Date: 2013-09-02T10:05:40+00:00

Actual source code: ex9.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Solves a problem associated to the Brusselator wave model in chemical reactions, illustrating the use of shell matrices.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
     25:   "  -L <L>, where <L> = bifurcation parameter.\n"
     26:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
     27:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

     29: #include <slepceps.h>

     31: /*
     32:    This example computes the eigenvalues with largest real part of the
     33:    following matrix

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

     38:    where

     40:         T = tridiag{1,-2,1}
     41:         h = 1/(n+1)
     42:         tau1 = delta1/(h*L)^2
     43:         tau2 = delta2/(h*L)^2
     44:  */

     47: /*
     48:    Matrix operations
     49: */
     50: PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
     51: PetscErrorCode MatShift_Brussel(PetscScalar*,Mat);
     52: PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);

     54: typedef struct {
     55:   Mat         T;
     56:   Vec         x1,x2,y1,y2;
     57:   PetscScalar alpha,beta,tau1,tau2,sigma;
     58: } CTX_BRUSSEL;

     62: int main(int argc,char **argv)
     63: {
     64:   Mat            A;               /* eigenvalue problem matrix */
     65:   EPS            eps;             /* eigenproblem solver context */
     66:   EPSType        type;
     67:   PetscScalar    delta1,delta2,L,h,value[3];
     68:   PetscInt       N=30,n,i,col[3],Istart,Iend,nev;
     69:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
     70:   CTX_BRUSSEL    *ctx;

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

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

     78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     79:         Generate the matrix
     80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     82:   /*
     83:      Create shell matrix context and set default parameters
     84:   */
     85:   PetscNew(CTX_BRUSSEL,&ctx);
     86:   ctx->alpha = 2.0;
     87:   ctx->beta  = 5.45;
     88:   delta1     = 0.008;
     89:   delta2     = 0.004;
     90:   L          = 0.51302;

     92:   /*
     93:      Look the command line for user-provided parameters
     94:   */
     95:   PetscOptionsGetScalar(NULL,"-L",&L,NULL);
     96:   PetscOptionsGetScalar(NULL,"-alpha",&ctx->alpha,NULL);
     97:   PetscOptionsGetScalar(NULL,"-beta",&ctx->beta,NULL);
     98:   PetscOptionsGetScalar(NULL,"-delta1",&delta1,NULL);
     99:   PetscOptionsGetScalar(NULL,"-delta2",&delta2,NULL);

    101:   /*
    102:      Create matrix T
    103:   */
    104:   MatCreate(PETSC_COMM_WORLD,&ctx->T);
    105:   MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N);
    106:   MatSetFromOptions(ctx->T);
    107:   MatSetUp(ctx->T);

    109:   MatGetOwnershipRange(ctx->T,&Istart,&Iend);
    110:   if (Istart==0) FirstBlock=PETSC_TRUE;
    111:   if (Iend==N) LastBlock=PETSC_TRUE;
    112:   value[0]=1.0; value[1]=-2.0; value[2]=1.0;
    113:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
    114:     col[0]=i-1; col[1]=i; col[2]=i+1;
    115:     MatSetValues(ctx->T,1,&i,3,col,value,INSERT_VALUES);
    116:   }
    117:   if (LastBlock) {
    118:     i=N-1; col[0]=N-2; col[1]=N-1;
    119:     MatSetValues(ctx->T,1,&i,2,col,value,INSERT_VALUES);
    120:   }
    121:   if (FirstBlock) {
    122:     i=0; col[0]=0; col[1]=1; value[0]=-2.0; value[1]=1.0;
    123:     MatSetValues(ctx->T,1,&i,2,col,value,INSERT_VALUES);
    124:   }

    126:   MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY);
    127:   MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY);
    128:   MatGetLocalSize(ctx->T,&n,NULL);

    130:   /*
    131:      Fill the remaining information in the shell matrix context
    132:      and create auxiliary vectors
    133:   */
    134:   h = 1.0 / (PetscReal)(N+1);
    135:   ctx->tau1 = delta1 / ((h*L)*(h*L));
    136:   ctx->tau2 = delta2 / ((h*L)*(h*L));
    137:   ctx->sigma = 0.0;
    138:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1);
    139:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2);
    140:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1);
    141:   VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2);

