Date: 2022-10-01T06:40:06+00:00

Actual source code: ex35.c
slepc-3.18.0 2022-10-01
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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;

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

     45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     46:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
     47:   if (!flag) m = n;
     48:   PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
     49:   N = n*m;
     50:   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));

     52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     53:      Compute the 5-point stencil Laplacian
     54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:                 Create the eigensolver and set various options
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

     98:     /* Set callback function for applying the operator (in this case we do not
     99:        provide a back-transformation callback since the mapping is not one-to-one) */
    100:     STShellSetApply(st,STApply_Fold);
    101:     PetscObjectSetName((PetscObject)st,"STFOLD");
    102:   }

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:                       Solve the eigensystem
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:                     Display solution and clean up
    116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    118:   /* show detailed info unless -terse option is given by user */
    119:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    120:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    121:   else {
    122:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    123:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
    124:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    125:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    126:   }
    127:   if (isShell) STDestroy_Fold(fold);
    128:   EPSDestroy(&eps);
    129:   MatDestroy(&A);
    130:   SlepcFinalize();
    131:   return 0;
    132: }

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

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

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

    149:   PetscNew(&newctx);
    150:   newctx->A = A;
    151:   PetscObjectReference((PetscObject)A);
    152:   newctx->target = target;
    153:   MatCreateVecs(A,&newctx->w,NULL);
    154:   *fold = newctx;
    155:   return 0;
    156: }

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

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

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

    174:   STShellGetContext(st,&fold);
    175:   sigma = -fold->target;
    176:   MatMult(fold->A,x,fold->w);
    177:   VecAXPY(fold->w,sigma,x);
    178:   MatMult(fold->A,fold->w,y);
    179:   VecAXPY(y,sigma,fold->w);
    180:   return 0;
    181: }

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

    186:    Input Parameter:
    187: .  fold - user-defined spectral transformation context
    188: */
    189: PetscErrorCode STDestroy_Fold(FoldShellST *fold)
    190: {
    192:   MatDestroy(&fold->A);
    193:   VecDestroy(&fold->w);
    194:   PetscFree(fold);
    195:   return 0;
    196: }

    198: /*TEST

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

    205: TEST*/