/* nag_kalman_sqrt_filt_info_invar (g13edc)  Example Program.
 *
 * Copyright 1993 Numerical Algorithms Group
 *
 * Mark 3, 1993
 * Mark 7 revised, 2001.
 * Mark 8 revised, 2004.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagf06.h>
#include <nagf03.h>
#include <nagg13.h>

typedef enum {read, print} ioflag;

static int ex1(void);
static int ex2(void);

int main(void)
{
  Integer exit_status_ex1=0;
  Integer exit_status_ex2=0;
  exit_status_ex1 = ex1();
  exit_status_ex2 = ex2();
  return exit_status_ex1 == 0 && exit_status_ex2 == 0 ? 0 : 1;
}

#define AINV(I,J) ainv[(I)*tdainv + J]
#define QINV(I,J) qinv[(I)*tdqinv + J]
#define RINV(I,J) rinv[(I)*tdrinv + J]
#define T(I,J) t[(I)*tdt + J]
#define AINVB(I,J) ainvb[(I)*tdainvb + J]
#define C(I,J) c[(I)*tdc + J]
static int ex1(void)
{
  Integer exit_status=0, i, istep, j, m, n, p, tdainv, tdainvb, tdc, tdqinv;
  Integer tdrinv, tdt;
  NagError fail;
  double *ainv=0, *ainvb=0, *c=0, *qinv=0, *rinv=0, *rinvy=0, *t=0, tol, *x=0;
  double *z=0;

  INIT_FAIL(fail);

  Vprintf("nag_kalman_sqrt_filt_info_invar (g13edc) Example 1 Program "
          "Results\n");

  /* Skip the heading in the data file   */
  Vscanf("%*[^\n]");


  Vscanf("%ld%ld%ld%lf",&n,&m,&p,&tol);
  if (n>=1 || m>=1 || p>=1)
    {
      if ( !( ainv = NAG_ALLOC(n*n, double)) ||
           !( qinv = NAG_ALLOC(m*m, double)) ||
           !( rinv = NAG_ALLOC(p*p, double)) ||
           !( t = NAG_ALLOC(n*n, double)) ||
           !( ainvb = NAG_ALLOC(n*m, double)) ||
           !( c = NAG_ALLOC(p*n, double)) ||
           !( x = NAG_ALLOC(n, double)) ||
           !( z = NAG_ALLOC(m, double)) ||
           !( rinvy = NAG_ALLOC(p, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tdainv = n;
      tdqinv = m;
      tdrinv = p;
      tdt = n;
      tdainvb = m;
      tdc = n;
    }
  else
    {
      Vprintf("Invalid n or m or p.\n");
      exit_status = 1;
      return exit_status;
    }

  /* Read data */
  for (i=0; i<n; ++i)
    for (j=0; j<n; ++j)
      Vscanf("%lf", &AINV(i,j));
  for (i=0; i<p; ++i)
    for (j=0; j<n; ++j)
      Vscanf("%lf", &C(i,j));
  if (rinv)
    for (i=0; i<p; ++i)
      for (j=0; j<p; ++j)
        Vscanf("%lf", &RINV(i,j));
  for (i=0; i<n; ++i)
    for (j=0; j<m; ++j)
      Vscanf("%lf", &AINVB(i,j));
  for (i=0; i<m; ++i)
    for (j=0; j<m; ++j)
      Vscanf("%lf", &QINV(i,j));
  for (i=0; i<n; ++i)
    for (j=0; j<n; ++j)
      Vscanf("%lf", &T(i,j));
  for (j=0; j<m; ++j)
    Vscanf("%lf", &z[j]);
  for (j=0; j<n; ++j)
    Vscanf("%lf", &x[j]);
  for (j=0; j<p; ++j)
    Vscanf("%lf", &rinvy[j]);

