LapPSI.c

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#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <sys/stat.h>
#include <math.h>
#include "evsl.h"
#include "io.h"

#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) < (b) ? (a) : (b))
int findarg(const char *argname, ARG_TYPE type, void *val, int argc, char **argv);
int lapgen(int nx, int ny, int nz, cooMat *Acoo);
int exeiglap3(int nx, int ny, int nz, double a, double b, int *m, double **vo);
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

int main(int argc, char *argv[]) {
  /*------------------------------------------------------------
    generates a laplacean matrix on an nx x ny x nz mesh 
    and computes all eigenvalues in a given interval [a  b]
    The default set values are
    nx = 41; ny = 53; nz = 1;
    a = 0.4; b = 0.8;
    nslices = 1 [one slice only] 
    other parameters 
    tol [tolerance for stopping - based on residual]
    Mdeg = pol. degree used for DOS
    nvec  = number of sample vectors used for DOS 
    ...
    This uses:
    Subspace iteration  with polynomial filtering
    ------------------------------------------------------------*/
  FILE *fstats = NULL;

  struct stat st = {0}; /* Make sure OUT directory exists */
  if (stat("OUT", &st) == -1) {
    mkdir("OUT", 0750);
  }

  if (!(fstats = fopen("OUT/LapPSI.out","w"))) {
    printf(" failed in opening output file in OUT/\n");
    fstats = stdout;
  }
  int n, nx, ny, nz, i, j, npts, nslices, nvec, Mdeg, nev, 
      max_its, sl, flg, ierr;
  //int ev_int;
  /* find the eigenvalues of A in the interval [a,b] */
  double a, b, lmax, lmin, ecount, tol, *sli, *mu;
  double xintv[4];
  double *vinit;
  polparams pol;
  /*-------------------- matrix A: coo format and csr format */
  cooMat Acoo;
  csrMat Acsr;
  /*-------------------- default values */
  nx   = 41;
  ny   = 53;
  nz   = 1;
  a    = 0.4;
  b    = 0.8;
  nslices = 4;
  //-----------------------------------------------------------------------
  //-------------------- reset some default values from command line
  /* user input from command line */
  flg = findarg("help", NA, NULL, argc, argv);
  if (flg) {
    printf("Usage: ./testL.ex -nx [int] -ny [int] -nz [int] -a [double] -b [double] -nslices [int]\n");
    return 0;
  }
  findarg("nx", INT, &nx, argc, argv);
  findarg("ny", INT, &ny, argc, argv);
  findarg("nz", INT, &nz, argc, argv);
  findarg("a", DOUBLE, &a, argc, argv);
  findarg("b", DOUBLE, &b, argc, argv);
  findarg("nslices", INT, &nslices, argc, argv);
  fprintf(fstats,"used nx = %3d ny = %3d nz = %3d",nx,ny,nz);
  fprintf(fstats," [ a = %4.2f  b= %4.2f],  nslices=%2d \n",a,b,nslices);
  //-------------------- eigenvalue bounds set by hand.
  lmin = 0.0;  
  lmax = nz == 1 ? 8.0 : 12.0;
  xintv[0] = a;
  xintv[1] = b;
  xintv[2] = lmin;
  xintv[3] = lmax;
  tol = 1e-8;
  n = nx * ny * nz;

  /* output the problem settings */
  fprintf(fstats, "- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -\n");
  fprintf(fstats, "Laplacian: %d x %d x %d, n = %d\n", nx, ny, nz, n);
  fprintf(fstats, "Interval: [%20.15f, %20.15f]  -- %d slices \n", a, b, nslices);

  /*-------------------- generate 2D/3D Laplacian matrix 
   *                     saved in coo format */
  ierr = lapgen(nx, ny, nz, &Acoo);
  /*-------------------- convert coo to csr */
  ierr = cooMat_to_csrMat(0, &Acoo, &Acsr);
  /* step 0: short Lanczos run to get bounds */
  fprintf(fstats, "Step 0: Eigenvalue bound s for A: [%.15e, %.15e]\n", lmin, lmax);
  /*-------------------- call kpmdos to get the DOS for dividing the spectrum*/
  /*-------------------- define kpmdos parameters */
  Mdeg = 300;
  nvec = 60;
  /*-------------------- start EVSL */
  EVSLStart();
   /*-------------------- set the left-hand side matrix A */
   SetAMatrix(&Acsr);         
  //-------------------- call kpmdos
  mu = malloc((Mdeg+1)*sizeof(double));
  double t = evsl_timer();
  ierr = kpmdos(Mdeg, 1, nvec, xintv, mu, &ecount);
  t = evsl_timer() - t;
  if (ierr) {
    printf("kpmdos error %d\n", ierr);
    return 1;
  }
  fprintf(fstats, " Time to build DOS (kpmdos) was : %10.2f \n",t);
  fprintf(fstats, " estimated eig count in interval: %10.2e \n",ecount);
  //-------------------- call splicer to slice the spectrum
  npts = 10 * ecount; //200; 
  sli = malloc((nslices+1)*sizeof(double));

