/* nag_dtgevc (f08ykc) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagx04.h>

int main(void)
{
  /* Scalars */
  Integer       i, icols, ihi, ilo, irows, j, m, n, pda, pdb, pdq, pdz;
  Integer       alpha_len, beta_len, scale_len, tau_len, select_len;
  Integer       exit_status = 0;
  Nag_Boolean   ileft, iright;

  NagError      fail;
  Nag_OrderType order;
  /* Arrays */
  double        *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0;
  double        *lscale = 0, *q = 0, *rscale = 0, *tau = 0, *z = 0;
  Nag_Boolean   *select = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J-1)*pda + I - 1]
#define B(I, J) b[(J-1)*pdb + I - 1]
#define Q(I, J) q[(J-1)*pdq + I - 1]
#define Z(I, J) z[(J-1)*pdz + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I-1)*pda + J - 1]
#define B(I, J) b[(I-1)*pdb + J - 1]
#define Q(I, J) q[(I-1)*pdq + J - 1]
#define Z(I, J) z[(I-1)*pdz + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_dtgevc (f08ykc) Example Program Results\n\n");

  /* ileft  is Nag_TRUE if left  eigenvectors are required */
  /* iright is Nag_TRUE if right eigenvectors are required */
  ileft = Nag_TRUE;
  iright = Nag_TRUE;

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%ld %*[^\n] ", &n);

  pda = n;
  pdb = n;
  pdq = n;
  pdz = n;
  alpha_len = n;
  beta_len = n;
  scale_len = n;
  tau_len = n;
  select_len = n;

  /* Allocate memory */
  if (
    !(a = NAG_ALLOC(n * n, double)) ||
    !(alphai = NAG_ALLOC(alpha_len, double)) ||
    !(alphar = NAG_ALLOC(alpha_len, double)) ||
    !(b = NAG_ALLOC(n * n, double)) ||
    !(beta = NAG_ALLOC(beta_len, double)) ||
    !(lscale = NAG_ALLOC(scale_len, double)) ||
    !(rscale = NAG_ALLOC(scale_len, double)) ||
    !(q = NAG_ALLOC(n * n, double)) ||
    !(tau = NAG_ALLOC(tau_len, double)) ||
    !(z = NAG_ALLOC(n * n, double)) ||
    !(select = NAG_ALLOC(select_len, Nag_Boolean)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* READ matrix A from data file */
  for (i = 1; i <= n; ++i)
    {
      for (j = 1; j <= n; ++j)
        scanf("%lf", &A(i, j));
    }
  scanf("%*[^\n] ");

  /* READ matrix B from data file */
  for (i = 1; i <= n; ++i)
    {
      for (j = 1; j <= n; ++j)
        scanf("%lf", &B(i, j));
    }
  scanf("%*[^\n] ");

  /* Balance matrix pair (A,B) */
  /* nag_dggbal (f08whc).
   * Balance a pair of real general matrices
   */
  nag_dggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale,
             rscale, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dggbal (f08whc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Matrix A after balancing */
  /* nag_gen_real_mat_print (x04cac).
   * Print real general matrix (easy-to-use)
   */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a,
                         pda, "Matrix A after balancing", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  /* Matrix B after balancing */
  /* nag_gen_real_mat_print (x04cac), see above. */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b,
                         pdb, "Matrix B after balancing", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  printf("\n");

  /* Reduce B to triangular form using QR */
  irows = ihi + 1 - ilo;
  icols = n + 1 - ilo;
  /* nag_dgeqrf (f08aec).
   * QR factorization of real general rectangular matrix
   */
  nag_dgeqrf(order, irows, icols, &B(ilo, ilo), pdb, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgeqrf (f08aec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Apply the orthogonal transformation to matrix A -  nag_dormqr (f08agc)
   * as determined by nag_dgeqrf (f08aec) or nag_dgeqpf (f08bec).
   */
  nag_dormqr(order, Nag_LeftSide, Nag_Trans, irows, icols, irows,
             &B(ilo, ilo), pdb, tau, &A(ilo, ilo), pda, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dormqr (f08agc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Initialize Q (if left eigenvectors are required) */
  if (ileft)
    {
      for (i = 1; i <= n; ++i)
        {
          for (j = 1; j <= n; ++j)
            Q(i, j) = 0.0;
          Q(i, i) = 1.0;
        }
      for (i = ilo+1; i <= ilo+irows-1; ++i)
        {
          for (j = ilo; j <= MIN(i, ilo+irows-2); ++j)
            Q(i, j) = B(i, j);
        }
      /* nag_dorgqr (f08afc).
       * Form all or part of orthogonal Q from QR factorization
       * determined by nag_dgeqrf (f08aec) or nag_dgeqpf (f08bec)
       */
      nag_dorgqr(order, irows, irows, irows, &Q(ilo, ilo), pdq, tau, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_dorgqr (f08afc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }
    }

