NAG Library Manual, Mark 27.3
Interfaces:  FL   CL   CPP   AD 

NAG CL Interface Introduction
Example description
/* nag_sparseig_real_monit (f12aec) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.3, 2021.
 */

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

static void mv(Integer, double *, double *);
static void av(Integer, double *, double *);
static int ytax(Integer, double *, double *, double *);
static int ytmx(Integer, double *, double *, double *);
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 c1, c2, c3, eigv, num, den;
  double estnrm, deni, denr, i2, numi, numr, r2;
  double sigmai, sigmar;
  Integer exit_status, info, irevcm, j, k, lcomm, n;
  Integer nconv, ncv, nev, niter, nshift;
  /* Nag types */
  Nag_Boolean first;
  NagError fail;

  /* Arrays */
  Complex *cdd = 0, *cdl = 0, *cdu = 0, *cdu2 = 0, *ctemp = 0;
  double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0;
  double *resid = 0, *v = 0;
  Integer *icomm = 0, *ipiv = 0;
  /* Pointers */
  double *mx = 0, *x = 0, *y = 0;

  exit_status = 0;
  INIT_FAIL(fail);

  printf("nag_sparseig_real_monit (f12aec) Example Program "
         "Results\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");

  /* Read problem parameter values from data file. */
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%lf%lf%*[^\n] ", &n, &nev, &ncv,
        &sigmar, &sigmai);
  /* Allocate memory */
  lcomm = 3 * n + 3 * ncv * ncv + 6 * ncv + 60;
  if (!(cdd = NAG_ALLOC(n, Complex)) || !(cdl = NAG_ALLOC(n, Complex)) ||
      !(cdu = NAG_ALLOC(n, Complex)) || !(cdu2 = NAG_ALLOC(n, Complex)) ||
      !(ctemp = NAG_ALLOC(n, Complex)) || !(comm = NAG_ALLOC(lcomm, double)) ||
      !(eigvr = NAG_ALLOC(ncv, double)) || !(eigvi = NAG_ALLOC(ncv, double)) ||
      !(eigest = NAG_ALLOC(ncv, double)) || !(resid = NAG_ALLOC(n, double)) ||
      !(v = NAG_ALLOC(n * ncv, double)) ||
      !(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_real_init (f12aac). */
  nag_sparseig_real_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_real_init (f12aac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Select the required spectrum using
     nag_sparseig_real_option (f12adc). */
  nag_sparseig_real_option("SHIFTED REAL", icomm, comm, &fail);
  /* Select the problem type using
     nag_sparseig_real_option (f12adc). */
  nag_sparseig_real_option("GENERALIZED", icomm, comm, &fail);
  /* Solve A*x = lambda*B*x in shift-invert mode. */
  /* The shift, sigma, is a complex number (sigmar, sigmai). */
  /* OP = Real_Part{inv[A-(sigmar,sigmai)*M]*M and  B = M. */
  c1 = nag_complex_create(-2. - sigmar, -sigmai);
  c2 = nag_complex_create(2. - sigmar * 4., sigmai * -4.);
  c3 = nag_complex_create(3. - sigmar, -sigmai);

  for (j = 0; j <= n - 2; ++j) {
    cdl[j] = c1;
    cdd[j] = c2;
    cdu[j] = c3;
  }
  cdd[n - 1] = c2;

  my_zgttrf(n, cdl, cdd, cdu, cdu2, ipiv, &info);

