/* nag_sparseig_complex_monit (f12asc) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.3, 2021.
 */

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

/* Table of constant values */
static Complex four = {4., 0.};

static void mv(Integer, Complex *, Complex *);
static void my_zgttrf(Integer, Complex *, Complex *, Complex *, Complex *,
                      Integer *, Integer *);
static void my_zgttrs(Integer, Complex *, Complex *, Complex *, Complex *,
                      Integer *, Complex *);

int main(void) {
  /* Constants */
  Integer licomm = 140, imon = 1;

  /* Scalars */
  Complex rho, s1, s2, s3, sigma;
  double estnrm, hr, hr1, sr, shs;
  Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv;
  Integer nev, niter, nshift, nx;
  /* Nag types */
  NagError fail;
  /* Arrays */
  Complex *comm = 0, *eigv = 0, *eigest = 0, *dd = 0, *dl = 0, *du = 0;
  Complex *du2 = 0, *resid = 0, *v = 0;
  Integer *icomm = 0, *ipiv = 0;
  /* Ponters */
  Complex *mx = 0, *x = 0, *y = 0;

  exit_status = 0;
  INIT_FAIL(fail);

  printf("nag_sparseig_complex_monit (f12asc) 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;
  lcomm = 3 * n + 3 * ncv * ncv + 5 * ncv + 60;
  /* Allocate memory */
  if (!(comm = NAG_ALLOC(lcomm, Complex)) ||
      !(eigv = NAG_ALLOC(ncv, Complex)) ||
      !(eigest = NAG_ALLOC(ncv, Complex)) || !(dd = NAG_ALLOC(n, Complex)) ||
      !(dl = NAG_ALLOC(n, Complex)) || !(du = NAG_ALLOC(n, Complex)) ||
      !(du2 = NAG_ALLOC(n, Complex)) || !(resid = NAG_ALLOC(n, Complex)) ||
      !(v = NAG_ALLOC(n * ncv, Complex)) ||
      !(icomm = NAG_ALLOC(licomm, Integer)) ||
      !(ipiv = NAG_ALLOC(n, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  /* Initialize communication arrays for problem using
     nag_sparseig_complex_init (f12anc). */
  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;
  }
  /* Select the required mode using
     nag_sparseig_complex_option (f12adc). */
  nag_sparseig_complex_option("SHIFTED INVERSE", icomm, comm, &fail);
  /* Select the  problem type using
     nag_sparseig_complex_option (f12adc). */
  nag_sparseig_complex_option("GENERALIZED", icomm, comm, &fail);
  /* Set values for sigma and rho */
  /* Assign to Complex type using nag_complex_create (a02bac) */
  sigma = nag_complex_create(5000.0, 0.0);
  rho = nag_complex_create(10.0, 0.0);
  hr1 = (double)(n + 1);
  hr = 1.0 / hr1;
  sr = 0.5 * rho.re;
  shs = sigma.re * hr / 6.0;
  /* Assign to Complex type using nag_complex_create (a02bac) */
  s1 = nag_complex_create(-hr1 - sr - shs, 0.0);
  s3 = nag_complex_create(-hr1 + sr - shs, 0.0);
  s2 = nag_complex_create(2.0 * hr1 - 4.0 * shs, 0.0);

  for (j = 0; j <= n - 2; ++j) {
    dl[j] = s1;
    dd[j] = s2;
    du[j] = s3;
  }
  dd[n - 1] = s2;

  my_zgttrf(n, dl, dd, du, du2, ipiv, &info);
  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 (irevcm != 5) {
    if (irevcm == -1) {
      /* Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x */
      mv(nx, x, y);
      my_zgttrs(n, dl, dd, du, du2, ipiv, y);
    } else if (irevcm == 1) {
      /* Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x, */
      /* MX stored in mx */
      for (j = 0; j < n; ++j) {
        y[j] = mx[j];
      }
      my_zgttrs(n, dl, dd, du, du2, ipiv, y);
    } else if (irevcm == 2) {
      /* Perform  y <--- M*x */
      mv(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);
      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);
    printf("\n");
    printf(" The %4" NAG_IFMT " generalized Ritz values closest", nconv);
    printf(" to ( %7.3f , %7.3f ) are:\n\n", sigma.re, sigma.im);
    for (j = 0; j <= nconv - 1; ++j) {
      printf("%8" NAG_IFMT "%5s( %12.4f , %12.4f )\n", j + 1, "", eigv[j].re,
             eigv[j].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(dd);
  NAG_FREE(dl);
  NAG_FREE(du);
  NAG_FREE(du2);
  NAG_FREE(resid);
  NAG_FREE(v);
  NAG_FREE(icomm);
  NAG_FREE(ipiv);

