Date: 2022-08-09T09:05:41+00:00

Actual source code: ex24.c
slepc-3.17.2 2022-08-09
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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 folding for a standard symmetric eigenproblem.\n\n"
     12:   "The problem matrix is the 2-D Laplacian.\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: /*
     20:    User context for spectrum folding
     21: */
     22: typedef struct {
     23:   Mat       A;
     24:   Vec       w;
     25:   PetscReal target;
     26: } CTX_FOLD;

     28: /*
     29:    Auxiliary routines
     30: */
     31: PetscErrorCode MatMult_Fold(Mat,Vec,Vec);
     32: PetscErrorCode RayleighQuotient(Mat,Vec,PetscScalar*);
     33: PetscErrorCode ComputeResidualNorm(Mat,PetscScalar,Vec,PetscReal*);

     35: int main(int argc,char **argv)
     36: {
     37:   Mat            A,M,P;       /* problem matrix, shell matrix and preconditioner */
     38:   Vec            x;           /* eigenvector */
     39:   EPS            eps;         /* eigenproblem solver context */
     40:   ST             st;          /* spectral transformation */
     41:   KSP            ksp;
     42:   PC             pc;
     43:   EPSType        type;
     44:   CTX_FOLD       *ctx;
     45:   PetscInt       nconv,N,n=10,m,nloc,mloc,Istart,Iend,II,i,j;
     46:   PetscReal      *error,*evals,target=0.0,tol;
     47:   PetscScalar    lambda;
     48:   PetscBool      flag,terse,errok,hasmat;

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

     52:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     53:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     54:   if (!flag) m=n;
     55:   PetscOptionsGetReal(NULL,NULL,"-target",&target,NULL);
     56:   N = n*m;
     57:   PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum Folding, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid) target=%f\n\n",N,n,m,(double)target);

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:      Compute the 5-point stencil Laplacian
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     63:   MatCreate(PETSC_COMM_WORLD,&A);
     64:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     65:   MatSetFromOptions(A);
     66:   MatSetUp(A);

     68:   MatGetOwnershipRange(A,&Istart,&Iend);
     69:   for (II=Istart;II<Iend;II++) {
     70:     i = II/n; j = II-i*n;
     71:     if (i>0) MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);
     72:     if (i<m-1) MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);
     73:     if (j>0) MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);
     74:     if (j<n-1) MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);
     75:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     76:   }

     78:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     79:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     80:   MatCreateVecs(A,&x,NULL);
     81:   MatGetLocalSize(A,&nloc,&mloc);

     83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     84:                 Create shell matrix to perform spectrum folding
     85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     86:   PetscNew(&ctx);
     87:   ctx->A = A;
     88:   ctx->target = target;
     89:   VecDuplicate(x,&ctx->w);

     91:   MatCreateShell(PETSC_COMM_WORLD,nloc,mloc,N,N,ctx,&M);
     92:   MatShellSetOperation(M,MATOP_MULT,(void(*)(void))MatMult_Fold);

     94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     95:                 Create the eigensolver and set various options
     96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     98:   EPSCreate(PETSC_COMM_WORLD,&eps);
     99:   EPSSetOperators(eps,M,NULL);
    100:   EPSSetProblemType(eps,EPS_HEP);
    101:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
    102:   EPSSetFromOptions(eps);

    104:   PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSGD,EPSJD,EPSBLOPEX,EPSLOBPCG,EPSRQCG,"");
    105:   if (flag) {
    106:     /*
    107:        Build preconditioner specific for this application (diagonal of A^2)
    108:     */
    109:     MatGetRowSum(A,x);
    110:     VecScale(x,-1.0);
    111:     VecShift(x,20.0);
    112:     MatCreate(PETSC_COMM_WORLD,&P);
    113:     MatSetSizes(P,PETSC_DECIDE,PETSC_DECIDE,N,N);
    114:     MatSetFromOptions(P);
    115:     MatSetUp(P);
    116:     MatDiagonalSet(P,x,INSERT_VALUES);
    117:     /*
    118:        Set diagonal preconditioner
    119:     */
    120:     EPSGetST(eps,&st);
    121:     STSetType(st,STPRECOND);
    122:     STSetPreconditionerMat(st,P);
    123:     MatDestroy(&P);
    124:     STGetKSP(st,&ksp);
    125:     KSPGetPC(ksp,&pc);
    126:     PCSetType(pc,PCJACOBI);
    127:     STPrecondGetKSPHasMat(st,&hasmat);
    128:     PetscPrintf(PETSC_COMM_WORLD," Preconditioned solver, hasmat=%s\n",hasmat?"true":"false");
    129:   }

    131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    132:                       Solve the eigensystem
    133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    135:   EPSSolve(eps);
    136:   EPSGetType(eps,&type);
    137:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    138:   EPSGetTolerances(eps,&tol,NULL);

