[i], p->dinfo) ||
          gretl_is_scalar(S[i]) ||
          get_matrix_by_name(S[i]) ||
          get_list_by_name(S[i]) ||
          get_string_by_name(S[i])) {
          /* variable already exists */
          p->err = E_DATA;
      } else if (check_varname(S[i])) {
          /* invalid name */
          p->err = E_DATA;
      } 
    }

    if (p->err) {
      gretl_errmsg_set(_("Invalid declaration"));
      free_strings_array(S, n);
    } else {
      *pS = S;
    }

    return n;
}

/* cross-sectional mean of observations on variables in @list
   at time @t */

static double mean_at_obs (const int *list, const double **Z, int t)
{
    double xi, xsum = 0.0;
    int i;

    for (i=1; i<=list[0]; i++) {
      xi = Z[list[i]][t];
      if (na(xi)) {
          return NADBL;
      }
      xsum += xi;
    }

    return xsum / list[0];
}

/* weighted cross-sectional mean of observations on variables in @list
   at time @t, weights given in @wlist */

static double weighted_mean_at_obs (const int *list, const int *wlist,
                            const double **Z, int t,
                            double *pwsum, int *pm)
{
    double w, xi, wsum = 0.0, wxbar = 0.0;
    int i, m = 0;

    for (i=1; i<=list[0]; i++) {
      w = Z[wlist[i]][t];
      if (na(w) || w < 0.0) {
          return NADBL;
      }
      if (w > 0.0) {
          wsum += w;
          m++;
      }
    }

    if (wsum <= 0.0) {
      return NADBL;
    }

    if (pwsum != NULL) {
      *pwsum = wsum;
    }

    if (pm != NULL) {
      *pm = m;
    }

    for (i=1; i<=list[0]; i++) {
      w = Z[wlist[i]][t] / wsum;
      if (w > 0) {
          xi = Z[list[i]][t];
          if (na(xi)) {
            return NADBL;
          }
          wxbar += xi * w;
      }
    }

    return wxbar;
}

/* Computes weighted mean of the variables in @list using the
   (possibly time-varying) weights given in @wlist, or the
   unweighted mean if @wlist is NULL.
*/

static int x_sectional_weighted_mean (double *x, const int *list, 
                              const int *wlist,
                              const double **Z, 
                              const DATAINFO *pdinfo)
{
    int n = list[0];
    int t, v;

    if (n == 0) {
      return 0; /* all NAs */
    } else if (n == 1) {
      v = list[1];
      for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
          x[t] = Z[v][t]; 
      }
      return 0;
    }

    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (wlist != NULL) {
          x[t] = weighted_mean_at_obs(list, wlist, Z, t, NULL, NULL);
      } else {
          x[t] = mean_at_obs(list, Z, t);
      }
    }

    return 0;
}

/* Computes weighted sample variance of the variables in @list using
   the (possibly time-varying) weights given in @wlist, or the
   unweighted sample variance if @wlist is NULL
*/

static int x_sectional_wtd_variance (double *x, const int *list,
                             const int *wlist,
                             const double **Z, 
                             const DATAINFO *pdinfo)
{
    double xdev, xbar, wsum;
    int m = 0, n = list[0];
    int i, t, v;

    if (n == 0) {
      return 0; /* all NAs */
    } else if (n == 1) {
      for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
          x[t] = 0.0;
      }
      return 0;
    }

