Date: 2020-01-13T12:00:45+00:00

Actual source code: ex9.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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[] = "Solves a problem associated to the Brusselator wave model in chemical reactions, illustrating the use of shell matrices.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
     14:   "  -L <L>, where <L> = bifurcation parameter.\n"
     15:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
     16:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

     18: #include <slepceps.h>

     20: /*
     21:    This example computes the eigenvalues with largest real part of the
     22:    following matrix

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

     27:    where

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

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

     43: typedef struct {
     44:   Mat         T;
     45:   Vec         x1,x2,y1,y2;
     46:   PetscScalar alpha,beta,tau1,tau2,sigma;
     47: } CTX_BRUSSEL;

     49: int main(int argc,char **argv)
     50: {
     51:   Mat            A;               /* eigenvalue problem matrix */
     52:   EPS            eps;             /* eigenproblem solver context */
     53:   EPSType        type;
     54:   PetscScalar    delta1,delta2,L,h;
     55:   PetscInt       N=30,n,i,Istart,Iend,nev;
     56:   CTX_BRUSSEL    *ctx;
     57:   PetscBool      terse;
     58:   PetscViewer    viewer;

     61:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     63:   PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
     64:   PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%D\n\n",N);

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:         Generate the matrix
     68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     70:   /*
     71:      Create shell matrix context and set default parameters
     72:   */
     73:   PetscNew(&ctx);
     74:   ctx->alpha = 2.0;
     75:   ctx->beta  = 5.45;
     76:   delta1     = 0.008;
     77:   delta2     = 0.004;
     78:   L          = 0.51302;

     80:   /*
     81:      Look the command line for user-provided parameters
     82:   */
     83:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
     84:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
     85:   PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
     86:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
     87:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

     89:   /*
     90:      Create matrix T
     91:   */
     92:   MatCreate(PETSC_COMM_WORLD,&ctx->T);
     93:   MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
     94:   MatSetFromOptions(ctx->T);
     95:   MatSetUp(ctx->T);

     97:   MatGetOwnershipRange(ctx->T,&Istart,&Iend);
     98:   for (i=Istart;i<Iend;i++) {
     99:     if (i>0) { MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES); }
    100:     if (i<N-1) { MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES); }
    101:     MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES);
    102:   }
    103:   MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
    104:   MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
    105:   MatGetLocalSize(ctx->T,&n,NULL);

    107:   /*
    108:      Fill the remaining information in the shell matrix context
    109:      and create auxiliary vectors
    110:   */
    111:   h = 1.0 / (PetscReal)(N+1);
    112:   ctx->tau1 = delta1 / ((h*L)*(h*L));
    113:   ctx->tau2 = delta2 / ((h*L)*(h*L));
    114:   ctx->sigma = 0.0;
    115:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1);
    116:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2);
    117:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1);
    118:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2);

    120:   /*
    121:      Create the shell matrix
    122:   */
    123:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
    124:   MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel);
    125:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Brussel);
    126:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel);

    128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    129:                 Create the eigensolver and set various options
    130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    132:   /*
    133:      Create eigensolver context
    134:   */
    135:   EPSCreate(PETSC_COMM_WORLD,&eps);

    137:   /*
    138:      Set operators. In this case, it is a standard eigenvalue problem
    139:   */
    140:   EPSSetOperators(eps,A,NULL);
    141:   EPSSetProblemType(eps,EPS_NHEP);

    143:   /*
    144:      Ask for the rightmost eigenvalues
    145:   */
    146:   EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);

    148:   /*
    149:      Set other solver options at runtime
    150:   */
    151:   EPSSetFromOptions(eps);

    153:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    154:                       Solve the eigensystem
    155:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    157:   EPSSolve(eps);

    159:   /*
    160:      Optional: Get some information from the solver and display it
    161:   */
    162:   EPSGetType(eps,&type);
    163:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    164:   EPSGetDimensions(eps,&nev,NULL,NULL);
    165:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    168:                     Display solution and clean up
    169:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    171:   /* show detailed info unless -terse option is given by user */
    172:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    173:   if (terse) {
    174:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    175:   } else {
    176:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    177:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    178:     EPSReasonView(eps,viewer);
    179:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
    180:     PetscViewerPopFormat(viewer);
    181:   }
    182:   EPSDestroy(&eps);
    183:   MatDestroy(&A);
    184:   MatDestroy(&ctx->T);
    185:   VecDestroy(&ctx->x1);
    186:   VecDestroy(&ctx->x2);
    187:   VecDestroy(&ctx->y1);
    188:   VecDestroy(&ctx->y2);
    189:   PetscFree(ctx);
    190:   SlepcFinalize();
    191:   return ierr;
    192: }

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

    203:   MatShellGetContext(A,(void**)&ctx);
    204:   MatGetLocalSize(ctx->T,&n,NULL);
    205:   VecGetArrayRead(x,&px);
    206:   VecGetArray(y,&py);
    207:   VecPlaceArray(ctx->x1,px);
    208:   VecPlaceArray(ctx->x2,px+n);
    209:   VecPlaceArray(ctx->y1,py);
    210:   VecPlaceArray(ctx->y2,py+n);

    212:   MatMult(ctx->T,ctx->x1,ctx->y1);
    213:   VecScale(ctx->y1,ctx->tau1);
    214:   VecAXPY(ctx->y1,ctx->beta-1.0+ctx->sigma,ctx->x1);
    215:   VecAXPY(ctx->y1,ctx->alpha*ctx->alpha,ctx->x2);