  return exit_status;
}

static void mv(Integer nx, Complex *v, Complex *y) {
  /* Compute the out-of--place matrix vector multiplication Y<---M*X, */
  /* where M is mass matrix formed by using piecewise linear elements */
  /* on [0,1]. */

  /* Scalars */
  Complex hsix, z1;
  Integer j, n;
  /* Function Body */
  n = nx * nx;
  /* Assign to Complex type using nag_complex_create (a02bac) */
  hsix = nag_complex_create(1.0 / (6.0 * (double)(n + 1)), 0.0);
  /* y[0] = (four*v[0]+v[1])*(h/six) */
  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  z1 = nag_complex_multiply(four, v[0]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  z1 = nag_complex_add(z1, v[1]);
  y[0] = nag_complex_multiply(z1, hsix);
  for (j = 1; j <= n - 2; ++j) {
    /* y[j] = (v[j-1] + four*v[j] + V[j+1])*(h/six) */
    /* Compute Complex multiply using nag_complex_multiply
       (a02ccc). */
    z1 = nag_complex_multiply(four, v[j]);
    /* Compute Complex addition using nag_complex_add (a02cac). */
    z1 = nag_complex_add(v[j - 1], z1);
    z1 = nag_complex_add(z1, v[j + 1]);
    y[j] = nag_complex_multiply(z1, hsix);
  }
  /* y[n-1] = (v[n-2] + four*v[n-1])*(h/six) */
  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  z1 = nag_complex_multiply(four, v[n - 1]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  z1 = nag_complex_add(v[n - 2], z1);
  y[n - 1] = nag_complex_multiply(z1, hsix);
  return;
} /* mv */

static void my_zgttrf(Integer n, Complex dl[], Complex d[], Complex du[],
                      Complex du2[], Integer ipiv[], Integer *info) {
  /* A simple C version of the Lapack routine zgttrf with argument
     checking removed */
  /* Scalars */
  Complex temp, fact, z1;
  Integer i;
  /* Function Body */
  *info = 0;
  for (i = 0; i < n; ++i) {
    ipiv[i] = i;
  }
  for (i = 0; i < n - 2; ++i) {
    du2[i] = nag_complex_create(0.0, 0.0);
  }
  for (i = 0; i < n - 2; ++i) {
    if (fabs(d[i].re) + fabs(d[i].im) >= fabs(dl[i].re) + fabs(dl[i].im)) {
      /* No row interchange required, eliminate dl[i]. */
      if (fabs(d[i].re) + fabs(d[i].im) != 0.0) {
        /* Compute Complex division using nag_complex_divide
           (a02cdc). */
        fact = nag_complex_divide(dl[i], d[i]);
        dl[i] = fact;
        /* Compute Complex multiply using nag_complex_multiply
           (a02ccc). */
        fact = nag_complex_multiply(fact, du[i]);
        /* Compute Complex subtraction using
           nag_complex_subtract (a02cbc). */
        d[i + 1] = nag_complex_subtract(d[i + 1], fact);
      }
    } else {
      /* Interchange rows I and I+1, eliminate dl[I] */
      /* Compute Complex division using nag_complex_divide
         (a02cdc). */
      fact = nag_complex_divide(d[i], dl[i]);
      d[i] = dl[i];
      dl[i] = fact;
      temp = du[i];
      du[i] = d[i + 1];
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      z1 = nag_complex_multiply(fact, d[i + 1]);
      /* Compute Complex subtraction using nag_complex_subtract
         (a02cbc). */
      d[i + 1] = nag_complex_subtract(temp, z1);
      du2[i] = du[i + 1];
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      du[i + 1] = nag_complex_multiply(fact, du[i + 1]);
      /* Perform Complex negation using nag_complex_negate
         (a02cec). */
      du[i + 1] = nag_complex_negate(du[i + 1]);
      ipiv[i] = i + 1;
    }
  }
  if (n > 1) {
    i = n - 2;
    if (fabs(d[i].re) + fabs(d[i].im) >= fabs(dl[i].re) + fabs(dl[i].im)) {
      if (fabs(d[i].re) + fabs(d[i].im) != 0.0) {
        /* Compute Complex division using nag_complex_divide
           (a02cdc). */
        fact = nag_complex_divide(dl[i], d[i]);
        dl[i] = fact;
        /* Compute Complex multiply using nag_complex_multiply
           (a02ccc). */
        fact = nag_complex_multiply(fact, du[i]);
        /* Compute Complex subtraction using
           nag_complex_subtract (a02cbc). */
        d[i + 1] = nag_complex_subtract(d[i + 1], fact);
      }
    } else {
      /* Compute Complex division using nag_complex_divide
         (a02cdc). */
      fact = nag_complex_divide(d[i], dl[i]);
      d[i] = dl[i];
      dl[i] = fact;
      temp = du[i];
      du[i] = d[i + 1];
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      z1 = nag_complex_multiply(fact, d[i + 1]);
      /* Compute Complex subtraction using nag_complex_subtract
         (a02cbc). */
      d[i + 1] = nag_complex_subtract(temp, z1);
      ipiv[i] = i + 1;
    }
  }
  /* Check for a zero on the diagonal of U. */
  for (i = 0; i < n; ++i) {
    if (fabs(d[i].re) + fabs(d[i].im) == 0.0) {
      *info = i;
      goto END;
    }
  }
END:
  return;
}