    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      if (wlist != NULL) {
          xbar = weighted_mean_at_obs(list, wlist, Z, t, &wsum, &m);
      } else {
          xbar = mean_at_obs(list, Z, t);
      }
      if (na(xbar)) {
          x[t] = NADBL;
          continue;
      }
      if (wlist != NULL && m < 2) {
          x[t] = (m == 1)? 0.0 : NADBL;
          continue;
      }
      x[t] = 0.0;
      for (i=1; i<=list[0]; i++) {
          v = list[i];
          xdev = Z[v][t] - xbar;
          if (wlist != NULL) {
            x[t] += xdev * xdev * Z[wlist[i]][t] / wsum;
          } else {
            x[t] += xdev * xdev;
          }
      }
      if (wlist != NULL) {
          x[t] *= m / (m - 1);
      } else {
          x[t] /= (n - 1);
      }
    }

    return 0;
}

static int x_sectional_wtd_stddev (double *x, const int *list, 
                           const int *wlist,
                           const double **Z, 
                           const DATAINFO *pdinfo)
{
    int t, err;

    err = x_sectional_wtd_variance(x, list, wlist, Z, pdinfo);

    if (!err) {
      for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
          if (!na(x[t])) {
            x[t] = sqrt(x[t]);
          }
      }
    }

    return err;
}

static int x_sectional_extremum (int f, double *x, const int *list, 
                         const int *wlist,
                         const double **Z, 
                         const DATAINFO *pdinfo)
{
    double xit, xx;
    int i, t, err = 0;

    for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
      xx = (f == F_MIN)? NADBL : -NADBL;
      for (i=1; i<=list[0]; i++) {
          xit = Z[list[i]][t];
          if (!na(xit)) { 
            if (f == F_MAX && xit > xx) {
                xx = xit;
            } else if (f == F_MIN && xit < xx) {
                xx = xit;
            }
          }
      }
      if (xx == -NADBL) {
          x[t] = NADBL;
      } else {
          x[t] = xx;
      }
    }

    return err;
}

int cross_sectional_stat (double *x, const int *list, 
                    const double **Z, 
                    const DATAINFO *pdinfo,
                    int f)
{
    if (f == F_MEAN) {
      return x_sectional_weighted_mean(x, list, NULL, Z, pdinfo);
    } else if (f == F_VCE) {
      return x_sectional_wtd_variance(x, list, NULL, Z, pdinfo);
    } else if (f == F_SD) {
      return x_sectional_wtd_stddev(x, list, NULL, Z, pdinfo);
    } else if (f == F_MIN || f == F_MAX) {
      return x_sectional_extremum(f, x, list, NULL, Z, pdinfo);
    } else {
      return E_DATA;
    }
}

int x_sectional_weighted_stat (double *x, const int *list, 
                         const int *wlist,
                         const double **Z, 
                         const DATAINFO *pdinfo,
                         int f)
{
    if (wlist[0] != list[0]) {
      gretl_errmsg_sprintf("Weighted stats: data list has %d members but weight "
                       "list has %d", list[0], wlist[0]);
      return E_DATA;
    }

    if (f == F_WMEAN) {
      return x_sectional_weighted_mean(x, list, wlist, Z, pdinfo);
    } else if (f == F_WVAR) {
      return x_sectional_wtd_variance(x, list, wlist, Z, pdinfo);
    } else if (f == F_WSD) {
      return x_sectional_wtd_stddev(x, list, wlist, Z, pdinfo);
    } else {
      return E_DATA;
    }
}

/* writes to the series @y a linear combination of the variables given
   in @list, using the coefficients given in the vector @b.
*/

int list_linear_combo (double *y, const int *list, 
                   const gretl_vector *b, const double **Z, 
                   const DATAINFO *pdinfo)
{
    int nb = gretl_vector_get_length(b);
    int nl = list[0];
    int err = 0;

    if (nb != nl) {
      err = E_DATA;
    } else {
      int i, t;
      double xit, yt;

      for (t=pdinfo->t1; t<=pdinfo->t2; t++) {
          yt = 0;
          for (i=0; i<nl; i++) {
            xit = Z[list[i+1]][t];
            if (na(xit)) {
                yt = NADBL;
                break;
            } else {
                yt += xit * gretl_vector_get(b, i);
            }
          }
          y[t] = yt;
      }
    }

    return err;
}

/* Imhof: draws on the RATS code in IMHOF.SRC from Estima, 2004.