  /* Perform three iterations of the Kalman filter recursion  */

  for (istep=1; istep<=3; ++istep)
    /* nag_kalman_sqrt_filt_info_invar (g13edc).
     * One iteration step of the time-invariant Kalman filter
     * recursion using the square root information
     * implementation with (A^(~-~1)(A^(~-~1)B)) in upper
     * controller Hessenberg form
     */
    nag_kalman_sqrt_filt_info_invar(n, m, p, t, tdt, ainv,
                                    tdainv, ainvb, tdainvb, rinv,
                                    tdrinv, c, tdc, qinv,
                                    tdqinv, x, rinvy, z, tol, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_kalman_sqrt_filt_info_invar (g13edc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  Vprintf("\nThe inverse of the square root of the state covariance "
          "matrix is \n\n");

  for (i=0; i<n; ++i)
    {
      for (j=0; j<n; ++j)
        Vprintf("%8.4f ", T(i,j));
      Vprintf("\n");
    }
  Vprintf("\nThe components of the estimated filtered state are\n\n");
  Vprintf("   k       x(k)  \n");
  for (i=0; i<n; ++i)
    {
      Vprintf("   %ld  ",  i);
      Vprintf("  %8.4f  \n", x[i]);
    }
 END:
  if (ainv) NAG_FREE(ainv);
  if (qinv) NAG_FREE(qinv);
  if (rinv) NAG_FREE(rinv);
  if (t) NAG_FREE(t);
  if (ainvb) NAG_FREE(ainvb);
  if (c) NAG_FREE(c);
  if (x) NAG_FREE(x);
  if (z) NAG_FREE(z);
  if (rinvy) NAG_FREE(rinvy);
  return exit_status;
}

static void mat_io(Integer n, Integer m, double mat[], Integer tdmat,
                   ioflag flag, const char *message);

#define AINV(I,J) ainv[(I)*tdainv + J]
#define AINVB(I,J) ainvb[(I)*tdainvb + J]
#define C(I,J) c[(I)*tdc + J]
#define AINVU(I,J) ainvu[(I)*tdainvu + J]
#define AINVBU(I,J) ainvbu[(I)*tdainvbu + J]
#define QINV(I,J) qinv[(I)*tdqinv + J]
#define RINV(I,J) rinv[(I)*tdrinv + J]
#define T(I,J) t[(I)*tdt + J]
#define RWORK(I,J) rwork[(I)*tdrwork + J]
#define TU(I,J) tu[(I)*tdtu + J]
#define IG(I,J) ig[(I)*tdig + J]
#define IH(I,J) ih[(I)*tdih + J]
#define CU(I,J) cu[(I)*tdcu + J]
#define U(I,J) u[(I)*tdu + J]
static int ex2(void)
{

  Integer dete, exit_status=0, i, ione=1, istep, j, m, n, p, tdainv, tdainvb;
  Integer tdainvbu, tdainvu, tdc, tdcu, tdig, tdih, tdqinv, tdrinv, tdrwork;
  Integer tdt, tdtu, tdu;
  NagError fail;
  Nag_ControllerForm reduceto=Nag_UH_Controller;
  Nag_ab_input inp_ab=Nag_ab_prod;
  double *ainv=0, *ainvb=0, *ainvbu=0, *ainvu=0, *c=0, *cu=0, detf, *diag=0;
  double *ig=0, *ih=0, one=1.0, *qinv=0, *rinv=0, *rinvy=0, *rwork=0, *t=0;
  double tol, *tu=0, *u=0, *ux=0, *x=0, *z=0, zero=0.0;

  INIT_FAIL(fail);

  Vprintf("\n\nnag_kalman_sqrt_filt_info_invar (g13edc) Example 2 Program "
          "Results\n");
  /* skip the heading in the data file */
  Vscanf(" %*[^\n]");

