Date: 2022-03-31T15:29:16+00:00

Actual source code: ex25.c
slepc-3.17.0 2022-03-31
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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[] = "Spectrum slicing on generalized symmetric eigenproblem.\n\n"
     12:   "The problem is similar to ex13.c.\n\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     15:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n";

     17: #include <slepceps.h>

     19: int main(int argc,char **argv)
     20: {
     21:   Mat            A,B;         /* matrices */
     22:   EPS            eps;         /* eigenproblem solver context */
     23:   ST             st;          /* spectral transformation context */
     24:   KSP            ksp;
     25:   PC             pc;
     26:   EPSType        type;
     27:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,*inertias,ns;
     28:   PetscReal      inta,intb,*shifts;
     29:   PetscBool      flag,show=PETSC_FALSE,terse;
     30: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
     31:   Mat            F;
     32: #endif

     34:   SlepcInitialize(&argc,&argv,(char*)0,help);

     36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     37:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     38:   PetscOptionsGetBool(NULL,NULL,"-show_inertias",&show,NULL);
     39:   if (!flag) m=n;
     40:   N = n*m;
     41:   PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum slicing on GHEP, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m);

     43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     44:      Compute the matrices that define the eigensystem, Ax=kBx
     45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     52:   MatCreate(PETSC_COMM_WORLD,&B);
     53:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
     54:   MatSetFromOptions(B);
     55:   MatSetUp(B);

     57:   MatGetOwnershipRange(A,&Istart,&Iend);
     58:   for (II=Istart;II<Iend;II++) {
     59:     i = II/n; j = II-i*n;
     60:     if (i>0) MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);
     61:     if (i<m-1) MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);
     62:     if (j>0) MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);
     63:     if (j<n-1) MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);
     64:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     65:     MatSetValue(B,II,II,4.0,INSERT_VALUES);
     66:   }

     68:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     69:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     70:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     71:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:                 Create the eigensolver and set various options
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     77:   /*
     78:      Create eigensolver context
     79:   */
     80:   EPSCreate(PETSC_COMM_WORLD,&eps);

     82:   /*
     83:      Set operators and set problem type
     84:   */
     85:   EPSSetOperators(eps,A,B);
     86:   EPSSetProblemType(eps,EPS_GHEP);

     88:   /*
     89:      Set interval for spectrum slicing
     90:   */
     91:   inta = 0.1;
     92:   intb = 0.2;
     93:   EPSSetInterval(eps,inta,intb);
     94:   EPSSetWhichEigenpairs(eps,EPS_ALL);

     96:   /*
     97:      Spectrum slicing requires Krylov-Schur
     98:   */
     99:   EPSSetType(eps,EPSKRYLOVSCHUR);

    101:   /*
    102:      Set shift-and-invert with Cholesky; select MUMPS if available
    103:   */

    105:   EPSGetST(eps,&st);
    106:   STSetType(st,STSINVERT);
    107:   EPSKrylovSchurGetKSP(eps,&ksp);
    108:   KSPSetType(ksp,KSPPREONLY);
    109:   KSPGetPC(ksp,&pc);
    110:   PCSetType(pc,PCCHOLESKY);

    112:   /*
    113:      Use MUMPS if available.
    114:      Note that in complex scalars we cannot use MUMPS for spectrum slicing,
    115:      because MatGetInertia() is not available in that case.
    116:   */
    117: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
    118:   EPSKrylovSchurSetDetectZeros(eps,PETSC_TRUE);  /* enforce zero detection */
    119:   PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
    120:   PCFactorSetUpMatSolverType(pc);
    121:   /*
    122:      Set several MUMPS options, the corresponding command-line options are:
    123:      '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
    124:      '-st_mat_mumps_icntl_24 1': detect null pivots in factorization (for the case that a shift is equal to an eigenvalue)
    125:      '-st_mat_mumps_cntl_3 <tol>': a tolerance used for null pivot detection (must be larger than machine epsilon)

    127:      Note: depending on the interval, it may be necessary also to increase the workspace:
    128:      '-st_mat_mumps_icntl_14 <percentage>': increase workspace with a percentage (50, 100 or more)
    129:   */
    130:   PCFactorGetMatrix(pc,&F);
    131:   MatMumpsSetIcntl(F,13,1);
    132:   MatMumpsSetIcntl(F,24,1);
    133:   MatMumpsSetCntl(F,3,1e-12);
    134: #endif

    136:   /*
    137:      Set solver parameters at runtime
    138:   */
    139:   EPSSetFromOptions(eps);

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:                       Solve the eigensystem
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    144:   EPSSetUp(eps);
    145:   if (show) {
    146:     EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
    147:     PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n");
    148:     for (i=0;i<ns;i++) PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]);
    149:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    150:     PetscFree(shifts);
    151:     PetscFree(inertias);
    152:   }
    153:   EPSSolve(eps);
    154:   if (show) {
    155:     EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
    156:     PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n");
    157:     for (i=0;i<ns;i++) PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]);
    158:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    159:     PetscFree(shifts);
    160:     PetscFree(inertias);
    161:   }

    163:   /*
    164:      Show eigenvalues in interval and print solution
    165:   */
    166:   EPSGetType(eps,&type);
    167:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    168:   EPSGetDimensions(eps,&nev,NULL,NULL);
    169:   EPSGetInterval(eps,&inta,&intb);
    170:   PetscPrintf(PETSC_COMM_WORLD," %" PetscInt_FMT " eigenvalues found in [%g, %g]\n",nev,(double)inta,(double)intb);

    172:   /*
    173:      Show detailed info unless -terse option is given by user
    174:    */
    175:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    176:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    177:   else {
    178:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    179:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    180:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    181:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    182:   }

    184:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    185:                     Clean up
    186:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    187:   EPSDestroy(&eps);
    188:   MatDestroy(&A);
    189:   MatDestroy(&B);
    190:   SlepcFinalize();
    191:   return 0;
    192: }

    194: /*TEST

    196:    testset:
    197:       args: -terse
    198:       test:
    199:          requires: !mumps
    200:       test:
    201:          requires: mumps !complex

    203: TEST*/