Date: 2024-12-02T08:57:04+00:00

Actual source code: test22.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[] = "Illustrates how to obtain invariant subspaces. "
     12:   "Based on ex9.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
     15:   "  -L <L>, where <L> = bifurcation parameter.\n"
     16:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
     17:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

     19: #include <slepceps.h>

     21: /*
     22:    This example computes the eigenvalues with largest real part of the
     23:    following matrix

     25:         A = [ tau1*T+(beta-1)*I     alpha^2*I
     26:                   -beta*I        tau2*T-alpha^2*I ],

     28:    where

     30:         T = tridiag{1,-2,1}
     31:         h = 1/(n+1)
     32:         tau1 = delta1/(h*L)^2
     33:         tau2 = delta2/(h*L)^2
     34:  */

     36: /* Matrix operations */
     37: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
     38: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);

     40: typedef struct {
     41:   Mat         T;
     42:   Vec         x1,x2,y1,y2;
     43:   PetscScalar alpha,beta,tau1,tau2,sigma;
     44: } CTX_BRUSSEL;

     46: int main(int argc,char **argv)
     47: {
     48:   EPS            eps;
     49:   Mat            A;
     50:   Vec            *Q,v;
     51:   PetscScalar    delta1,delta2,L,h,kr,ki;
     52:   PetscReal      errest,tol,re,im,lev;
     53:   PetscInt       N=30,n,i,j,Istart,Iend,nev,nconv;
     54:   CTX_BRUSSEL    *ctx;
     55:   PetscBool      errok,trueres;

     57:   PetscFunctionBeginUser;
     58:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     59:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
     60:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));

     62:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     63:         Generate the matrix
     64:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     66:   PetscCall(PetscNew(&ctx));
     67:   ctx->alpha = 2.0;
     68:   ctx->beta  = 5.45;
     69:   delta1     = 0.008;
     70:   delta2     = 0.004;
     71:   L          = 0.51302;

     73:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
     74:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL));
     75:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL));
     76:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
     77:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));

     79:   /* Create matrix T */
     80:   PetscCall(MatCreate(PETSC_COMM_WORLD,&ctx->T));
     81:   PetscCall(MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N));
     82:   PetscCall(MatSetFromOptions(ctx->T));
     83:   PetscCall(MatGetOwnershipRange(ctx->T,&Istart,&Iend));
     84:   for (i=Istart;i<Iend;i++) {
     85:     if (i>0) PetscCall(MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES));
     86:     if (i<N-1) PetscCall(MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES));
     87:     PetscCall(MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES));
     88:   }
     89:   PetscCall(MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY));
     90:   PetscCall(MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY));
     91:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));

     93:   /* Fill the remaining information in the shell matrix context
     94:      and create auxiliary vectors */
     95:   h = 1.0 / (PetscReal)(N+1);
     96:   ctx->tau1 = delta1 / ((h*L)*(h*L));
     97:   ctx->tau2 = delta2 / ((h*L)*(h*L));
     98:   ctx->sigma = 0.0;
     99:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1));
    100:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2));
    101:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1));
    102:   PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2));

    104:   /* Create the shell matrix */
    105:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A));
    106:   PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel));
    107:   PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel));

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:                 Create the eigensolver and solve the problem
    111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    113:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
    114:   PetscCall(EPSSetOperators(eps,A,NULL));
    115:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
    116:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
    117:   PetscCall(EPSSetTrueResidual(eps,PETSC_FALSE));
    118:   PetscCall(EPSSetFromOptions(eps));
    119:   PetscCall(EPSSolve(eps));

    121:   PetscCall(EPSGetTrueResidual(eps,&trueres));
    122:   /*if (trueres) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computing true residuals explicitly\n\n"));*/

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                     Display solution and clean up
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    128:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    129:   PetscCall(EPSGetTolerances(eps,&tol,NULL));
    130:   PetscCall(EPSGetConverged(eps,&nconv));
    131:   if (nconv<nev) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Problem: less than %" PetscInt_FMT " eigenvalues converged\n\n",nev));
    132:   else {
    133:     /* Check that all converged eigenpairs satisfy the requested tolerance
    134:        (in this example we use the solver's error estimate instead of computing
    135:        the residual norm explicitly) */
    136:     errok = PETSC_TRUE;
    137:     for (i=0;i<nev;i++) {
    138:       PetscCall(EPSGetErrorEstimate(eps,i,&errest));
    139:       PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL));
    140:       errok = (errok && errest<5.0*SlepcAbsEigenvalue(kr,ki)*tol)? PETSC_TRUE: PETSC_FALSE;
    141:     }
    142:     if (!errok) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Problem: some of the first %" PetscInt_FMT " relative errors are higher than the tolerance\n\n",nev));
    143:     else {
    144:       PetscCall(PetscPrintf(PETSC_COMM_WORLD," All requested eigenvalues computed up to the required tolerance:"));
    145:       for (i=0;i<=(nev-1)/8;i++) {
    146:         PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n     "));
    147:         for (j=0;j<PetscMin(8,nev-8*i);j++) {
    148:           PetscCall(EPSGetEigenpair(eps,8*i+j,&kr,&ki,NULL,NULL));
    149: #if defined(PETSC_USE_COMPLEX)
    150:           re = PetscRealPart(kr);
    151:           im = PetscImaginaryPart(kr);
    152: #else
    153:           re = kr;
    154:           im = ki;
    155: #endif
    156:           if (im!=0.0 && PetscAbs(re)/PetscAbs(im)<PETSC_SMALL) re = 0.0;
    157:           if (re!=0.0 && PetscAbs(im)/PetscAbs(re)<PETSC_SMALL) im = 0.0;
    158:           if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%.5f%+.5fi",(double)re,(double)im));
    159:           else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%.5f",(double)re));
    160:           if (8*i+j+1<nev) PetscCall(PetscPrintf(PETSC_COMM_WORLD,", "));
    161:         }
    162:       }
    163:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n\n"));
    164:     }
    165:   }