  ierr = spslicer(sli, mu, Mdeg, xintv, nslices,  npts);  
  if (ierr) {
    printf("spslicer error %d\n", ierr);
    return 1;
  }
  printf("====================  SLICES FOUND  ====================\n");
  for (j=0; j<nslices;j++)
    printf(" %2d: [% .15e , % .15e]\n", j+1, sli[j],sli[j+1]);
  //-------------------- # eigs per slice
  // ev_int = (int) (1 + ecount / ((double) nslices));
  //-------------------- initial vector  
  vinit = (double *) malloc(n*sizeof(double));
  rand_double(n, vinit);
  //-------------------- debug only :
  //  save_vec(n, vinit, "OUT/vinit.mtx");
  //-------------------- For each slice call ChebLanr
  // set polynomial defaults
  // forced degree 
  for (sl=0; sl<nslices; sl++){
    printf("======================================================\n");
    int nevOut;
    double *lam, *Y, *res;
    int *ind;
    int nev_ex;
    double *lam_ex;
    //-------------------- 
    a = sli[sl];
    b = sli[sl+1];
    printf(" subinterval: [%.4e , %.4e]\n", a, b); 
    //-------------------- approximate number of eigenvalues wanted
    // this factor insures that #eigs per slice is slightly overestimated 
    double fac = 1.2;   
    nev = (int) (1 + ecount / ((double) nslices));  // # eigs per slice
    nev = (int)(fac*nev);                        // want an overestimate of ev_int 
    max_its = 1000;
    //-------------------- ChebLanTr
    xintv[0] = a;     xintv[1] = b;
    xintv[2] = lmin;  xintv[3] = lmax;
    set_pol_def(&pol);
    //-------------------- this is to show how you can reset some of the
    //                     parameters to determine the filter polynomial
    pol.damping = 0;
    pol.thresh_int = 0.5;
    // pol.deg = 20 //<< this will force this exact degree . not recommended
    //                   it is better to change the values of the thresholds
    //                   pol.thresh_ext and plot.thresh_int
    //-------------------- get polynomial to use :
    find_pol(xintv, &pol);       

    fprintf(fstats, " polynomial [type = %d], deg %d, bar %e gam %e\n",
            pol.type, pol.deg, pol.bar, pol.gam);
    //-------------------- then call ChenLanNr

    double *V0;
    V0 = (double *) malloc(n*nev*sizeof(double));
    rand_double(n*nev, V0);

    ierr = ChebSI(nev, xintv, max_its, tol, V0, &pol, &nevOut, 
                  &lam, &Y, &res, fstats);
    if (ierr) {
      printf("ChebSI error %d\n", ierr);
      return 1;
    }

    free(V0);
    /* sort the eigenvals: ascending order
     * ind: keep the orginal indices */
    ind = (int *) malloc(nevOut*sizeof(int));
    sort_double(nevOut, lam, ind);
    /* compute exact eigenvalues */
    exeiglap3(nx, ny, nz, a, b, &nev_ex, &lam_ex);
    printf(" number of eigenvalues: %d, found: %d\n", nev_ex, nevOut);

    /* print eigenvalues */
    fprintf(fstats, "                                   Eigenvalues in [a, b]\n");
    fprintf(fstats, "    Computed [%d]       ||Res||              Exact [%d]",
            nevOut, nev_ex);
    if (nevOut == nev_ex) {
      fprintf(fstats, "                 Err");
    }
    fprintf(fstats, "\n");
    for (i=0; i<max(nevOut, nev_ex); i++) {
      if (i < nevOut) {
        fprintf(fstats, "% .15e  %.1e", lam[i], res[ind[i]]);
      } else {
        fprintf(fstats, "                               ");
      }
      if (i < nev_ex) { 
        fprintf(fstats, "        % .15e", lam_ex[i]);
      }
      if (nevOut == nev_ex) {
        fprintf(fstats, "        % .1e", lam[i]-lam_ex[i]);
      }
      fprintf(fstats,"\n");
      if (i>50) {
        fprintf(fstats,"                        -- More not shown --\n");
        break;
      } 
    }
    //-------------------- free allocated space withing this scope
    if (lam)  free(lam);
    if (Y) free(Y);
    if (res)  free(res);
    free_pol(&pol);
    free(ind);
    free(lam_ex);
  }
  //-------------------- free other allocated space 
  free(vinit);
  free(sli);
  free_coo(&Acoo);
  free_csr(&Acsr);
  free(mu);
  fclose(fstats);
  /*-------------------- finalize EVSL */
  EVSLFinish();
  return 0;
}