   Imhof Procedure for computing P(u'Au < x) for a quadratic form in
   Normal(0,1) variables. This can be used for ratios of quadratic
   forms as well, since P((u'Au/u'Bu) < x) = P(u'(A-xB)u < 0).

   In the Durbin-Watson context, 'B' is the identity matrix and
   'x' is the Durbin-Watson statistic.

   References:

   Imhof, J.P (1961), Computing the Distribution of Quadratic Forms of
   Normal Variables, Biometrika 48, 419-426.

   Abrahamse, A.P.J and Koerts, J. (1969), On the Theory and
   Application of the General Linear Model, Rotterdam University
   Press.
*/

static double imhof_bound (const double *lambda, int k, int *err)
{
    double e1 = 0.0001; /* Max truncation error due to finite 
                     upper bound on domain */
    double e2 = 0.0001; /* Cutoff for deciding whether an 
                     eigenvalue is effectively zero */
    double absl, bound;
    double nl = 0.0, sum = 0.0;
    int i;

    for (i=0; i<k; i++) {
      absl = fabs(lambda[i]);
      if (absl > e2) {
          nl += 1.0;
          sum += log(absl);
      }
    }

    if (nl == 0.0) {
      fprintf(stderr, "imhof_bound: got no non-zero eigenvalues\n");
      *err = E_DATA;
      return NADBL;
    }

    /* The key factor in the integrand is the product of 
       (1+(lambda(i)*x)**2)**(1/4) across i. Since, for those 
       factors with small |lambda(i)|, this won't go to zero very
       quickly, we count only the terms on the bigger eigenvalues.
    */

    nl = 0.5 * nl;
    sum = 0.5 * sum + log(M_PI * nl);
    bound = exp(-(sum + log(e1)) / nl);
    bound += 5.0 / nl;

    if (bound < 0) {
      fprintf(stderr, "imhof_bound: got negative result\n");
      *err = E_DATA;
      bound = NADBL;
    }

    return bound;
}

static double vecsum (const double *x, int k)
{
    double sum = 0.0;
    int i;

    for (i=0; i<k; i++) {
      sum += x[i];
    }

    return sum;
}

static double imhof_f (double u, const double *lambda, int k, double arg)
{
    double ul, rho = 0.0;
    double theta = -u * arg;
    int i;

    /* The value at zero isn't directly computable as
       it produces 0/0. The limit is computed below.
    */
    if (u == 0.0) {
      return 0.5 * (-arg + vecsum(lambda, k));
    }

    for (i=0; i<k; i++) {
      ul = u * lambda[i];
      theta += atan(ul);
      rho += log(1.0 + ul * ul);
    }

    return sin(0.5 * theta) / (u * exp(0.25 * rho));
}

#define gridlimit 2048

/*
  Adaptation of Abrahamse and Koert's Pascal code.  Evaluates the
  integral by Simpson's rule with grid size halving each time until
  the change from moving to a tighter grid is negligible. By halving
  the grid, only the odd terms need to be computed, as the old ones
  are already in the sum. Points entering get x 4 weights, which then
  get reduced to x 2 on the next iteration.
*/

static double imhof_integral (double arg, const double *lambda, int k,
                        double bound, int *err)
{
    double e3 = 0.0001;
    double base, step, sum1;
    double int0 = 0.0, int1 = 0.0;
    double eps4 = 3.0 * M_PI * e3;
    double sum4 = 0.0;
    double ret = NADBL;
    int j, n = 2;

    base = imhof_f(0, lambda, k, arg);
    base += imhof_f(bound, lambda, k, arg);

