Date: 2023-01-26T12:18:55+00:00

Actual source code: ex9.c
slepc-3.18.2 2023-01-26
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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[] = "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: */

     35: /*
     36:    Matrix operations
     37: */
     38: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
     39: PetscErrorCode MatMultTranspose_Brussel(Mat,Vec,Vec);
     40: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);

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

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

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

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

     65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66:         Generate the matrix
     67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     69:   /*
     70:      Create shell matrix context and set default parameters
     71:   */
     72:   PetscNew(&ctx);
     73:   ctx->alpha = 2.0;
     74:   ctx->beta  = 5.45;
     75:   delta1     = 0.008;
     76:   delta2     = 0.004;
     77:   L          = 0.51302;

     79:   /*
     80:      Look the command line for user-provided parameters
     81:   */
     82:   PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
     83:   PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL);
     84:   PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL);
     85:   PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
     86:   PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL);

     88:   /*
     89:      Create matrix T
     90:   */
     91:   MatCreate(PETSC_COMM_WORLD,&ctx->T);
     92:   MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
     93:   MatSetFromOptions(ctx->T);
     94:   MatSetUp(ctx->T);

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

    106:   /*
    107:      Fill the remaining information in the shell matrix context
    108:      and create auxiliary vectors
    109:   */
    110:   h = 1.0 / (PetscReal)(N+1);
    111:   ctx->tau1 = delta1 / ((h*L)*(h*L));
    112:   ctx->tau2 = delta2 / ((h*L)*(h*L));
    113:   ctx->sigma = 0.0;
    114:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1);
    115:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2);
    116:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1);
    117:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2);

    119:   /*
    120:      Create the shell matrix
    121:   */
    122:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
    123:   MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel);
    124:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Brussel);
    125:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel);

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:                 Create the eigensolver and set various options
    129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    131:   /*
    132:      Create eigensolver context
    133:   */
    134:   EPSCreate(PETSC_COMM_WORLD,&eps);

    136:   /*
    137:      Set operators. In this case, it is a standard eigenvalue problem
    138:   */
    139:   EPSSetOperators(eps,A,NULL);
    140:   EPSSetProblemType(eps,EPS_NHEP);

    142:   /*
    143:      Ask for the rightmost eigenvalues
    144:   */
    145:   EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);

    147:   /*
    148:      Set other solver options at runtime
    149:   */
    150:   EPSSetFromOptions(eps);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:                       Solve the eigensystem
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   EPSSolve(eps);

    158:   /*
    159:      Optional: Get some information from the solver and display it
    160:   */
    161:   EPSGetType(eps,&type);
    162:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    163:   EPSGetDimensions(eps,&nev,NULL,NULL);
    164:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:                     Display solution and clean up
    168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

    228: PetscErrorCode MatMultTranspose_Brussel(Mat A,Vec x,Vec y)
    229: {
    230:   PetscInt          n;
    231:   const PetscScalar *px;
    232:   PetscScalar       *py;
    233:   CTX_BRUSSEL       *ctx;

    236:   MatShellGetContext(A,&ctx);
    237:   MatGetLocalSize(ctx->T,&n,NULL);
    238:   VecGetArrayRead(x,&px);
    239:   VecGetArray(y,&py);
    240:   VecPlaceArray(ctx->x1,px);
    241:   VecPlaceArray(ctx->x2,px+n);
    242:   VecPlaceArray(ctx->y1,py);
    243:   VecPlaceArray(ctx->y2,py+n);

    245:   MatMultTranspose(ctx->T,ctx->x1,ctx->y1);
    246:   VecScale(ctx->y1,ctx->tau1);
    247:   VecAXPY(ctx->y1,ctx->beta-1.0+ctx->sigma,ctx->x1);
    248:   VecAXPY(ctx->y1,-ctx->beta,ctx->x2);

    250:   MatMultTranspose(ctx->T,ctx->x2,ctx->y2);
    251:   VecScale(ctx->y2,ctx->tau2);
    252:   VecAXPY(ctx->y2,ctx->alpha*ctx->alpha,ctx->x1);
    253:   VecAXPY(ctx->y2,-ctx->alpha*ctx->alpha+ctx->sigma,ctx->x2);

    255:   VecRestoreArrayRead(x,&px);
    256:   VecRestoreArray(y,&py);
    257:   VecResetArray(ctx->x1);
    258:   VecResetArray(ctx->x2);
    259:   VecResetArray(ctx->y1);
    260:   VecResetArray(ctx->y2);
    261:   return 0;
    262: }

    264: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
    265: {
    266:   Vec            d1,d2;
    267:   PetscInt       n;
    268:   PetscScalar    *pd;
    269:   MPI_Comm       comm;
    270:   CTX_BRUSSEL    *ctx;

    273:   MatShellGetContext(A,&ctx);
    274:   PetscObjectGetComm((PetscObject)A,&comm);
    275:   MatGetLocalSize(ctx->T,&n,NULL);
    276:   VecGetArray(diag,&pd);
    277:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1);
    278:   VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2);

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

    283:   VecDestroy(&d1);
    284:   VecDestroy(&d2);
    285:   VecRestoreArray(diag,&pd);
    286:   return 0;
    287: }

    289: /*TEST

    291:    test:
    292:       suffix: 1
    293:       args: -n 50 -eps_nev 4 -eps_two_sided {{0 1}} -eps_type {{krylovschur lapack}} -terse
    294:       requires: !single
    295:       filter: grep -v method

    297:    test:
    298:       suffix: 2
    299:       args: -eps_nev 8 -eps_max_it 300 -eps_target -28 -rg_type interval -rg_interval_endpoints -40,-20,-.1,.1 -terse
    300:       requires: !single

    302:    test:
    303:       suffix: 3
    304:       args: -n 50 -eps_nev 4 -eps_balance twoside -terse
    305:       requires: double
    306:       filter: grep -v method
    307:       output_file: output/ex9_1.out

    309:    test:
    310:       suffix: 4
    311:       args: -eps_smallest_imaginary -eps_ncv 24 -terse
    312:       requires: !complex !single

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

    319:    test:
    320:       suffix: 5
    321:       args: -eps_nev 4 -eps_target_real -eps_target -3 -terse
    322:       requires: !single

    324:    test:
    325:       suffix: 6
    326:       args: -eps_nev 2 -eps_target_imaginary -eps_target 3i -terse
    327:       requires: complex !single

    329:    test:
    330:       suffix: 7
    331:       args: -n 40 -eps_nev 1 -eps_type arnoldi -eps_smallest_real -eps_refined -eps_ncv 40 -eps_max_it 300 -terse
    332:       requires: double

    334:    test:
    335:       suffix: 8
    336:       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
    337:       requires: !single
    338:       filter: sed -e "s/[+-]0\.0*i//g"
    339:       timeoutfactor: 2

    341:    test:
    342:       suffix: 9
    343:       args: -eps_largest_imaginary -eps_ncv 24 -terse
    344:       requires: !single

    346: TEST*/