    167:   /* Get an orthogonal basis of the invariant subspace and check it is indeed
    168:      orthogonal (note that eigenvectors are not orthogonal in this case) */
    169:   if (nconv>1) {
    170:     PetscCall(MatCreateVecs(A,&v,NULL));
    171:     PetscCall(VecDuplicateVecs(v,nconv,&Q));
    172:     PetscCall(EPSGetInvariantSubspace(eps,Q));
    173:     PetscCall(VecCheckOrthonormality(Q,nconv,NULL,nconv,NULL,NULL,&lev));
    174:     if (lev<10*tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n"));
    175:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)lev));
    176:     PetscCall(VecDestroyVecs(nconv,&Q));
    177:     PetscCall(VecDestroy(&v));
    178:   }

    180:   PetscCall(EPSDestroy(&eps));
    181:   PetscCall(MatDestroy(&A));
    182:   PetscCall(MatDestroy(&ctx->T));
    183:   PetscCall(VecDestroy(&ctx->x1));
    184:   PetscCall(VecDestroy(&ctx->x2));
    185:   PetscCall(VecDestroy(&ctx->y1));
    186:   PetscCall(VecDestroy(&ctx->y2));
    187:   PetscCall(PetscFree(ctx));
    188:   PetscCall(SlepcFinalize());
    189:   return 0;
    190: }

    192: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
    193: {
    194:   PetscInt          n;
    195:   const PetscScalar *px;
    196:   PetscScalar       *py;
    197:   CTX_BRUSSEL       *ctx;

    199:   PetscFunctionBeginUser;
    200:   PetscCall(MatShellGetContext(A,&ctx));
    201:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
    202:   PetscCall(VecGetArrayRead(x,&px));
    203:   PetscCall(VecGetArray(y,&py));
    204:   PetscCall(VecPlaceArray(ctx->x1,px));
    205:   PetscCall(VecPlaceArray(ctx->x2,px+n));
    206:   PetscCall(VecPlaceArray(ctx->y1,py));
    207:   PetscCall(VecPlaceArray(ctx->y2,py+n));

    209:   PetscCall(MatMult(ctx->T,ctx->x1,ctx->y1));
    210:   PetscCall(VecScale(ctx->y1,ctx->tau1));
    211:   PetscCall(VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1));
    212:   PetscCall(VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2));

    214:   PetscCall(MatMult(ctx->T,ctx->x2,ctx->y2));
    215:   PetscCall(VecScale(ctx->y2,ctx->tau2));
    216:   PetscCall(VecAXPY(ctx->y2,-ctx->beta,ctx->x1));
    217:   PetscCall(VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2));

    219:   PetscCall(VecRestoreArrayRead(x,&px));
    220:   PetscCall(VecRestoreArray(y,&py));
    221:   PetscCall(VecResetArray(ctx->x1));
    222:   PetscCall(VecResetArray(ctx->x2));
    223:   PetscCall(VecResetArray(ctx->y1));
    224:   PetscCall(VecResetArray(ctx->y2));
    225:   PetscFunctionReturn(PETSC_SUCCESS);
    226: }

    228: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
    229: {
    230:   Vec            d1,d2;
    231:   PetscInt       n;
    232:   PetscScalar    *pd;
    233:   MPI_Comm       comm;
    234:   CTX_BRUSSEL    *ctx;

    236:   PetscFunctionBeginUser;
    237:   PetscCall(MatShellGetContext(A,&ctx));
    238:   PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
    239:   PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
    240:   PetscCall(VecGetArray(diag,&pd));
    241:   PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1));
    242:   PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2));

    244:   PetscCall(VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma));
    245:   PetscCall(VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma));

    247:   PetscCall(VecDestroy(&d1));
    248:   PetscCall(VecDestroy(&d2));
    249:   PetscCall(VecRestoreArray(diag,&pd));
    250:   PetscFunctionReturn(PETSC_SUCCESS);
    251: }

    253: /*TEST

    255:    test:
    256:       suffix: 1
    257:       args: -eps_nev 4 -eps_true_residual {{0 1}}
    258:       requires: !single

    260:    test:
    261:       suffix: 2
    262:       args: -eps_nev 4 -eps_true_residual -eps_balance oneside -eps_tol 1e-7
    263:       requires: !single

    265:    test:
    266:       suffix: 3
    267:       args: -n 50 -eps_nev 4 -eps_ncv 16 -eps_type subspace -eps_largest_magnitude -bv_orthog_block {{gs tsqr chol tsqrchol svqb}}
    268:       requires: !single

    270: TEST*/