    while (n < gridlimit) {
      step = bound / n;
      sum1 = base + sum4 * 2.0;
      base = sum1;
      sum4 = 0.0;
      for (j=1; j<=n; j+=2) {
          sum4 += imhof_f(j * step, lambda, k, arg);
      }
      int1 = (sum1 + 4 * sum4) * step;
      if (n > 8 && fabs(int1 - int0) < eps4) {
          break;
      }
      int0 = int1;
      n *= 2;
    }

    if (n > gridlimit) {
      fprintf(stderr, "n = %d, Imhof integral failed to converge\n", n);
      *err = E_NOCONV;
    } else {
      ret = 0.5 - int1 / (3.0 * M_PI);
      if (ret < 0 && ret > -1.0e-14) {
          ret = 0.0;
      } else if (ret < 0) {
          fprintf(stderr, "n = %d, Imhof integral gave negative value %g\n", n, ret);
          *err = E_DATA;
          ret = NADBL;
      }
    }

    return ret;
}

static int imhof_get_eigenvals (const gretl_matrix *m,
                        double **plam, int *pk)
{
    gretl_matrix *E, *A;
    int err = 0;

    A = gretl_matrix_copy(m);
    if (A == NULL) {
      return E_ALLOC;
    }

    E = gretl_general_matrix_eigenvals(A, 0, &err);

    if (!err) {
      *pk = E->rows;
      *plam = gretl_matrix_steal_data(E);
    }

    gretl_matrix_free(A);
    gretl_matrix_free(E);

    return err;
}

/* Implements the "imhof" function in genr: computes the probability
   P(u'Au < arg) for a quadratic form in Normal(0,1) variables.  The
   argument @m may be either the square matrix A or a column
   vector containing the precomputed eigenvalues of A.
*/

double imhof (const gretl_matrix *m, double arg, int *err)
{
    double *lambda = NULL;
    double bound, ret = NADBL;
    int k = 0, free_lambda = 0;

    errno = 0;

    if (m->cols == 1) {
      /* we'll assume m is a column vector of eigenvalues */
      lambda = m->val;
      k = m->rows;
    } else if (m->rows == m->cols) {
      /* we'll assume m is the 'A' matrix */
      *err = imhof_get_eigenvals(m, &lambda, &k);
      free_lambda = 1;
    } else {
      /* huh? */
      *err = E_DATA;
    }

    if (!*err) {
      bound = imhof_bound(lambda, k, err);
    }

    if (!*err) {
      ret = imhof_integral(arg, lambda, k, bound, err);
    }

    if (errno != 0) {
      fprintf(stderr, "imhof: %s\n", strerror(errno));
      if (!*err) {
          *err = E_NOCONV;
      }
      ret = NADBL;
      errno = 0;
    }

    if (free_lambda) {
      free(lambda);
    }

    return ret;
}

/* Implements the "dwpval" function in genr: given the residual vector
   @u and the matrix of regressors, @X, calculates the Durbin-Watson
   statistic then finds its p-value via the Imhof/Koerts/Abrahamse
   procedure.
*/

double dw_pval (const gretl_matrix *u, const gretl_matrix *X, 
            double *pDW, int *perr)
{
    gretl_matrix *M = NULL;
    gretl_matrix *A = NULL;
    gretl_matrix *MA = NULL;
    gretl_matrix *XX = NULL;
    gretl_matrix *E = NULL;
    double uu, DW;
    double pv = NADBL;
    int k = X->cols;
    int n = X->rows;
    int i, err = 0;

    M = gretl_identity_matrix_new(n);
    A = gretl_DW_matrix_new(n);
    MA = gretl_matrix_alloc(n, n);
    XX = gretl_matrix_alloc(k, k);

    if (M == NULL || A == NULL || MA == NULL || XX == NULL) {
      err = E_ALLOC;
      goto bailout;
    }

    gretl_matrix_multiply_mod(X, GRETL_MOD_TRANSPOSE,
                        X, GRETL_MOD_NONE,
                        XX, GRETL_MOD_NONE);

    err = gretl_invert_symmetric_matrix(XX);

