Actual source code: ex10.c

  1: static char help[] = "Illustrates the use of shell spectral transformations. "
  2:   "The problem to be solved is the same as ex1.c and"
  3:   "corresponds to the Laplacian operator in 1 dimension.\n\n"
  4:   "The command line options are:\n\n"
  5:   "  -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";

 7:  #include slepceps.h

  9: /* Define context for user-provided spectral transformation */
 10: typedef struct {
 11:   KSP        ksp;
 12: } SampleShellST;

 14: /* Declare routines for user-provided spectral transformation */
 15: extern int SampleShellSTCreate(SampleShellST**);
 16: extern int SampleShellSTSetUp(SampleShellST*,ST);
 17: extern int SampleShellSTApply(void*,Vec,Vec);
 18: extern int SampleShellSTBackTransform(void*,PetscScalar*,PetscScalar*);
 19: extern int SampleShellSTDestroy(SampleShellST*);

 23: int main( int argc, char **argv )
 24: {
 25:   Mat           A;               /* operator matrix */
 26:   EPS           eps;             /* eigenproblem solver context */
 27:   ST            st;              /* spectral transformation context */
 28:   SampleShellST *shell;          /* user-defined spectral transform context */
 29:   EPSType       type;
 30:   PetscReal     error, tol, re, im;
 31:   PetscScalar   kr, ki;
 32:   int           n=30, nev, ierr, maxit, i, its, nconv,
 33:                 col[3], Istart, Iend, FirstBlock=0, LastBlock=0;
 34:   PetscScalar   value[3];
 35:   PetscTruth    isShell;

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

 39:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 40:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem (shell-enabled), n=%d\n\n",n);
 41: 

 43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 44:      Compute the operator matrix that defines the eigensystem, Ax=kx
 45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 47:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);
 48:   MatSetFromOptions(A);
 49: 
 50:   MatGetOwnershipRange(A,&Istart,&Iend);
 51:   if (Istart==0) FirstBlock=PETSC_TRUE;
 52:   if (Iend==n) LastBlock=PETSC_TRUE;
 53:   value[0]=-1.0; value[1]=2.0; value[2]=-1.0;
 54:   for( i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++ ) {
 55:     col[0]=i-1; col[1]=i; col[2]=i+1;
 56:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 57:   }
 58:   if (LastBlock) {
 59:     i=n-1; col[0]=n-2; col[1]=n-1;
 60:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 61:   }
 62:   if (FirstBlock) {
 63:     i=0; col[0]=0; col[1]=1; value[0]=2.0; value[1]=-1.0;
 64:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 65:   }

 67:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 68:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 71:                 Create the eigensolver and set various options
 72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 74:   /* 
 75:      Create eigensolver context
 76:   */
 77:   EPSCreate(PETSC_COMM_WORLD,&eps);

 79:   /* 
 80:      Set operators. In this case, it is a standard eigenvalue problem
 81:   */
 82:   EPSSetOperators(eps,A,PETSC_NULL);

 84:   /*
 85:      Set solver parameters at runtime
 86:   */
 87:   EPSSetFromOptions(eps);

 89:   /*
 90:      Initialize shell spectral transformation if selected by user
 91:   */
 92:   EPSGetST(eps,&st);
 93:   PetscTypeCompare((PetscObject)st,STSHELL,&isShell);
 94:   if (isShell) {
 95:     /* (Optional) Create a context for the user-defined spectral tranform;
 96:        this context can be defined to contain any application-specific data. */
 97:     SampleShellSTCreate(&shell);

 99:     /* (Required) Set the user-defined routine for applying the operator */
100:     STShellSetApply(st,SampleShellSTApply,(void*)shell);

102:     /* (Optional) Set the user-defined routine for back-transformation */
103:     STShellSetBackTransform(st,SampleShellSTBackTransform);

105:     /* (Optional) Set a name for the transformation, used for STView() */
106:     STShellSetName(st,"MyTransformation");

108:     /* (Optional) Do any setup required for the new transformation */
109:     SampleShellSTSetUp(shell,st);
110:   }

112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
113:                       Solve the eigensystem
114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

116:   EPSSolve(eps);
117:   EPSGetIterationNumber(eps, &its);
118:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);
119: 

121:   /*
122:      Optional: Get some information from the solver and display it
123:   */
124:   EPSGetType(eps,&type);
125:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
126:   EPSGetDimensions(eps,&nev,PETSC_NULL);
127:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
128: 
129:   EPSGetTolerances(eps,&tol,&maxit);
130:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);
131: 

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
134:                     Display solution and clean up
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

137:   /* 
138:      Get number of converged approximate eigenpairs
139:   */
140:   EPSGetConverged(eps,&nconv);
141:   PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %d\n\n",nconv);
142: 

144:   if (nconv>0) {
145:     /*
146:        Display eigenvalues and relative errors
147:     */
148:     PetscPrintf(PETSC_COMM_WORLD,
149:          "           k          ||Ax-kx||/||kx||\n"
150:          "   ----------------- ------------------\n" );