static void my_zgttrs(Integer n, Complex dl[], Complex d[], Complex du[],
                      Complex du2[], Integer ipiv[], Complex b[]) {
  /* A simple C version of the Lapack routine zgttrs with argument
     checking removed, the number of right-hand-sides=1, Trans='N' */
  /* Scalars */
  Complex temp, z1;
  Integer i;
  /* Solve L*x = b. */
  for (i = 0; i < n - 1; ++i) {
    if (ipiv[i] == i) {
      /* b[i+1] = b[i+1] - dl[i]*b[i] */
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      temp = nag_complex_multiply(dl[i], b[i]);
      /* Compute Complex subtraction using nag_complex_subtract
         (a02cbc). */
      b[i + 1] = nag_complex_subtract(b[i + 1], temp);
    } else {
      temp = b[i];
      b[i] = b[i + 1];
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      z1 = nag_complex_multiply(dl[i], b[i]);
      /* Compute Complex subtraction using nag_complex_subtract
         (a02cbc). */
      b[i + 1] = nag_complex_subtract(temp, z1);
    }
  }
  /* Solve U*x = b. */
  /* Compute Complex division using nag_complex_divide (a02cdc). */
  b[n - 1] = nag_complex_divide(b[n - 1], d[n - 1]);
  if (n > 1) {
    /* Compute Complex multiply using nag_complex_multiply
       (a02ccc). */
    temp = nag_complex_multiply(du[n - 2], b[n - 1]);
    /* Compute Complex subtraction using nag_complex_subtract
       (a02cbc). */
    z1 = nag_complex_subtract(b[n - 2], temp);
    /* Compute Complex division using nag_complex_divide (a02cdc). */
    b[n - 2] = nag_complex_divide(z1, d[n - 2]);
  }
  for (i = n - 3; i >= 0; --i) {
    /* b[i] = (b[i]-du[i]*b[i+1]-du2[i]*b[i+2])/d[i]; */
    /* Compute Complex multiply using nag_complex_multiply
       (a02ccc). */
    temp = nag_complex_multiply(du[i], b[i + 1]);
    z1 = nag_complex_multiply(du2[i], b[i + 2]);
    /* Compute Complex addition using nag_complex_add
       (a02cac). */
    temp = nag_complex_add(temp, z1);
    /* Compute Complex subtraction using nag_complex_subtract
       (a02cbc). */
    z1 = nag_complex_subtract(b[i], temp);
    /* Compute Complex division using nag_complex_divide
       (a02cdc). */
    b[i] = nag_complex_divide(z1, d[i]);
  }
  return;
}