    if (!err) {
      /* M = I - X(X'X)^{-1}X' */
      err = gretl_matrix_qform(X, GRETL_MOD_NONE,
                         XX, M, GRETL_MOD_DECREMENT);
    }

    if (!err) {
      err = gretl_matrix_multiply(M, A, MA);
    }

    if (!err) {
      uu = gretl_matrix_dot_product(u, GRETL_MOD_TRANSPOSE,
                              u, GRETL_MOD_NONE,
                              &err);
    }

    if (!err) {
      DW = gretl_scalar_qform(u, A, &err);
    }

    if (!err) {
      DW /= uu;
      E = gretl_general_matrix_eigenvals(MA, 0, &err);
    }

    if (!err) {
      k = n - k;
      for (i=0; i<k; i++) {
          E->val[i] -= DW;
      }
      gretl_matrix_reuse(E, k, 1);
      pv = imhof(E, 0.0, &err);
      if (!err && pDW != NULL) {
          *pDW = DW;
      }
    }

 bailout:

    gretl_matrix_free(M);
    gretl_matrix_free(A);
    gretl_matrix_free(MA);
    gretl_matrix_free(XX);
    gretl_matrix_free(E);

    *perr = err;

    return pv;
}

/* create a matrix containing ACF and PACF values for each
   column of the input matrix, @m, with lag order @p.
*/

gretl_matrix *multi_acf (const gretl_matrix *m, 
                   const int *list,
                   const double **Z,
                   const DATAINFO *pdinfo,
                   int p, int *err)
{
    gretl_matrix *a, *A = NULL;
    const double *x;
    double xa;
    int nv, T, acol, pcol;
    int i, j;
    
    if (list == NULL && gretl_is_null_matrix(m)) {
      *err = E_DATA;
      return NULL;
    }

    if (m != NULL) {
      nv = m->cols;
    } else {
      nv = list[0];
    }

    A = gretl_matrix_alloc(p, 2 * nv);
    if (A == NULL) {
      *err = E_ALLOC;
      return NULL;
    }

    if (m != NULL) {
      x = m->val;
      T = m->rows;
    } else {
      x = Z[list[1]] + pdinfo->t1;
      T = sample_size(pdinfo);
    }

    acol = 0;
    pcol = nv;

    for (j=0; j<nv; j++) {
      /* get ACF/PACF for column/series */
      a = acf_vec(x, p, NULL, T, err);
      if (*err) {
          gretl_matrix_free(a);
          gretl_matrix_free(A);
          return NULL;
      }

      /* transcribe into A matrix and free */
      for (i=0; i<p; i++) {
          xa = gretl_matrix_get(a, i, 0);
          gretl_matrix_set(A, i, acol, xa);
          xa = gretl_matrix_get(a, i, 1);
          gretl_matrix_set(A, i, pcol, xa);
      }
      acol++;
      pcol++;

      gretl_matrix_free(a);

      /* move to next data read position */
      if (j < nv - 1) {
          if (m != NULL) {
            x += m->rows;
          } else {
            x = Z[list[j+2]] + pdinfo->t1;
          }
      }
    }

    return A;
}

gretl_matrix *multi_xcf (const void *px, int xtype,
                   const void *py, int ytype,
                   const double **Z,
                   const DATAINFO *pdinfo,
                   int p, int *err)
{
    const int *xlist = NULL;
    const gretl_matrix *Xmat = NULL;
    const double *xvec = NULL;
    const double *yvec = NULL;
    gretl_matrix *xj, *XCF = NULL;
    int T = sample_size(pdinfo);
    int np = 2 * p + 1;
    int Ty, nx = 1;
    int i, j;