    140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:                     Display solution and clean up
    142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    144:   EPSGetConverged(eps,&nconv);
    145:   PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv);
    146:   if (nconv>0) {
    147:     PetscMalloc2(nconv,&evals,nconv,&error);
    148:     for (i=0;i<nconv;i++) {
    149:       /*  Get i-th eigenvector, compute eigenvalue approximation from
    150:           Rayleigh quotient and compute residual norm */
    151:       EPSGetEigenpair(eps,i,NULL,NULL,x,NULL);
    152:       RayleighQuotient(A,x,&lambda);
    153:       ComputeResidualNorm(A,lambda,x,&error[i]);
    154: #if defined(PETSC_USE_COMPLEX)
    155:       evals[i] = PetscRealPart(lambda);
    156: #else
    157:       evals[i] = lambda;
    158: #endif
    159:     }
    160:     PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    161:     if (!terse) {
    162:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,
    163:            "           k              ||Ax-kx||\n"
    164:            "   ----------------- ------------------\n"));
    165:       for (i=0;i<nconv;i++) PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12.2g\n",(double)evals[i],(double)error[i]);
    166:     } else {
    167:       errok = PETSC_TRUE;
    168:       for (i=0;i<nconv;i++) errok = (errok && error[i]<5.0*tol)? PETSC_TRUE: PETSC_FALSE;
    169:       if (!errok) PetscPrintf(PETSC_COMM_WORLD," Problem: some of the first %" PetscInt_FMT " relative errors are higher than the tolerance\n\n",nconv);
    170:       else {
    171:         PetscPrintf(PETSC_COMM_WORLD," nconv=%" PetscInt_FMT " eigenvalues computed up to the required tolerance:",nconv);
    172:         for (i=0;i<nconv;i++) PetscPrintf(PETSC_COMM_WORLD," %.5f",(double)evals[i]);
    173:       }
    174:     }
    175:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    176:     PetscFree2(evals,error);
    177:   }

    179:   EPSDestroy(&eps);
    180:   MatDestroy(&A);
    181:   MatDestroy(&M);
    182:   VecDestroy(&ctx->w);
    183:   VecDestroy(&x);
    184:   PetscFree(ctx);
    185:   SlepcFinalize();
    186:   return 0;
    187: }

    189: /*
    190:     Matrix-vector product subroutine for the spectrum folding.
    191:        y <-- (A-t*I)^2*x
    192:  */
    193: PetscErrorCode MatMult_Fold(Mat M,Vec x,Vec y)
    194: {
    195:   CTX_FOLD       *ctx;
    196:   PetscScalar    sigma;

    199:   MatShellGetContext(M,&ctx);
    200:   sigma = -ctx->target;
    201:   MatMult(ctx->A,x,ctx->w);
    202:   VecAXPY(ctx->w,sigma,x);
    203:   MatMult(ctx->A,ctx->w,y);
    204:   VecAXPY(y,sigma,ctx->w);
    205:   PetscFunctionReturn(0);
    206: }

    208: /*
    209:     Computes the Rayleigh quotient of a vector x
    210:        r <-- x^T*A*x       (assumes x has unit norm)
    211:  */
    212: PetscErrorCode RayleighQuotient(Mat A,Vec x,PetscScalar *r)
    213: {
    214:   Vec            Ax;

    217:   VecDuplicate(x,&Ax);
    218:   MatMult(A,x,Ax);
    219:   VecDot(Ax,x,r);
    220:   VecDestroy(&Ax);
    221:   PetscFunctionReturn(0);
    222: }

    224: /*
    225:     Computes the residual norm of an approximate eigenvector x, |A*x-lambda*x|
    226:  */
    227: PetscErrorCode ComputeResidualNorm(Mat A,PetscScalar lambda,Vec x,PetscReal *r)
    228: {
    229:   Vec            Ax;

    232:   VecDuplicate(x,&Ax);
    233:   MatMult(A,x,Ax);
    234:   VecAXPY(Ax,-lambda,x);
    235:   VecNorm(Ax,NORM_2,r);
    236:   VecDestroy(&Ax);
    237:   PetscFunctionReturn(0);
    238: }

    240: /*TEST

    242:    testset:
    243:       args: -n 15 -eps_nev 1 -eps_ncv 12 -eps_max_it 1000 -eps_tol 1e-5 -terse
    244:       filter: grep -v Solution
    245:       test:
    246:          suffix: 1
    247:       test:
    248:          suffix: 1_lobpcg
    249:          args: -eps_type lobpcg
    250:          requires: !single
    251:       test:
    252:          suffix: 1_gd
    253:          args: -eps_type gd
    254:          requires: !single

    256: TEST*/