Date: 2024-12-02T08:57:10+00:00

Actual source code: ex24.c
slepc-3.22.2 2024-12-02
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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:   PetscFunctionBeginUser;
     51:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

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

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:      Compute the 5-point stencil Laplacian
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

    104:   PetscCall(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:     PetscCall(MatGetRowSum(A,x));
    110:     PetscCall(VecScale(x,-1.0));
    111:     PetscCall(VecShift(x,20.0));
    112:     PetscCall(MatCreate(PETSC_COMM_WORLD,&P));
    113:     PetscCall(MatSetSizes(P,PETSC_DECIDE,PETSC_DECIDE,N,N));
    114:     PetscCall(MatSetFromOptions(P));
    115:     PetscCall(MatDiagonalSet(P,x,INSERT_VALUES));
    116:     /*
    117:        Set diagonal preconditioner
    118:     */
    119:     PetscCall(EPSGetST(eps,&st));
    120:     PetscCall(STSetType(st,STPRECOND));
    121:     PetscCall(STSetPreconditionerMat(st,P));
    122:     PetscCall(MatDestroy(&P));
    123:     PetscCall(STGetKSP(st,&ksp));
    124:     PetscCall(KSPGetPC(ksp,&pc));
    125:     PetscCall(PCSetType(pc,PCJACOBI));
    126:     PetscCall(STPrecondGetKSPHasMat(st,&hasmat));
    127:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Preconditioned solver, hasmat=%s\n",hasmat?"true":"false"));
    128:   }

    130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    131:                       Solve the eigensystem
    132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    140:                     Display solution and clean up
    141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    188: /*
    189:     Matrix-vector product subroutine for the spectrum folding.
    190:        y <-- (A-t*I)^2*x
    191:  */
    192: PetscErrorCode MatMult_Fold(Mat M,Vec x,Vec y)
    193: {
    194:   CTX_FOLD       *ctx;
    195:   PetscScalar    sigma;

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

    207: /*
    208:     Computes the Rayleigh quotient of a vector x
    209:        r <-- x^T*A*x       (assumes x has unit norm)
    210:  */
    211: PetscErrorCode RayleighQuotient(Mat A,Vec x,PetscScalar *r)
    212: {
    213:   Vec            Ax;

    215:   PetscFunctionBeginUser;
    216:   PetscCall(VecDuplicate(x,&Ax));
    217:   PetscCall(MatMult(A,x,Ax));
    218:   PetscCall(VecDot(Ax,x,r));
    219:   PetscCall(VecDestroy(&Ax));
    220:   PetscFunctionReturn(PETSC_SUCCESS);
    221: }

    223: /*
    224:     Computes the residual norm of an approximate eigenvector x, |A*x-lambda*x|
    225:  */
    226: PetscErrorCode ComputeResidualNorm(Mat A,PetscScalar lambda,Vec x,PetscReal *r)
    227: {
    228:   Vec            Ax;

    230:   PetscFunctionBeginUser;
    231:   PetscCall(VecDuplicate(x,&Ax));
    232:   PetscCall(MatMult(A,x,Ax));
    233:   PetscCall(VecAXPY(Ax,-lambda,x));
    234:   PetscCall(VecNorm(Ax,NORM_2,r));
    235:   PetscCall(VecDestroy(&Ax));
    236:   PetscFunctionReturn(PETSC_SUCCESS);
    237: }

    239: /*TEST

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

    255: TEST*/