/* nag_sparseig_complex_init (f12anc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.1, 2023.
 */

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

static void av(Integer, Complex *, Complex *);
static void tv(Integer, Complex *, Complex *);

int main(void) {
  /* Constants */
  Integer imon = 0;
  /* Scalars */
  Complex sigma;
  double estnrm;
  Integer exit_status, i, irevcm, lcomm, licomm, n, nconv, ncv;
  Integer nev, niter, nshift, nx;
  /* Nag types */
  NagError fail;

  /* Arrays */
  Complex *comm = 0, *eigest = 0, *eigv = 0, *resid = 0, *v = 0;
  Integer *icomm = 0;
  /* Ponters */
  Complex *mx = 0, *x = 0, *y = 0;

  /* Assign to Complex type using nag_complex_create (a02bac) */
  sigma = nag_complex_create(0.0, 0.0);
  exit_status = 0;
  INIT_FAIL(fail);

  printf("nag_sparseig_complex_init (f12anc) Example "
         "Program Results\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &nx, &nev, &ncv);
  n = nx * nx;
  /* Allocate memory */
  if (!(eigv = NAG_ALLOC(ncv, Complex)) ||
      !(eigest = NAG_ALLOC(ncv, Complex)) || !(resid = NAG_ALLOC(n, Complex)) ||
      !(v = NAG_ALLOC(n * ncv, Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  /* Initialize communication arrays for problem using
     nag_sparseig_complex_init (f12anc).
     The first call sets lcomm = licomm = -1 to perform a workspace
     query. */
  lcomm = licomm = -1;
  if (!(comm = NAG_ALLOC(1, Complex)) || !(icomm = NAG_ALLOC(1, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  nag_sparseig_complex_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_complex_init (f12anc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  lcomm = (Integer)comm[0].re;
  licomm = icomm[0];
  NAG_FREE(comm);
  NAG_FREE(icomm);
  if (!(comm = NAG_ALLOC(lcomm, Complex)) ||
      !(icomm = NAG_ALLOC(licomm, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  nag_sparseig_complex_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_complex_init (f12anc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  irevcm = 0;
REVCOMLOOP:
  /* repeated calls to reverse communication routine
     nag_sparseig_complex_iter (f12apc). */
  nag_sparseig_complex_iter(&irevcm, resid, v, &x, &y, &mx, &nshift, comm,
                            icomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_complex_iter (f12apc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  if (irevcm != 5 && irevcm != 0) {
    if (irevcm == -1 || irevcm == 1) {
      /* Perform matrix vector multiplication y <--- Op*x */
      av(nx, x, y);
    } else if (irevcm == 4 && imon == 1) {
      /* If imon=1, get monitoring information using
         nag_sparseig_complex_monit (f12asc). */
      nag_sparseig_complex_monit(&niter, &nconv, eigv, eigest, icomm, comm);
      /* Compute 2-norm of Ritz estimates using
         nag_blast_zge_norm (f16uac). */
      nag_blast_zge_norm(Nag_ColMajor, Nag_FrobeniusNorm, nev, 1, eigest, nev,
                         &estnrm, &fail);
      if (fail.code != NE_NOERROR) {
        printf("Error from nag_sparseig_complex_monit"
               " (f12asc).\n%s\n",
               fail.message);
        exit_status = 1;
        goto END;
      }
      printf("Iteration %3" NAG_IFMT ", ", niter);
      printf(" No. converged = %3" NAG_IFMT ",", nconv);
      printf(" norm of estimates = %17.8e\n", estnrm);
    }
    goto REVCOMLOOP;
  }
  if (fail.code == NE_NOERROR) {
    /* Post-Process using nag_sparseig_complex_proc
       (f12aqc) to compute eigenvalues/vectors. */
    nag_sparseig_complex_proc(&nconv, eigv, v, sigma, resid, v, comm, icomm,
                              &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_sparseig_complex_proc "
             "(f12aqc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    printf("\n The %" NAG_IFMT " Ritz values", nconv);
    printf(" of largest magnitude are:\n\n");
    for (i = 0; i <= nconv - 1; ++i) {
      printf("%8" NAG_IFMT "%5s(%12.4f, %12.4f)\n", i + 1, "", eigv[i].re,
             eigv[i].im);
    }
  } else {
    printf("Error from nag_sparseig_complex_iter "
           "(f12apc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(comm);
  NAG_FREE(eigv);
  NAG_FREE(eigest);
  NAG_FREE(resid);
  NAG_FREE(v);
  NAG_FREE(icomm);
  return exit_status;
}

