Date: 2026-01-20T11:35:45+00:00

Actual source code: ex35.c

      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.\n\n"
     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:   PetscFunctionBeginUser;
     43:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     46:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     47:   if (!flag) m = n;
     48:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL));
     49:   N = n*m;
     50:   PetscCall(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:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     57:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     58:   PetscCall(MatSetFromOptions(A));

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

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

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

     84:   /*
     85:      Initialize shell spectral transformation
     86:   */
     87:   PetscCall(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:     PetscCall(EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL));

     93:     /* Create the context for the user-defined spectral transform */
     94:     PetscCall(STCreate_Fold(A,target,&fold));
     95:     PetscCall(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:     PetscCall(STShellSetApply(st,STApply_Fold));
    100:     PetscCall(PetscObjectSetName((PetscObject)st,"STFOLD"));
    101:   }

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

    107:   PetscCall(EPSSolve(eps));
    108:   PetscCall(EPSGetType(eps,&type));
    109:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
    110:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    111:   PetscCall(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:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    119:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    120:   else {
    121:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    122:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
    123:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    124:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    125:   }
    126:   if (isShell) PetscCall(STDestroy_Fold(fold));
    127:   PetscCall(EPSDestroy(&eps));
    128:   PetscCall(MatDestroy(&A));
    129:   PetscCall(SlepcFinalize());
    130:   return 0;
    131: }

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

    136:    Input Parameters:
    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;

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

    172:   PetscFunctionBeginUser;
    173:   PetscCall(STShellGetContext(st,&fold));
    174:   sigma = -fold->target;
    175:   PetscCall(MatMult(fold->A,x,fold->w));
    176:   PetscCall(VecAXPY(fold->w,sigma,x));
    177:   PetscCall(MatMult(fold->A,fold->w,y));
    178:   PetscCall(VecAXPY(y,sigma,fold->w));
    179:   PetscFunctionReturn(PETSC_SUCCESS);
    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: {
    190:   PetscFunctionBeginUser;
    191:   PetscCall(MatDestroy(&fold->A));
    192:   PetscCall(VecDestroy(&fold->w));
    193:   PetscCall(PetscFree(fold));
    194:   PetscFunctionReturn(PETSC_SUCCESS);
    195: }

    197: /*TEST

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

    204: TEST*/