  irevcm = 0;
REVCOMLOOP:
  /* repeated calls to reverse communication routine
     nag_sparseig_real_iter (f12abc). */
  nag_sparseig_real_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(n, x, y);
      for (j = 0; j <= n - 1; ++j) {
        ctemp[j].re = y[j], ctemp[j].im = 0.;
      }
      my_zgttrs(n, cdl, cdd, cdu, cdu2, ipiv, ctemp);
      for (j = 0; j <= n - 1; ++j) {
        y[j] = ctemp[j].re;
      }
    } else if (irevcm == 1) {
      /* Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x, */
      /* M*X stored in MX. */
      for (j = 0; j <= n - 1; ++j) {
        ctemp[j].re = mx[j], ctemp[j].im = 0.;
      }
      my_zgttrs(n, cdl, cdd, cdu, cdu2, ipiv, ctemp);
      for (j = 0; j <= n - 1; ++j) {
        y[j] = ctemp[j].re;
      }
    } else if (irevcm == 2) {
      /* Perform  y <--- M*x */
      mv(n, x, y);
    } else if (irevcm == 4 && imon == 1) {
      /* If imon=1, get monitoring information using
         nag_sparseig_real_monit (f12aec). */
      nag_sparseig_real_monit(&niter, &nconv, eigvr, eigvi, eigest, icomm,
                              comm);
      /* Compute 2-norm of Ritz estimates using
         nag_blast_dge_norm (f16rac). */
      nag_blast_dge_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_real_proc
       (f12acc) to compute eigenvalues/vectors. */
    nag_sparseig_real_proc(&nconv, eigvr, eigvi, v, sigmar, sigmai, resid, v,
                           comm, icomm, &fail);
    first = Nag_TRUE;
    k = 0;
    for (j = 0; j <= nconv - 1; ++j) {
      /* Use Rayleigh Quotient to recover eigenvalues of the */
      /* original problem. */
      if (eigvi[j] == 0.) {
        /* Ritz value is real. */
        /* Numerator = Vj . AVj where Vj is j-th Ritz vector */
        if (ytax(n, &v[k], &v[k], &numr)) {
          goto END;
        }
        /* Denominator = Vj . MVj */
        if (ytmx(n, &v[k], &v[k], &denr)) {
          goto END;
        }
        eigvr[j] = numr / denr;
      } else if (first) {
        /* Ritz value is complex: (x,y). */
        /* Compute x'(Ax)  and y'(Ax). */
        if (ytax(n, &v[k], &v[k], &numr)) {
          goto END;
        }
        if (ytax(n, &v[k], &v[k + n], &numi)) {
          goto END;
        }
        /* Compute y'(Ay)  and x'(Ay). */
        if (ytax(n, &v[k + n], &v[k + n], &r2)) {
          goto END;
        }
        if (ytax(n, &v[k + n], &v[k], &i2)) {
          goto END;
        }
        numr += r2;
        numi = i2 - numi;
        /* Assign to Complex type using nag_complex_create (a02bac). */
        num = nag_complex_create(numr, numi);
        /* Compute x'(Mx)  and y'(Mx). */
        if (ytmx(n, &v[k], &v[k], &denr)) {
          goto END;
        }
        if (ytmx(n, &v[k], &v[k + n], &deni)) {
          goto END;
        }
        /* Compute y'(Ay)  and x'(Ay). */
        if (ytmx(n, &v[k + n], &v[k + n], &r2)) {
          goto END;
        }
        if (ytmx(n, &v[k + n], &v[k], &i2)) {
          goto END;
        }
        denr += r2;
        deni = i2 - deni;
        /* Assign to Complex type using nag_complex_create (a02bac). */
        den = nag_complex_create(denr, deni);
        /* eigv = x'(Ax)/x'(Mx) */
        /* Compute Complex division using nag_complex_divide
           (a02cdc). */
        eigv = nag_complex_divide(num, den);
        eigvr[j] = eigv.re;
        eigvi[j] = eigv.im;
        first = Nag_FALSE;
      } else {
        /* Second of complex conjugate pair. */
        eigvr[j] = eigvr[j - 1];
        eigvi[j] = -eigvi[j - 1];
        first = Nag_TRUE;
      }
      k = k + n;
    }
    /* Print computed eigenvalues. */
    printf("\n The %4" NAG_IFMT " generalized Ritz values closest", nconv);
    printf(" to ( %8.4f ,  %8.4f ) are:\n\n", sigmar, sigmai);
    for (j = 0; j <= nconv - 1; ++j) {
      printf("%8" NAG_IFMT "%5s( %7.4f, %7.4f )\n", j + 1, "", eigvr[j],
             eigvi[j]);
    }
  } else {
    printf(" Error from nag_sparseig_real_iter (f12abc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(cdd);
  NAG_FREE(cdl);
  NAG_FREE(cdu);
  NAG_FREE(cdu2);
  NAG_FREE(ctemp);
  NAG_FREE(comm);
  NAG_FREE(eigvr);
  NAG_FREE(eigvi);
  NAG_FREE(eigest);
  NAG_FREE(resid);
  NAG_FREE(v);
  NAG_FREE(icomm);
  NAG_FREE(ipiv);

  return exit_status;
}

static void mv(Integer n, double *v, double *y) {
  /* Compute the matrix vector multiplication y<---M*x, */
  /* where M is mass matrix formed by using piecewise linear elements */
  /* on [0,1]. */

  /* Scalars */
  Integer j;

  /* Function Body */
  y[0] = v[0] * 4. + v[1];
  for (j = 1; j <= n - 2; ++j) {
    y[j] = v[j - 1] + v[j] * 4. + v[j + 1];
  }
  y[n - 1] = v[n - 2] + v[n - 1] * 4.;
  return;
} /* mv */

static void av(Integer n, double *v, double *w) {
  /* Scalars */
  Integer j;

  /* Function Body */
  w[0] = v[0] * 2. + v[1] * 3.;
  for (j = 1; j <= n - 2; ++j) {
    w[j] = v[j - 1] * -2. + v[j] * 2. + v[j + 1] * 3.;
  }
  w[n - 1] = v[n - 2] * -2. + v[n - 1] * 2.;
  return;
} /* av */

static int ytax(Integer n, double x[], double y[], double *r) {
  /* Given the vectors x and y, Performs the operation */
  /* y'Ax and returns the scalar value. */

  /* Scalars */
  Integer exit_status, j;
  /* Arrays */
  double *ax = 0;

  /* Function Body */
  exit_status = 0;
  /* Allocate memory */
  if (!(ax = NAG_ALLOC(n, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto YTAXEND;
  }
  av(n, x, ax);
  *r = 0.0;
  for (j = 0; j <= n - 1; ++j) {
    *r = *r + y[j] * ax[j];
  }
YTAXEND:
  NAG_FREE(ax);
  return exit_status;
} /* ytax */

static int ytmx(Integer n, double x[], double y[], double *r) {
  /* Given the vectors x and y, Performs the operation */
  /* y'Mx and returns the scalar value. */

  /* Scalars */
  Integer exit_status, j;
  /* Arrays */
  double *mx = 0;

  /* Function Body */
  exit_status = 0;
  /* Allocate memory */
  if (!(mx = NAG_ALLOC(n, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto YTMXEND;
  }
  mv(n, x, mx);
  *r = 0.0;
  for (j = 0; j <= n - 1; ++j) {
    *r = *r + y[j] * mx[j];
  }
YTMXEND:
  NAG_FREE(mx);
  return exit_status;
} /* ytmx */

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;
}