    if (xtype == LVEC) {
      xlist = px;
      nx = xlist[0];
      if (nx < 1) {
          *err = E_DATA;
          return NULL;
      }         
      xvec = Z[xlist[1]] + pdinfo->t1; 
    } else if (xtype == MAT) {
      Xmat = px;
      if (gretl_is_null_matrix(Xmat)) {
          *err = E_DATA;
          return NULL;
      }
      nx = Xmat->cols;
      T = Xmat->rows;
      xvec = Xmat->val;
    } else {
      xvec = px;
    }

    if (ytype == MAT) {
      const gretl_matrix *ymat = py;

      if (ymat->cols != 1) {
          *err = E_NONCONF;
          return NULL;
      }       
      yvec = ymat->val;
      Ty = ymat->rows;
    } else {
      yvec = (const double *) py + pdinfo->t1;
      Ty = sample_size(pdinfo);
    }

    if (Ty != T) {
      *err = E_NONCONF;
      return NULL;
    }

    if (nx > 1) {
      XCF = gretl_matrix_alloc(np, nx);
      if (XCF == NULL) {
          *err = E_ALLOC;
          return NULL;
      }
    }

    for (j=0; j<nx; j++) {
      /* get XCF for left-hand column/series and y */
      xj = xcf_vec(xvec, yvec, p, NULL, T, err);
      if (*err) {
          gretl_matrix_free(XCF);
          return NULL;
      }

      if (nx == 1) {
          XCF = xj;
          break;
      } 

      /* transcribe into big XCF matrix and free */
      for (i=0; i<np; i++) {
          gretl_matrix_set(XCF, i, j, xj->val[i]);
      }
      gretl_matrix_free(xj);

      /* move to next data read position */
      if (j < nx - 1) {
          if (Xmat != NULL) {
            xvec += Xmat->rows;
          } else {
            xvec = Z[xlist[j+2]] + pdinfo->t1;
          }
      }
    }

    return XCF;
}

static int theil_decomp (double *m, double MSE,
                   const double *y, const double *f,
                   int t1, int t2)
{
    double da, dp;
    double Abar, Pbar;
    double sa, sp, r;
    int t, T = t2 - t1 + 1;
    int err = 0;

    if (MSE <= 0.0) {
      m[0] = m[1] = m[2] = M_NA;
      return E_DATA;
    }

    Abar = Pbar = 0.0;

    for (t=t1; t<=t2; t++) {
      Abar += y[t];
      Pbar += f[t];
    }

    Abar /= T;
    Pbar /= T;

    sa = sp = r = 0.0;

    for (t=t1; t<=t2; t++) {
      da = y[t] - Abar;
      sa += da * da;
      dp = f[t] - Pbar;
      sp += dp * dp;
      r += da * dp;
    }    

    sa = sqrt(sa / T);
    sp = sqrt(sp / T);
    r /= T * sa * sp;

    if (sa == 0.0 || sp == 0.0) {
      err = E_DATA;
      m[0] = m[1] = m[2] = M_NA;
    } else {
      m[0] = (Abar - Pbar) * (Abar - Pbar) / MSE; /* U^M */
      m[1] = (sp - r * sa) * (sp - r * sa) / MSE; /* U^R */
      m[2] = (1.0 - r * r) * sa * sa / MSE;       /* U^D */

      if (m[2] > 0.99999999999999) {
          /* U^M and U^R are just machine noise? */
          m[2] = 1.0;
          m[0] = m[1] = 0.0;
      } 
    }

    return err;
}

/* cf. http://www.economicsnetwork.ac.uk/showcase/cook_forecast
   by Steven Cook of Swansea University <s.cook@Swansea.ac.uk>

   OPT_D indicates that we should include the Theil decomposition.
*/

gretl_matrix *forecast_stats (const double *y, const double *f,
                        int t1, int t2, gretlopt opt,
                        int *err)
{
    gretl_matrix *m = NULL;
    double ME, MSE, MAE, MPE, MAPE, U;
    double x, u[2];
    int t, T = t2 - t1 + 1;

    for (t=t1; t<=t2; t++) {
      if (na(y[t]) || na(f[t])) {
          *err = E_MISSDATA;
          return NULL;
      }
    }