    217:   MatMult(ctx->T,ctx->x2,ctx->y2);
    218:   VecScale(ctx->y2,ctx->tau2);
    219:   VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
    220:   VecAXPY(ctx->y2,-ctx->alpha*ctx->alpha+ctx->sigma,ctx->x2);

    222:   VecRestoreArrayRead(x,&px);
    223:   VecRestoreArray(y,&py);
    224:   VecResetArray(ctx->x1);
    225:   VecResetArray(ctx->x2);
    226:   VecResetArray(ctx->y1);
    227:   VecResetArray(ctx->y2);
    228:   return(0);
    229: }

    231: PetscErrorCode MatMultTranspose_Brussel(Mat A,Vec x,Vec y)
    232: {
    233:   PetscInt          n;
    234:   const PetscScalar *px;
    235:   PetscScalar       *py;
    236:   CTX_BRUSSEL       *ctx;
    237:   PetscErrorCode    ierr;

    240:   MatShellGetContext(A,(void**)&ctx);
    241:   MatGetLocalSize(ctx->T,&n,NULL);
    242:   VecGetArrayRead(x,&px);
    243:   VecGetArray(y,&py);
    244:   VecPlaceArray(ctx->x1,px);
    245:   VecPlaceArray(ctx->x2,px+n);
    246:   VecPlaceArray(ctx->y1,py);
    247:   VecPlaceArray(ctx->y2,py+n);

    249:   MatMultTranspose(ctx->T,ctx->x1,ctx->y1);
    250:   VecScale(ctx->y1,ctx->tau1);
    251:   VecAXPY(ctx->y1,ctx->beta-1.0+ctx->sigma,ctx->x1);
    252:   VecAXPY(ctx->y1,-ctx->beta,ctx->x2);

    254:   MatMultTranspose(ctx->T,ctx->x2,ctx->y2);
    255:   VecScale(ctx->y2,ctx->tau2);
    256:   VecAXPY(ctx->y2,ctx->alpha*ctx->alpha,ctx->x1);
    257:   VecAXPY(ctx->y2,-ctx->alpha*ctx->alpha+ctx->sigma,ctx->x2);

    259:   VecRestoreArrayRead(x,&px);
    260:   VecRestoreArray(y,&py);
    261:   VecResetArray(ctx->x1);
    262:   VecResetArray(ctx->x2);
    263:   VecResetArray(ctx->y1);
    264:   VecResetArray(ctx->y2);
    265:   return(0);
    266: }

    268: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
    269: {
    270:   Vec            d1,d2;
    271:   PetscInt       n;
    272:   PetscScalar    *pd;
    273:   MPI_Comm       comm;
    274:   CTX_BRUSSEL    *ctx;

    278:   MatShellGetContext(A,(void**)&ctx);
    279:   PetscObjectGetComm((PetscObject)A,&comm);
    280:   MatGetLocalSize(ctx->T,&n,NULL);
    281:   VecGetArray(diag,&pd);
    282:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
    283:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);

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

    288:   VecDestroy(&d1);
    289:   VecDestroy(&d2);
    290:   VecRestoreArray(diag,&pd);
    291:   return(0);
    292: }

    294: /*TEST

    296:    test:
    297:       suffix: 1
    298:       args: -n 50 -eps_nev 4 -eps_two_sided {{0 1}} -eps_type {{krylovschur lapack}} -terse
    299:       requires: !single
    300:       filter: grep -v method

    302:    test:
    303:       suffix: 2
    304:       args: -eps_nev 8 -eps_max_it 300 -eps_target -28 -rg_type interval -rg_interval_endpoints -40,-20,-.1,.1 -terse
    305:       requires: !single

    307:    test:
    308:       suffix: 3
    309:       args: -n 50 -eps_nev 4 -eps_balance twoside -terse
    310:       requires: double
    311:       filter: grep -v method
    312:       output_file: output/ex9_1.out

    314:    test:
    315:       suffix: 4
    316:       args: -eps_smallest_imaginary -eps_ncv 24 -terse
    317:       requires: !complex !single

    319:    test:
    320:       suffix: 4_complex
    321:       args: -eps_smallest_imaginary -eps_ncv 24 -terse
    322:       requires: complex !single

    324:    test:
    325:       suffix: 5
    326:       args: -eps_nev 4 -eps_target_real -eps_target -3 -terse
    327:       requires: !single

    329:    test:
    330:       suffix: 6
    331:       args: -eps_nev 2 -eps_target_imaginary -eps_target 3i -terse
    332:       requires: complex !single

    334:    test:
    335:       suffix: 7
    336:       args: -n 40 -eps_nev 1 -eps_type arnoldi -eps_smallest_real -eps_refined -eps_ncv 40 -eps_max_it 200 -terse
    337:       requires: double

    339:    test:
    340:       suffix: 8
    341:       args: -eps_nev 2 -eps_target -30 -eps_type jd -st_matmode shell -eps_jd_fix 0.0001 -eps_jd_const_correction_tol 0 -terse
    342:       requires: double
    343:       filter: sed -e "s/[+-]0.0*i//"

    345:    test:
    346:       suffix: 9
    347:       args: -eps_largest_imaginary -eps_ncv 24 -terse
    348:       requires: !single

    350: TEST*/