static void av(Integer nx, Complex *x, Complex *y) {
  /* Scalars */
  double hr;
  Integer i, j, lo;
  /* Function Body */

  /* Allocate memory */
  hr = (double)-(nx + 1) * (nx + 1);
  tv(nx, x, y);
  for (j = 0; j <= nx - 1; ++j) {
    y[j].re = y[j].re + hr * x[nx + j].re;
    y[j].im = y[j].im + hr * x[nx + j].im;
  }
  for (j = 2; j <= nx - 1; ++j) {
    lo = (j - 1) * nx;
    tv(nx, &x[lo], &y[lo]);
    for (i = 0; i <= nx - 1; ++i) {
      y[lo + i].re =
          y[lo + i].re + hr * (x[lo - nx + i].re + x[lo + nx + i].re);
      y[lo + i].im =
          y[lo + i].im + hr * (x[lo - nx + i].im + x[lo + nx + i].im);
    }
  }
  lo = (nx - 1) * nx;
  tv(nx, &x[lo], &y[lo]);
  for (j = 0; j <= nx - 1; ++j) {
    y[lo + j].re = y[lo + j].re + hr * x[lo - nx + j].re;
    y[lo + j].im = y[lo + j].im + hr * x[lo - nx + j].im;
  }
} /* av */

static void tv(Integer nx, Complex *x, Complex *y) {
  /* Compute the matrix vector multiplication y<---T*x where T is a */
  /* nx by nx tridiagonal matrix. */

  /* Scalars */
  Complex dd, dl, du, h2, h, rho, z1, z2, z3;
  Integer j;

  /* Function Body */
  /* Assign to Complex type using nag_complex_create (a02bac) */
  h = nag_complex_create((double)(nx + 1), 0.);
  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  h2 = nag_complex_multiply(h, h);
  dd = nag_complex_multiply(nag_complex_create(4.0, 0.0), h2);
  z1 = nag_complex_multiply(nag_complex_create(-1.0, 0.0), h2);
  /* Assign to Complex type using nag_complex_create (a02bac) */
  rho = nag_complex_create(1.0e2, 0.0);
  z2 = nag_complex_multiply(rho, h);
  z3 = nag_complex_multiply(nag_complex_create(5.0e-1, 0.0), z2);
  /* Compute Complex subtraction using nag_complex_subtract
     (a02cbc). */
  dl = nag_complex_subtract(z1, z3);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  du = nag_complex_add(z1, z3);

  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  z1 = nag_complex_multiply(dd, x[0]);
  z2 = nag_complex_multiply(du, x[1]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  y[0] = nag_complex_add(z1, z2);
  for (j = 1; j <= nx - 2; ++j) {
    /* Compute Complex multiply using nag_complex_multiply
       (a02ccc). */
    z1 = nag_complex_multiply(dl, x[j - 1]);
    z2 = nag_complex_multiply(dd, x[j]);
    z3 = nag_complex_multiply(du, x[j + 1]);
    /* Compute Complex addition using nag_complex_add (a02cac). */
    y[j] = nag_complex_add(z1, z2);
    y[j] = nag_complex_add(y[j], z3);
  }
  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  z1 = nag_complex_multiply(dl, x[nx - 2]);
  z2 = nag_complex_multiply(dd, x[nx - 1]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  y[nx - 1] = nag_complex_add(z1, z2);
  return;
} /* tv */