Date: 2026-03-31T13:23:36+00:00

Actual source code: ex25.c

      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,NULL,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));

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

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

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

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:                 Create the eigensolver and set various options
     74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     76:   /*
     77:      Create eigensolver context
     78:   */
     79:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

     81:   /*
     82:      Set operators and set problem type
     83:   */
     84:   PetscCall(EPSSetOperators(eps,A,B));
     85:   PetscCall(EPSSetProblemType(eps,EPS_GHEP));

     87:   /*
     88:      Set interval for spectrum slicing
     89:   */
     90:   inta = 0.1;
     91:   intb = 0.2;
     92:   PetscCall(EPSSetInterval(eps,inta,intb));
     93:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_ALL));

     95:   /*
     96:      Spectrum slicing requires Krylov-Schur
     97:   */
     98:   PetscCall(EPSSetType(eps,EPSKRYLOVSCHUR));

    100:   /*
    101:      Set shift-and-invert with Cholesky; select MUMPS if available
    102:   */

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

    111:   /*
    112:      Use MUMPS if available.
    113:      Note that in complex scalars we cannot use MUMPS for spectrum slicing,
    114:      because MatGetInertia() is not available in that case.
    115:   */
    116: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
    117:   PetscCall(EPSKrylovSchurSetDetectZeros(eps,PETSC_TRUE));  /* enforce zero detection */
    118:   PetscCall(PCFactorSetMatSolverType(pc,MATSOLVERMUMPS));
    119:   PetscCall(PCFactorSetUpMatSolverType(pc));
    120:   /*
    121:      Set several MUMPS options, the corresponding command-line options are:
    122:      '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
    123:      '-st_mat_mumps_icntl_24 1': detect null pivots in factorization (for the case that a shift is equal to an eigenvalue)
    124:      '-st_mat_mumps_cntl_3 <tol>': a tolerance used for null pivot detection (must be larger than machine epsilon)

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

    135:   /*
    136:      Set solver parameters at runtime
    137:   */
    138:   PetscCall(EPSSetFromOptions(eps));

    140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:                       Solve the eigensystem
    142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    143:   PetscCall(EPSSetUp(eps));
    144:   if (show) {
    145:     PetscCall(EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias));
    146:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n"));
    147:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]));
    148:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    149:     PetscCall(PetscFree(shifts));
    150:     PetscCall(PetscFree(inertias));
    151:   }
    152:   PetscCall(EPSSolve(eps));
    153:   if (show) {
    154:     PetscCall(EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias));
    155:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n"));
    156:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]));
    157:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    158:     PetscCall(PetscFree(shifts));
    159:     PetscCall(PetscFree(inertias));
    160:   }

    162:   /*
    163:      Show eigenvalues in interval and print solution
    164:   */
    165:   PetscCall(EPSGetType(eps,&type));
    166:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
    167:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    168:   PetscCall(EPSGetInterval(eps,&inta,&intb));
    169:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," %" PetscInt_FMT " eigenvalues found in [%g, %g]\n",nev,(double)inta,(double)intb));

    171:   /*
    172:      Show detailed info unless -terse option is given by user
    173:    */
    174:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    175:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    176:   else {
    177:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    178:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
    179:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    180:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    181:   }

    183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    184:                     Clean up
    185:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    186:   PetscCall(EPSDestroy(&eps));
    187:   PetscCall(MatDestroy(&A));
    188:   PetscCall(MatDestroy(&B));
    189:   PetscCall(SlepcFinalize());
    190:   return 0;
    191: }

    193: /*TEST

    195:    testset:
    196:       args: -terse -show_inertias
    197:       output_file: output/ex25_1.out
    198:       test:
    199:          suffix: 1
    200:          requires: !mumps
    201:       test:
    202:          suffix: 1_mumps
    203:          requires: mumps !complex

    205: TEST*/