    143:   /*
    144:      Create the shell matrix
    145:   */
    146:   MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A);
    147:   MatShellSetOperation(A,MATOP_MULT,(void(*)())MatMult_Brussel);
    148:   MatShellSetOperation(A,MATOP_SHIFT,(void(*)())MatShift_Brussel);
    149:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)())MatGetDiagonal_Brussel);

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:                 Create the eigensolver and set various options
    153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    155:   /*
    156:      Create eigensolver context
    157:   */
    158:   EPSCreate(PETSC_COMM_WORLD,&eps);

    160:   /*
    161:      Set operators. In this case, it is a standard eigenvalue problem
    162:   */
    163:   EPSSetOperators(eps,A,NULL);
    164:   EPSSetProblemType(eps,EPS_NHEP);

    166:   /*
    167:      Ask for the rightmost eigenvalues
    168:   */
    169:   EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);

    171:   /*
    172:      Set other solver options at runtime
    173:   */
    174:   EPSSetFromOptions(eps);

    176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    177:                       Solve the eigensystem
    178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    180:   EPSSolve(eps);

    182:   /*
    183:      Optional: Get some information from the solver and display it
    184:   */
    185:   EPSGetType(eps,&type);
    186:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    187:   EPSGetDimensions(eps,&nev,NULL,NULL);
    188:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    191:                     Display solution and clean up
    192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    194:   EPSPrintSolution(eps,NULL);
    195:   EPSDestroy(&eps);
    196:   MatDestroy(&A);
    197:   MatDestroy(&ctx->T);
    198:   VecDestroy(&ctx->x1);
    199:   VecDestroy(&ctx->x2);
    200:   VecDestroy(&ctx->y1);
    201:   VecDestroy(&ctx->y2);
    202:   PetscFree(ctx);
    203:   SlepcFinalize();
    204:   return 0;
    205: }

    209: PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
    210: {
    211:   PetscInt          n;
    212:   const PetscScalar *px;
    213:   PetscScalar       *py;
    214:   CTX_BRUSSEL       *ctx;
    215:   PetscErrorCode    ierr;

    218:   MatShellGetContext(A,(void**)&ctx);
    219:   MatGetLocalSize(ctx->T,&n,NULL);
    220:   VecGetArrayRead(x,&px);
    221:   VecGetArray(y,&py);
    222:   VecPlaceArray(ctx->x1,px);
    223:   VecPlaceArray(ctx->x2,px+n);
    224:   VecPlaceArray(ctx->y1,py);
    225:   VecPlaceArray(ctx->y2,py+n);

    227:   MatMult(ctx->T,ctx->x1,ctx->y1);
    228:   VecScale(ctx->y1,ctx->tau1);
    229:   VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1);
    230:   VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2);

    232:   MatMult(ctx->T,ctx->x2,ctx->y2);
    233:   VecScale(ctx->y2,ctx->tau2);
    234:   VecAXPY(ctx->y2,-ctx->beta,ctx->x1);
    235:   VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2);

    237:   VecRestoreArrayRead(x,&px);
    238:   VecRestoreArray(y,&py);
    239:   VecResetArray(ctx->x1);
    240:   VecResetArray(ctx->x2);
    241:   VecResetArray(ctx->y1);
    242:   VecResetArray(ctx->y2);
    243:   return(0);
    244: }

    248: PetscErrorCode MatShift_Brussel(PetscScalar* a,Mat Y)
    249: {
    250:   CTX_BRUSSEL    *ctx;

    254:   MatShellGetContext(Y,(void**)&ctx);
    255:   ctx->sigma += *a;
    256:   return(0);
    257: }

    261: PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
    262: {
    263:   Vec            d1,d2;
    264:   PetscInt       n;
    265:   PetscScalar    *pd;
    266:   MPI_Comm       comm;
    267:   CTX_BRUSSEL    *ctx;

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

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

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