/* nag_lapackeig_ztrsyl (f08qvc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

#include <math.h>
#include <nag.h>
#include <stdio.h>

int main(void) {
  /* Scalars */
  Complex alpha, beta;
  Integer i, j, m, n, pda, pdb, pdc, pdd, pde, pdf;
  Integer exit_status = 0;
  double norm, scale;
  NagError fail;
  Nag_OrderType order;
  Nag_SignType sign = Nag_Minus;
  /* Arrays */
  Complex *a = 0, *b = 0, *c = 0, *d = 0, *e = 0, *f = 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 C(I, J) c[(J - 1) * pdc + I - 1]
#define D(I, J) d[(J - 1) * pdd + I - 1]
#define E(I, J) e[(J - 1) * pde + I - 1]
#define F(I, J) f[(J - 1) * pdf + 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 C(I, J) c[(I - 1) * pdc + J - 1]
#define D(I, J) d[(I - 1) * pdd + J - 1]
#define E(I, J) e[(I - 1) * pde + J - 1]
#define F(I, J) f[(I - 1) * pdf + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_ztrsyl (f08qvc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &m, &n);
  pda = m;
  pdb = n;
#ifdef NAG_COLUMN_MAJOR
  pdc = m;
  pdd = m;
  pde = m;
  pdf = m;
#else
  pdc = n;
  pdd = n;
  pde = n;
  pdf = n;
#endif

  /* Allocate memory */
  if (!(a = NAG_ALLOC(m * m, Complex)) || !(b = NAG_ALLOC(n * m, Complex)) ||
      !(c = NAG_ALLOC(m * n, Complex)) || !(d = NAG_ALLOC(m * n, Complex)) ||
      !(e = NAG_ALLOC(m * n, Complex)) || !(f = NAG_ALLOC(m * n, Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read A, B and C from data file */
  for (i = 1; i <= m; ++i) {
    for (j = 1; j <= m; ++j)
      scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im);
  }
  scanf("%*[^\n] ");
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j)
      scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im);
  }
  scanf("%*[^\n] ");
  for (i = 1; i <= m; ++i) {
    for (j = 1; j <= n; ++j)
      scanf(" ( %lf , %lf ) ", &C(i, j).re, &C(i, j).im);
  }
  scanf("%*[^\n] ");

  /* Copy C into F */
  for (i = 1; i <= m; i++) {
    for (j = 1; j <= m; j++) {
      F(i, j).re = C(i, j).re;
      F(i, j).im = C(i, j).im;
    }
  }

  /* nag_file_print_matrix_complex_gen_comp (x04dbc): Print matrix C */
  fflush(stdout);
  nag_file_print_matrix_complex_gen_comp(
      order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, c, pdc, Nag_BracketForm,
      "%7.4f", "Matrix C", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0,
      &fail);
  printf("\n");
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Reorder the Schur factorization T */
  /* nag_lapackeig_ztrsyl (f08qvc).
   * Solve complex Sylvester matrix equation AX + XB = C, A
   * and B are upper triangular or conjugate-transposes
   */
  nag_lapackeig_ztrsyl(order, Nag_NoTrans, Nag_NoTrans, sign, m, n, a, pda, b,
                       pdb, c, pdc, &scale, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_ztrsyl (f08qvc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_blast_zgemm (f16zac): Compute aC - (A*X + X*B*sign) from the solution
   */
  /* and store in matrix E */
  alpha.re = 1.0;
  alpha.im = 0.0;
  beta.re = 0.0;
  beta.im = 0.0;
  nag_blast_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, m, alpha, a, pda, c,
                  pdc, beta, d, pdd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zgemm (f16zac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  if (sign == Nag_Minus)
    alpha.re = -1.0;
  else
    alpha.re = 1.0;
  beta.re = 1.0;
  nag_blast_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, c, pdc, b,
                  pdb, beta, d, pdd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zgemm (f16zac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  for (i = 1; i <= m; i++) {
    for (j = 1; j <= n; j++) {
      E(i, j).re = scale * F(i, j).re - D(i, j).re;
      E(i, j).im = scale * F(i, j).im - D(i, j).im;
    }
  }

  /* nag_blast_zge_norm (f16uac): Find norm of matrix E and print warning if */
  /* it is too large */
  nag_blast_zge_norm(order, Nag_OneNorm, m, n, e, pde, &norm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  if (norm > pow(x02ajc(), 0.8)) {
    printf("%s\n%s\n", "Norm of aC - (A*X + X*B*sign) is much greater than 0.",
           "Schur factorization has failed.");
  } else {
    printf(" SCALE = %11.2e\n", scale);
  }

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(e);
  NAG_FREE(f);

  return exit_status;
}