  /* Initialize Z (if right eigenvectors are required) */
  if (iright)
    {
      for (i = 1; i <= n; ++i)
        {
          for (j = 1; j <= n; ++j)
            Z(i, j) = 0.0;
          Z(i, i) = 1.0;
        }
    }

  /* Compute the generalized Hessenberg form of (A,B) */
  /* nag_dgghrd (f08wec).
   * Orthogonal reduction of a pair of real general matrices
   * to generalized upper Hessenberg form
   */
  nag_dgghrd(order, Nag_UpdateSchur, Nag_UpdateZ, n, ilo, ihi, a, pda,
             b, pdb, q, pdq, z, pdz, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgghrd (f08wec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Matrix A in generalized Hessenberg form */
  /* nag_gen_real_mat_print (x04cac), see above. */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a,
                         pda, "Matrix A in Hessenberg form", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  printf("\n");

  /* Matrix B in generalized Hessenberg form */
  /* nag_gen_real_mat_print (x04cac), see above. */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b,
                         pdb, "Matrix B in Hessenberg form", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  /* nag_dhgeqz (f08xec).
   * Eigenvalues and generalized Schur factorization of real
   * generalized upper Hessenberg form reduced from a pair of
   * real general matrices.
   */
  nag_dhgeqz(order, Nag_Schur, Nag_AccumulateQ, Nag_AccumulateZ, n, ilo, ihi,
             a, pda, b, pdb, alphar, alphai, beta, q, pdq, z, pdz, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dhgeqz (f08xec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print the generalized eigenvalue parameters */
  printf("\n Generalized eigenvalues\n");
  for (i = 1; i <= n; ++i)
    {
      if (beta[i-1] != 0.0)
        {
          printf(" %4ld     (%7.3f,%7.3f)\n", i,
                  alphar[i-1]/beta[i-1], alphai[i-1]/beta[i-1]);
        }
      else
        printf(" %4ldEigenvalue is infinite\n", i);
    }
  printf("\n");

  /* Compute left and right generalized eigenvectors
   * of the balanced matrix - nag_dtgevc (f08ykc).
   */
  nag_dtgevc(order, Nag_BothSides, Nag_BackTransform, select, n, a, pda,
             b, pdb, q, pdq, z, pdz, n, &m, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dtgevc (f08ykc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  if (iright)
    {
      /* Compute right eigenvectors of the original matrix pair
       * supplied tonag_dggbal (f08whc) using nag_dggbak (f08wjc).
       */
      nag_dggbak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, lscale,
                 rscale, n, z, pdz, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_dggbak (f08wjc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }
      /* Normalize the right eigenvectors */
      for(j=1; j<=n; j++)
        {
          for(i=n; i>=1; i--)
            {
              Z(i, j) = Z(i, j) / Z(1,j);
            }
        }
      
      /* Print the right eigenvectors */
      /* nag_gen_real_mat_print (x04cac), see above. */
      fflush(stdout);
      nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n,
                             z, pdz, "Right eigenvectors", 0, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      printf("\n");
    }

  /* Compute left eigenvectors of the original matrix */
  if (ileft)
    {
      /* nag_dggbak (f08wjc), see above. */
      nag_dggbak(order, Nag_DoBoth, Nag_LeftSide, n, ilo, ihi, lscale,
                 rscale, n, q, pdq, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_dggbak (f08wjc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }
      /* Normalize the left eigenvectors */
      for(j=1; j<=n; j++)
        {
          for(i=n; i>=1; i--)
            {
              Q(i, j) = Q(i, j) / Q(1,j);
            }
        }
      /* Print the left eigenvectors */
      /* nag_gen_real_mat_print (x04cac), see above. */
      fflush(stdout);
      nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n,
                             q, pdq, "Left eigenvectors", 0, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
    }
 END:
  if (a) NAG_FREE(a);
  if (alphai) NAG_FREE(alphai);
  if (alphar) NAG_FREE(alphar);
  if (b) NAG_FREE(b);
  if (beta) NAG_FREE(beta);
  if (lscale) NAG_FREE(lscale);
  if (q) NAG_FREE(q);
  if (rscale) NAG_FREE(rscale);
  if (tau) NAG_FREE(tau);
  if (z) NAG_FREE(z);
  if (select) NAG_FREE(select);

  return exit_status;
}