    ME = MSE = MAE = MPE = MAPE = U = 0.0;
    u[0] = u[1] = 0.0;

    for (t=t1; t<=t2; t++) {
      x = y[t] - f[t];
      ME += x;
      MSE += x * x;
      MAE += fabs(x);
      if (y[t] == 0.0) {
          MPE = MAPE = U = M_NA;
      } else {
          MPE += 100 * x / y[t];
          MAPE += 100 * fabs(x) / y[t];
          if (t < t2) {
            x = (f[t+1] - y[t+1]) / y[t];
            u[0] += x * x;
            x = (y[t+1] - y[t]) / y[t];
            u[1] += x * x;
          }
      }
    }

    ME /= T;
    MSE /= T;
    MAE /= T;

    if (!isnan(MPE)) {
      MPE /= T;
    }

    if (!isnan(MAPE)) {
      MAPE /= T;
    }

    if (!isnan(U) && u[1] > 0.0) {
      U = sqrt(u[0] / T) / sqrt(u[1] / T);
    }

    if (opt & OPT_D) {
      m = gretl_column_vector_alloc(9);
    } else {
      m = gretl_column_vector_alloc(6);
    }
    
    if (m == NULL) {
      *err = E_ALLOC;
      return NULL;
    }

    gretl_vector_set(m, 0, ME);
    gretl_vector_set(m, 1, MSE);
    gretl_vector_set(m, 2, MAE);
    gretl_vector_set(m, 3, MPE);
    gretl_vector_set(m, 4, MAPE);
    gretl_vector_set(m, 5, U);

    if (opt & OPT_D) {
      theil_decomp(m->val + 6, MSE, y, f, t1, t2);
    } 

    return m;
}

double gretl_round (double x)
{
    double fx = floor(x);

    if (x < 0) {
      return (x - fx <= 0.5)? fx : ceil(x);
    } else {
      return (x - fx < 0.5)? fx : ceil(x);
    }
}

#define neg_x_real_v_err(t) (t == 'J' || t == 'I')

/* evaluates bessel function for scalar nu and x */

double gretl_bessel (char type, double v, double x, int *err)
{
    if (na(x) || na(v)) {
      return NADBL;
    }

    if (x < 0) {
      /* catch invalid cases for x < 0 */
      if (type == 'K') {
          *err = E_INVARG;
          return NADBL;
      } else if (v != floor(v) && (type == 'J' || type == 'I')) {
          *err = E_INVARG;
          return NADBL;
      }
    }

    switch (type) {
    case 'J':
      return cephes_bessel_Jv(v, x);
    case 'Y':
      return cephes_bessel_Yv(v, x);
    case 'I':
      if (v == 0) {
          return cephes_bessel_I0(x);
      } else if (v == 1) {
          return cephes_bessel_I1(x);
      } else if (v > 0) {
          return cephes_bessel_Iv(v, x);
      } else {
          /* cephes_bessel_Iv is not right for v < 0 */
          double b1 = netlib_bessel_K(-v, x, 1);
          double b2 = cephes_bessel_Iv(-v, x);

          return (2*b1*sin(-v*M_PI)) / M_PI + b2;
      }
      break;
    case 'K':
      /* bessel K is symmetric around v = 0 */
      v = fabs(v);
      if (v == 0) {
          return cephes_bessel_K0(x);
      } else if (v == 1) {
          return cephes_bessel_K1(x);
      } else if (v == floor(v) && v <= 30.0) {
          /* cephes doesn't do non-integer v, and also loses
             accuracy beyond |v| = 30
          */
          return cephes_bessel_Kn(v, x);
      } else {
          /* accurate but expensive */
          return netlib_bessel_K(v, x, 1);
      }
      break;
    default:
      /* unknown function type */
      return NADBL;
    }
}



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