Actual source code: ex47.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[] = "Shows how to recover symmetry when solving a GHEP as non-symmetric.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     16: #include <slepceps.h>

     18: /*
     19:    User context for shell matrix
     20: */
     21: typedef struct {
     22:   KSP       ksp;
     23:   Mat       B;
     24:   Vec       w;
     25: } CTX_SHELL;

     27: /*
     28:     Matrix-vector product function for user matrix
     29:        y <-- A^{-1}*B*x
     30:     The matrix A^{-1}*B*x is not symmetric, but it is self-adjoint with respect
     31:     to the B-inner product. Here we assume A is symmetric and B is SPD.
     32:  */
     33: PetscErrorCode MatMult_Sinvert0(Mat S,Vec x,Vec y)
     34: {
     35:   CTX_SHELL      *ctx;

     37:   PetscFunctionBeginUser;
     38:   PetscCall(MatShellGetContext(S,&ctx));
     39:   PetscCall(MatMult(ctx->B,x,ctx->w));
     40:   PetscCall(KSPSolve(ctx->ksp,ctx->w,y));
     41:   PetscFunctionReturn(PETSC_SUCCESS);
     42: }

     44: int main(int argc,char **argv)
     45: {
     46:   Mat               A,B,S;      /* matrices */
     47:   EPS               eps;        /* eigenproblem solver context */
     48:   BV                bv;
     49:   Vec               *X,v;
     50:   PetscReal         lev=0.0,tol=1000*PETSC_MACHINE_EPSILON;
     51:   PetscInt          N,n=45,m,Istart,Iend,II,i,j,nconv;
     52:   PetscBool         flag;
     53:   CTX_SHELL         *ctx;

     55:   PetscFunctionBeginUser;
     56:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     57:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     58:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     59:   if (!flag) m=n;
     60:   N = n*m;
     61:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

     63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     64:          Compute the matrices that define the eigensystem, Ax=kBx
     65:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     67:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     68:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     69:   PetscCall(MatSetFromOptions(A));

     71:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
     72:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N));
     73:   PetscCall(MatSetFromOptions(B));

     75:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     76:   for (II=Istart;II<Iend;II++) {
     77:     i = II/n; j = II-i*n;
     78:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
     79:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
     80:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
     81:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
     82:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
     83:     PetscCall(MatSetValue(B,II,II,2.0/PetscLogScalar(II+2),INSERT_VALUES));
     84:   }

     86:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     87:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
     88:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
     89:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
     90:   PetscCall(MatCreateVecs(B,&v,NULL));

     92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     93:               Create a shell matrix S = A^{-1}*B
     94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     95:   PetscCall(PetscNew(&ctx));
     96:   PetscCall(KSPCreate(PETSC_COMM_WORLD,&ctx->ksp));
     97:   PetscCall(KSPSetOperators(ctx->ksp,A,A));
     98:   PetscCall(KSPSetTolerances(ctx->ksp,tol,PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
     99:   PetscCall(KSPSetFromOptions(ctx->ksp));
    100:   ctx->B = B;
    101:   PetscCall(MatCreateVecs(A,&ctx->w,NULL));
    102:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,(void*)ctx,&S));
    103:   PetscCall(MatShellSetOperation(S,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Sinvert0));

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:                 Create the eigensolver and set various options
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
    110:   PetscCall(EPSSetOperators(eps,S,NULL));
    111:   PetscCall(EPSSetProblemType(eps,EPS_HEP));  /* even though S is not symmetric */
    112:   PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT));
    113:   PetscCall(EPSSetFromOptions(eps));

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:                       Solve the eigensystem
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    119:   PetscCall(EPSSetUp(eps));   /* explicitly call setup */
    120:   PetscCall(EPSGetBV(eps,&bv));
    121:   PetscCall(BVSetMatrix(bv,B,PETSC_FALSE));  /* set inner product matrix to recover symmetry */
    122:   PetscCall(EPSSolve(eps));

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                  Display solution and check B-orthogonality
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    128:   PetscCall(EPSGetTolerances(eps,&tol,NULL));
    129:   PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    130:   PetscCall(EPSGetConverged(eps,&nconv));
    131:   if (nconv>1) {
    132:     PetscCall(VecDuplicateVecs(v,nconv,&X));
    133:     for (i=0;i<nconv;i++) PetscCall(EPSGetEigenvector(eps,i,X[i],NULL));
    134:     PetscCall(VecCheckOrthonormality(X,nconv,NULL,nconv,B,NULL,&lev));
    135:     if (lev<10*tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n"));
    136:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)lev));
    137:     PetscCall(VecDestroyVecs(nconv,&X));
    138:   }

    140:   PetscCall(EPSDestroy(&eps));
    141:   PetscCall(MatDestroy(&A));
    142:   PetscCall(MatDestroy(&B));
    143:   PetscCall(VecDestroy(&v));
    144:   PetscCall(KSPDestroy(&ctx->ksp));
    145:   PetscCall(VecDestroy(&ctx->w));
    146:   PetscCall(PetscFree(ctx));
    147:   PetscCall(MatDestroy(&S));
    148:   PetscCall(SlepcFinalize());
    149:   return 0;
    150: }

    152: /*TEST

    154:    test:
    155:       args: -n 18 -eps_nev 4 -eps_max_it 1500
    156:       requires: !single

    158: TEST*/