Actual source code: ex35.c

slepc-3.16.0 2021-09-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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);if (ierr) return ierr;

 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=%D (%Dx%D 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: %D\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) {
121:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
122:   } else {
123:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
124:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
125:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
126:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
127:   }
128:   if (isShell) {
129:     STDestroy_Fold(fold);
130:   }
131:   EPSDestroy(&eps);
132:   MatDestroy(&A);
133:   SlepcFinalize();
134:   return ierr;
135: }

137: /*
138:    STCreate_Fold - Creates the spectrum folding ST context.

140:    Input Parameter:
141: +  A - problem matrix
142: -  target - target value

144:    Output Parameter:
145: .  fold - user-defined spectral transformation context
146: */
147: PetscErrorCode STCreate_Fold(Mat A,PetscScalar target,FoldShellST **fold)
148: {
149:   FoldShellST    *newctx;

153:   PetscNew(&newctx);
154:   newctx->A = A;
155:   PetscObjectReference((PetscObject)A);
156:   newctx->target = target;
157:   MatCreateVecs(A,&newctx->w,NULL);
158:   *fold = newctx;
159:   return(0);
160: }

162: /*
163:    STApply_Fold - Applies the operator (A-target*I)^2 to a given vector.

165:    Input Parameters:
166: +  st - spectral transformation context
167: -  x  - input vector

169:    Output Parameter:
170: .  y - output vector
171: */
172: PetscErrorCode STApply_Fold(ST st,Vec x,Vec y)
173: {
174:   FoldShellST    *fold;
175:   PetscScalar    sigma;

179:   STShellGetContext(st,&fold);
180:   sigma = -fold->target;
181:   MatMult(fold->A,x,fold->w);
182:   VecAXPY(fold->w,sigma,x);
183:   MatMult(fold->A,fold->w,y);
184:   VecAXPY(y,sigma,fold->w);
185:   return(0);
186: }

188: /*
189:    STDestroy_Fold - This routine destroys the shell ST context.

191:    Input Parameter:
192: .  fold - user-defined spectral transformation context
193: */
194: PetscErrorCode STDestroy_Fold(FoldShellST *fold)
195: {

199:   MatDestroy(&fold->A);
200:   VecDestroy(&fold->w);
201:   PetscFree(fold);
202:   return(0);
203: }

205: /*TEST

207:    test:
208:       args: -m 11 -eps_nev 4 -terse
209:       suffix: 1
210:       requires: !single

212: TEST*/