  Vscanf("%ld%ld%ld%lf",&n,&m,&p,&tol);
  if (n>=1 || m>=1 || p>=1)
    {
      if ( !( ainv = NAG_ALLOC(n*n, double)) ||
           !( ainvb = NAG_ALLOC(n*m, double)) ||
           !( c = NAG_ALLOC(p*n, double)) ||
           !( ainvu = NAG_ALLOC(n*n, double)) ||
           !( ainvbu = NAG_ALLOC(n*m, double))||
           !( qinv = NAG_ALLOC(m*m, double)) ||
           !( rinv = NAG_ALLOC(p*p, double)) ||
           !( t = NAG_ALLOC(n*n, double)) ||
           !( x = NAG_ALLOC(n, double)) ||
           !( z = NAG_ALLOC(n, double)) ||
           !( rwork = NAG_ALLOC(n*n, double)) ||
           !( tu = NAG_ALLOC(n*n, double)) ||
           !( rinvy = NAG_ALLOC(p, double)) ||
           !( ig = NAG_ALLOC(n*n, double)) ||
           !( ih = NAG_ALLOC(n*n, double)) ||
           !( cu = NAG_ALLOC(p*n, double)) ||
           !( u = NAG_ALLOC(n*n, double)) ||
           !( ux = NAG_ALLOC(n, double)) ||
           !( diag = NAG_ALLOC(n, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tdainv = n;
      tdainvb = m;
      tdc = n;
      tdainvu = n;
      tdainvbu = m;
      tdqinv = m;
      tdrinv = p;
      tdt = n;
      tdrwork = n;
      tdtu = n;
      tdig = n;
      tdih = n;
      tdcu = n;
      tdu = n;

    }
  else
    {
      Vprintf("Invalid n or m or p.\n");
      exit_status = 1;
      return exit_status;
    }

  /* Read data */
  mat_io(n, n, ainv, tdainv, read, "");
  mat_io(p, n, c, tdc, read, "");
  if (rinv)
    mat_io(p, p, rinv, tdrinv, read,"");
  mat_io(n, m, ainvb, tdainvb, read, "");
  mat_io(m, m, qinv, tdqinv, read, "");
  mat_io(n, n, t, tdt, read, "");
  for (j=0; j<m; ++j)
    Vscanf("%lf", &z[j]);
  for (j=0; j<n; ++j)
    Vscanf("%lf", &x[j]);
  for (j=0; j<p; ++j)
    Vscanf("%lf", &rinvy[j]);

  for (i=0; i<n; ++i)     /* Initialise the identity matrix u */
    {
      for (j=0; j<n; ++j)
        U(i,j) = zero;
      U(i,i) = one;
    }

  /* Copy the arrays ainv[] and ainvb[] into ainvu[] and ainvbu[] */
  for (i=0; i< n; ++i)
    f06efc(n, &AINV(0,i), tdainv, &AINVU(0,i), tdainvu);
  for (j=0; j<m; ++j)
    f06efc(n, &AINVB(0,j), tdainvb, &AINVBU(0,j), tdainvbu);

  /* Transform (ainvu[],ainvbu[]) to reduceto controller Hessenberg form */
  /* nag_trans_hessenberg_controller (g13exc).
   * Unitary state-space transformation to reduce (BA) to
   * lower or upper controller Hessenberg form
   */
  nag_trans_hessenberg_controller(n, m, reduceto, ainvu, tdainvu, ainvbu,
                                  tdainvbu, u, tdu, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_trans_hessenberg_controller (g13exc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  /* Calculate the matrix cu = c*u'    */
  f06yac(NoTranspose, Transpose, p, n, n, one, c, tdc,
         u, tdu, zero, cu, tdcu);

  /* Calculate the vector ux = u*x     */
  f06pac(NoTranspose, n, n, one, u, tdu, x, ione,
         zero, ux, ione);

  /* Form the information matrices ih = u*ig*u' and ig = t'*t     */
  f06yac(Transpose, NoTranspose, n, n, n, one, t, tdt,
         t, tdt, zero, ig, tdig);
  f06yac(NoTranspose, Transpose, n, n, n, one, ig, tdig,
         u, tdu, zero, rwork, tdrwork);
  f06yac(NoTranspose, NoTranspose, n, n, n, one, u, tdu,
         rwork, tdrwork, zero, ih, tdih);

  /* Now find the reduceto triangular (right) cholesky factor of ih */
  /* nag_real_cholesky (f03aec).
   * LL^T factorization and determinant of real symmetric
   * positive-definite matrix
   */
  nag_real_cholesky(n, ih, tdih, diag, &detf, &dete, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_real_cholesky (f03aec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  for (i=0; i< n; ++i)
    {
      TU(i,i) = one/diag[i];
      for (j=0; j<i; ++j)
        {
          TU(j,i) = IH(i,j);
          TU(i,j) = zero;
        }
    }

