Date: 2022-08-09T09:05:42+00:00

Actual source code: ex35.c
slepc-3.17.2 2022-08-09
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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[] = "Shell spectral transformations with a non-injective mapping. "
     12:   "Implements spectrum folding for the 2-D Laplacian, as in ex24.c.\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: /* Context for spectrum folding spectral transformation */
     20: typedef struct {
     21:   Mat         A;
     22:   Vec         w;
     23:   PetscScalar target;
     24: } FoldShellST;

     26: /* Routines for shell spectral transformation */
     27: PetscErrorCode STCreate_Fold(Mat,PetscScalar,FoldShellST**);
     28: PetscErrorCode STApply_Fold(ST,Vec,Vec);
     29: PetscErrorCode STDestroy_Fold(FoldShellST*);

     31: int main (int argc,char **argv)
     32: {
     33:   Mat            A;               /* operator matrix */
     34:   EPS            eps;             /* eigenproblem solver context */
     35:   ST             st;              /* spectral transformation context */
     36:   FoldShellST    *fold;           /* user-defined spectral transform context */
     37:   EPSType        type;
     38:   PetscInt       N,n=10,m,i,j,II,Istart,Iend,nev;
     39:   PetscBool      isShell,terse,flag;
     40:   PetscScalar    target=1.1;

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

     44:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     45:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     46:   if (!flag) m = n;
     47:   PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
     48:   N = n*m;
     49:   PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum Folding via shell ST, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid) target=%3.2f\n\n",N,n,m,(double)PetscRealPart(target));

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:      Compute the 5-point stencil Laplacian
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   MatCreate(PETSC_COMM_WORLD,&A);
     56:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     57:   MatSetFromOptions(A);
     58:   MatSetUp(A);

     60:   MatGetOwnershipRange(A,&Istart,&Iend);
     61:   for (II=Istart;II<Iend;II++) {
     62:     i = II/n; j = II-i*n;
     63:     if (i>0) MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);
     64:     if (i<m-1) MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);
     65:     if (j>0) MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);
     66:     if (j<n-1) MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);
     67:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
     68:   }
     69:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     70:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:                 Create the eigensolver and set various options
     74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     76:   EPSCreate(PETSC_COMM_WORLD,&eps);
     77:   EPSSetOperators(eps,A,NULL);
     78:   EPSSetProblemType(eps,EPS_HEP);
     79:   EPSSetTarget(eps,target);
     80:   EPSGetST(eps,&st);
     81:   STSetType(st,STSHELL);
     82:   EPSSetFromOptions(eps);

     84:   /*
     85:      Initialize shell spectral transformation
     86:   */
     87:   PetscObjectTypeCompare((PetscObject)st,STSHELL,&isShell);
     88:   if (isShell) {
     89:     /* Change sorting criterion since this shell ST computes eigenvalues
     90:        of the transformed operator closest to 0 */
     91:     EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);

     93:     /* Create the context for the user-defined spectral transform */
     94:     STCreate_Fold(A,target,&fold);
     95:     STShellSetContext(st,fold);

     97:     /* Set callback function for applying the operator (in this case we do not
     98:        provide a back-transformation callback since the mapping is not one-to-one) */
     99:     STShellSetApply(st,STApply_Fold);
    100:     PetscObjectSetName((PetscObject)st,"STFOLD");
    101:   }

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:                       Solve the eigensystem
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    107:   EPSSolve(eps);
    108:   EPSGetType(eps,&type);
    109:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    110:   EPSGetDimensions(eps,&nev,NULL,NULL);
    111:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

    113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    114:                     Display solution and clean up
    115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    117:   /* show detailed info unless -terse option is given by user */
    118:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    119:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    120:   else {
    121:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    122:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    123:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    124:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    125:   }
    126:   if (isShell) STDestroy_Fold(fold);
    127:   EPSDestroy(&eps);
    128:   MatDestroy(&A);
    129:   SlepcFinalize();
    130:   return 0;
    131: }

    133: /*
    134:    STCreate_Fold - Creates the spectrum folding ST context.

    136:    Input Parameter:
    137: +  A - problem matrix
    138: -  target - target value

    140:    Output Parameter:
    141: .  fold - user-defined spectral transformation context
    142: */
    143: PetscErrorCode STCreate_Fold(Mat A,PetscScalar target,FoldShellST **fold)
    144: {
    145:   FoldShellST    *newctx;

    148:   PetscNew(&newctx);
    149:   newctx->A = A;
    150:   PetscObjectReference((PetscObject)A);
    151:   newctx->target = target;
    152:   MatCreateVecs(A,&newctx->w,NULL);
    153:   *fold = newctx;
    154:   PetscFunctionReturn(0);
    155: }

    157: /*
    158:    STApply_Fold - Applies the operator (A-target*I)^2 to a given vector.

    160:    Input Parameters:
    161: +  st - spectral transformation context
    162: -  x  - input vector

    164:    Output Parameter:
    165: .  y - output vector
    166: */
    167: PetscErrorCode STApply_Fold(ST st,Vec x,Vec y)
    168: {
    169:   FoldShellST    *fold;
    170:   PetscScalar    sigma;

    173:   STShellGetContext(st,&fold);
    174:   sigma = -fold->target;
    175:   MatMult(fold->A,x,fold->w);
    176:   VecAXPY(fold->w,sigma,x);
    177:   MatMult(fold->A,fold->w,y);
    178:   VecAXPY(y,sigma,fold->w);
    179:   PetscFunctionReturn(0);
    180: }

    182: /*
    183:    STDestroy_Fold - This routine destroys the shell ST context.

    185:    Input Parameter:
    186: .  fold - user-defined spectral transformation context
    187: */
    188: PetscErrorCode STDestroy_Fold(FoldShellST *fold)
    189: {
    191:   MatDestroy(&fold->A);
    192:   VecDestroy(&fold->w);
    193:   PetscFree(fold);
    194:   PetscFunctionReturn(0);
    195: }

    197: /*TEST

    199:    test:
    200:       args: -m 11 -eps_nev 4 -terse
    201:       suffix: 1
    202:       requires: !single

    204: TEST*/