Date: 2020-01-13T12:00:39+00:00

Actual source code: test21.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Illustrates region filtering. "
     12:   "Based on ex5.\n"
     13:   "The command line options are:\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

     16: #include <slepceps.h>

     18: /*
     19:    User-defined routines
     20: */
     21: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     23: int main(int argc,char **argv)
     24: {
     25:   Mat            A;
     26:   EPS            eps;
     27:   ST             st;
     28:   RG             rg;
     29:   PetscReal      radius,tol=1000*PETSC_MACHINE_EPSILON;
     30:   PetscScalar    target=0.5;
     31:   PetscInt       N,m=15,nev;
     33:   char           str[50];

     35:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     36:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     37:   N = m*(m+1)/2;
     38:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
     39:   PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
     40:   SlepcSNPrintfScalar(str,50,target,PETSC_FALSE);
     41:   PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);

     43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     44:      Compute the operator matrix that defines the eigensystem, Ax=kx
     45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     47:   MatCreate(PETSC_COMM_WORLD,&A);
     48:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     49:   MatSetFromOptions(A);
     50:   MatSetUp(A);
     51:   MatMarkovModel(m,A);

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:                 Create a standalone spectral transformation
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     57:   STCreate(PETSC_COMM_WORLD,&st);
     58:   STSetType(st,STSINVERT);
     59:   STSetShift(st,target);

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:                     Create a region for filtering
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     65:   RGCreate(PETSC_COMM_WORLD,&rg);
     66:   RGSetType(rg,RGELLIPSE);
     67:   radius = (1.0-PetscRealPart(target))/2.0;
     68:   RGEllipseSetParameters(rg,target+radius,radius,0.1);

     70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:                 Create the eigensolver and set various options
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     74:   EPSCreate(PETSC_COMM_WORLD,&eps);
     75:   EPSSetST(eps,st);
     76:   EPSSetRG(eps,rg);
     77:   EPSSetOperators(eps,A,NULL);
     78:   EPSSetProblemType(eps,EPS_NHEP);
     79:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);
     80:   EPSSetTarget(eps,target);
     81:   EPSSetFromOptions(eps);

     83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     84:                       Solve the eigensystem
     85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     87:   EPSSolve(eps);
     88:   EPSGetDimensions(eps,&nev,NULL,NULL);
     89:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

     91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     92:                     Display solution and clean up
     93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     95:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
     96:   EPSDestroy(&eps);
     97:   STDestroy(&st);
     98:   RGDestroy(&rg);
     99:   MatDestroy(&A);
    100:   SlepcFinalize();
    101:   return ierr;
    102: }

    104: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    105: {
    106:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    107:   PetscReal       pd,pu;
    108:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    109:   PetscErrorCode  ierr;

    112:   MatGetOwnershipRange(A,&Istart,&Iend);
    113:   for (i=1;i<=m;i++) {
    114:     jmax = m-i+1;
    115:     for (j=1;j<=jmax;j++) {
    116:       ix = ix + 1;
    117:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    118:       if (j!=jmax) {
    119:         pd = cst*(PetscReal)(i+j-1);
    120:         /* north */
    121:         if (i==1) {
    122:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    123:         } else {
    124:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    125:         }
    126:         /* east */
    127:         if (j==1) {
    128:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    129:         } else {
    130:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    131:         }
    132:       }
    133:       /* south */
    134:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    135:       if (j>1) {
    136:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    137:       }
    138:       /* west */
    139:       if (i>1) {
    140:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    141:       }
    142:     }
    143:   }
    144:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    145:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    146:   return(0);
    147: }

    149: /*TEST

    151:    test:
    152:       suffix: 1
    153:       args: -eps_nev 4 -eps_ncv 20
    154:       output_file: output/test11_1.out
    155:       requires: !single

    157: TEST*/