  /* Do three iterations of the Kalman filter recursion  */
  for (istep=1; istep<=3; ++istep)
    {
      /* nag_kalman_sqrt_filt_info_var (g13ecc).
       * One iteration step of the time-varying Kalman filter
       * recursion using the square root information
       * implementation
       */
      nag_kalman_sqrt_filt_info_var(n, m, p, inp_ab, t, tdt, ainv,
                                    tdainv, ainvb, tdainvb, rinv, tdrinv,
                                    c, tdc, qinv, tdqinv, x,
                                    rinvy, z, tol,&fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_kalman_sqrt_filt_info_var (g13ecc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      /* nag_kalman_sqrt_filt_info_invar (g13edc), see above. */
      nag_kalman_sqrt_filt_info_invar(n, m, p, tu, tdtu, ainvu, tdainvu,
                                      ainvbu, tdainvbu, rinv, tdrinv, cu,
                                      tdcu, qinv, tdqinv, ux, rinvy,
                                      z, tol, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_kalman_sqrt_filt_info_invar (g13edc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
    }

  /* Print Results */
  Vprintf("\nResults from nag_kalman_sqrt_filt_info_var (g13ecc) \n\n");
  /* let ig = t' * t */
  f06yac(Transpose, NoTranspose, n, n, n, one, t, tdt,
         t, tdt, zero, ig, tdig);
  mat_io(n, n, ig, tdig, print,"The information matrix ig is\n");
  Vprintf("\nThe components of the estimated filtered state are\n\n");
  Vprintf("  k       x(k)  \n");
  for (i=0; i<n; ++i)
    Vprintf("  %ld   %8.4f \n", i, x[i]);
  Vprintf("\nResults from nag_kalman_sqrt_filt_info_invar (g13edc) \n\n");
  /* let ih = tu' * tu */
  f06yac(Transpose, NoTranspose, n, n, n, one, tu, tdtu,
         tu, tdtu, zero, ih, tdih);
  mat_io(n, n, ih, tdih, print,"The information matrix ih is\n");

  /* Calculate ih = u'*ih*u   */
  f06yac(NoTranspose, NoTranspose, n, n, n, one, ih, tdih,
         u, tdu, zero, rwork, tdrwork);
  f06yac(Transpose, NoTranspose, n, n, n, one, u, tdu,
         rwork, tdrwork, zero, ih, tdih);
  mat_io(n, n, ih, tdih, print,"\nThe matrix u' * ih * u is\n");

  /* Calculate x = u' * ux */
  f06pac(Transpose, n, n, one, u, tdu, ux, ione,
         zero, x, ione);
  Vprintf("\nThe components of the estimated filtered state are \n\n");
  Vprintf("  k       x(k)  \n");
  for (i=0; i<n; ++i)
    Vprintf("  %ld   %8.4f \n", i, x[i]);
 END:
  if (ainv) NAG_FREE(ainv);
  if (ainvb) NAG_FREE(ainvb);
  if (c) NAG_FREE(c);
  if (ainvu) NAG_FREE(ainvu);
  if (ainvbu) NAG_FREE(ainvbu);
  if (qinv) NAG_FREE(qinv);
  if (rinv) NAG_FREE(rinv);
  if (t) NAG_FREE(t);
  if (x) NAG_FREE(x);
  if (z) NAG_FREE(z);
  if (rwork) NAG_FREE(rwork);
  if (tu) NAG_FREE(tu);
  if (rinvy) NAG_FREE(rinvy);
  if (ig) NAG_FREE(ig);
  if (ih) NAG_FREE(ih);
  if (cu) NAG_FREE(cu);
  if (u) NAG_FREE(u);
  if (ux) NAG_FREE(ux);
  if (diag) NAG_FREE(diag);
  return exit_status;
}

static void mat_io(Integer n, Integer m, double mat[], Integer tdmat,
                   ioflag flag, const char * message)
{  Integer i, j;
#define MAT(I,J) mat[((I)-1) * tdmat + (J) - 1]
 if (flag==print) Vprintf("%s \n", message);
 for (i=1; i<=n; ++i)
   {
     for (j=1; j<=m; ++j)
       {
         if (flag==read) Vscanf("%lf", &MAT(i,j));
         if (flag==print) Vprintf("%8.4f ", MAT(i,j));
       }
     if (flag==print) Vprintf("\n");
   }
} /* mat_io */