152:     for( i=0; i<nconv; i++ ) {
153:       /* 
154:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
155:         ki (imaginary part)
156:       */
157:       EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
158:       /*
159:          Compute the relative error associated to each eigenpair
160:       */
161:       EPSComputeRelativeError(eps,i,&error);

163: #ifdef PETSC_USE_COMPLEX
164:       re = PetscRealPart(kr);
165:       im = PetscImaginaryPart(kr);
166: #else
167:       re = kr;
168:       im = ki;
169: #endif 
170:       if (im!=0.0) {
171:         PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12f\n",re,im,error);
172:       } else {
173:         PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12f\n",re,error);
174:       }
175:     }
176:     PetscPrintf(PETSC_COMM_WORLD,"\n" );
177:   }
178: 
179:   /* 
180:      Free work space
181:   */
182:   if (isShell) {
183:     SampleShellSTDestroy(shell);
184:   }
185:   EPSDestroy(eps);
186:   MatDestroy(A);
187:   SlepcFinalize();
188:   return 0;
189: }

191: /***********************************************************************/
192: /*          Routines for a user-defined shell transformation           */
193: /***********************************************************************/

197: /*
198:    SampleShellSTCreate - This routine creates a user-defined
199:    spectral transformation context.

201:    Output Parameter:
202: .  shell - user-defined spectral transformation context
203: */
204: int SampleShellSTCreate(SampleShellST **shell)
205: {
206:   SampleShellST *newctx;
207:   int           ierr;

209:   PetscNew(SampleShellST,&newctx);
210:   KSPCreate(PETSC_COMM_WORLD,&newctx->ksp);
211:   KSPAppendOptionsPrefix(newctx->ksp,"st_");
212:   *shell = newctx;
213:   return 0;
214: }
215: /* ------------------------------------------------------------------- */
218: /*
219:    SampleShellSTSetUp - This routine sets up a user-defined
220:    spectral transformation context.  

222:    Input Parameters:
223: .  shell - user-defined spectral transformation context
224: .  st    - spectral transformation context containing the operator matrices

226:    Output Parameter:
227: .  shell - fully set up user-defined transformation context

229:    Notes:
230:    In this example, the user-defined transformation is simply OP=A^-1.
231:    Therefore, the eigenpairs converge in reversed order. The KSP object
232:    used for the solution of linear systems with A is handled via the
233:    user-defined context SampleShellST.
234: */
235: int SampleShellSTSetUp(SampleShellST *shell,ST st)
236: {
237:   Mat  A,B;
238:   int  ierr;

240:   STGetOperators( st, &A, &B );
241:   if (B) { SETERRQ(0,"Warning: This transformation is not intended for generalized problems"); }
242:   KSPSetOperators(shell->ksp,A,A,DIFFERENT_NONZERO_PATTERN);
243:   KSPSetFromOptions(shell->ksp);

245:   return 0;
246: }
247: /* ------------------------------------------------------------------- */
250: /*
251:    SampleShellSTApply - This routine demonstrates the use of a
252:    user-provided spectral transformation.

254:    Input Parameters:
255: .  ctx - optional user-defined context, as set by STShellSetApply()
256: .  x - input vector

258:    Output Parameter:
259: .  y - output vector

261:    Notes:
262:    The transformation implemented in this code is just OP=A^-1 and
263:    therefore it is of little use, merely as an example of working with
264:    a STSHELL.
265: */
266: int SampleShellSTApply(void *ctx,Vec x,Vec y)
267: {
268:   SampleShellST *shell = (SampleShellST*)ctx;
269:   int           ierr;

271:   KSPSetRhs(shell->ksp,x);
272:   KSPSetSolution(shell->ksp,y);
273:   KSPSolve(shell->ksp);

275:   return 0;
276: }
277: /* ------------------------------------------------------------------- */
280: /*
281:    SampleShellSTBackTransform - This routine demonstrates the use of a
282:    user-provided spectral transformation.

284:    Input Parameters:
285: .  ctx  - optional user-defined context, as set by STShellSetApply()
286: .  eigr - pointer to real part of eigenvalues
287: .  eigi - pointer to imaginary part of eigenvalues

289:    Output Parameters:
290: .  eigr - modified real part of eigenvalues
291: .  eigi - modified imaginary part of eigenvalues

293:    Notes:
294:    This code implements the back transformation of eigenvalues in
295:    order to retrieve the eigenvalues of the original problem. In this
296:    example, simply set k_i = 1/k_i.
297: */
298: int SampleShellSTBackTransform(void *ctx,PetscScalar *eigr,PetscScalar *eigi)
299: {
300:   *eigr = 1.0 / *eigr;

302:   return 0;
303: }
304: /* ------------------------------------------------------------------- */
307: /*
308:    SampleShellSTDestroy - This routine destroys a user-defined
309:    spectral transformation context.

311:    Input Parameter:
312: .  shell - user-defined spectral transformation context
313: */
314: int SampleShellSTDestroy(SampleShellST *shell)
315: {

318:   KSPDestroy(shell->ksp);
319:   PetscFree(shell);

321:   return 0;
322: }