Date: 2023-09-05T10:18:04+00:00

Actual source code: ex25.c
slepc-3.19.2 2023-09-05
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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:   PetscFunctionBeginUser;
     35:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

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

     44:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     45:      Compute the matrices that define the eigensystem, Ax=kBx
     46:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

     58:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     59:   for (II=Istart;II<Iend;II++) {
     60:     i = II/n; j = II-i*n;
     61:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
     62:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
     63:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
     64:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
     65:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
     66:     PetscCall(MatSetValue(B,II,II,4.0,INSERT_VALUES));
     67:   }

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

     74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     75:                 Create the eigensolver and set various options
     76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

    102:   /*
    103:      Set shift-and-invert with Cholesky; select MUMPS if available
    104:   */

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

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

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

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

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:                       Solve the eigensystem
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    145:   PetscCall(EPSSetUp(eps));
    146:   if (show) {
    147:     PetscCall(EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias));
    148:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n"));
    149:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]));
    150:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    151:     PetscCall(PetscFree(shifts));
    152:     PetscCall(PetscFree(inertias));
    153:   }
    154:   PetscCall(EPSSolve(eps));
    155:   if (show) {
    156:     PetscCall(EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias));
    157:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n"));
    158:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]));
    159:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    160:     PetscCall(PetscFree(shifts));
    161:     PetscCall(PetscFree(inertias));
    162:   }

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

    173:   /*
    174:      Show detailed info unless -terse option is given by user
    175:    */
    176:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    177:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    178:   else {
    179:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    180:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
    181:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    182:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    183:   }

    185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    186:                     Clean up
    187:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    188:   PetscCall(EPSDestroy(&eps));
    189:   PetscCall(MatDestroy(&A));
    190:   PetscCall(MatDestroy(&B));
    191:   PetscCall(SlepcFinalize());
    192:   return 0;
    193: }

    195: /*TEST

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

    204: TEST*/