Actual source code: ex9.c

  1: /*$Id: ex9.c,v 1.53 2001/08/07 21:30:54 bsmith Exp $*/

  3: static char help[] = "The solution of 2 different linear systems with different linear solvers.n
  4: Also, this example illustrates the repeatedn
  5: solution of linear systems, while reusing matrix, vector, and solver datan
  6: structures throughout the process.  Note the various stages of event logging.nn";

  8: /*T
  9:    Concepts: SLES^repeatedly solving linear systems;
 10:    Concepts: PetscLog^profiling multiple stages of code;
 11:    Concepts: PetscLog^user-defined event profiling;
 12:    Processors: n
 13: T*/

 15: /* 
 16:   Include "petscsles.h" so that we can use SLES solvers.  Note that this file
 17:   automatically includes:
 18:      petsc.h       - base PETSc routines   petscvec.h - vectors
 19:      petscsys.h    - system routines       petscmat.h - matrices
 20:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 21:      petscviewer.h - viewers               petscpc.h  - preconditioners
 22: */
 23:  #include petscsles.h

 25: /* 
 26:    Declare user-defined routines
 27: */
 28: extern int CheckError(Vec,Vec,Vec,int,int);
 29: extern int MyKSPMonitor(KSP,int,PetscReal,void*);

 31: int main(int argc,char **args)
 32: {
 33:   Vec          x1,b1,x2,b2; /* solution and RHS vectors for systems #1 and #2 */
 34:   Vec          u;              /* exact solution vector */
 35:   Mat          C1,C2;         /* matrices for systems #1 and #2 */
 36:   SLES         sles1,sles2;   /* SLES contexts for systems #1 and #2 */
 37:   KSP          ksp1;           /* KSP context for system #1 */
 38:   int          ntimes = 3;     /* number of times to solve the linear systems */
 39:   int          CHECK_ERROR;    /* event number for error checking */
 40:   int          ldim,ierr,low,high,iglobal,Istart,Iend,Istart2,Iend2;
 41:   int          I,J,i,j,m = 3,n = 2,rank,size,its,t;
 42:   int          stages[3];
 43:   PetscTruth   flg;
 44:   PetscScalar  v;

 46:   PetscInitialize(&argc,&args,(char *)0,help);
 47:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 48:   PetscOptionsGetInt(PETSC_NULL,"-t",&ntimes,PETSC_NULL);
 49:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 50:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 51:   n = 2*size;

 53:   /* 
 54:      Register various stages for profiling
 55:   */
 56:   PetscLogStageRegister(&stages[0],"Prelim setup");
 57:   PetscLogStageRegister(&stages[1],"Linear System 1");
 58:   PetscLogStageRegister(&stages[2],"Linear System 2");

 60:   /* 
 61:      Register a user-defined event for profiling (error checking).
 62:   */
 63:   CHECK_ERROR = 0;
 64:   PetscLogEventRegister(&CHECK_ERROR,"Check Error",SLES_COOKIE);

 66:   /* - - - - - - - - - - - - Stage 0: - - - - - - - - - - - - - -
 67:                         Preliminary Setup
 68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 70:   PetscLogStagePush(stages[0]);

 72:   /* 
 73:      Create data structures for first linear system.
 74:       - Create parallel matrix, specifying only its global dimensions.
 75:         When using MatCreate(), the matrix format can be specified at
 76:         runtime. Also, the parallel partitioning of the matrix is
 77:         determined by PETSc at runtime.
 78:       - Create parallel vectors.
 79:         - When using VecSetSizes(), we specify only the vector's global
 80:           dimension; the parallel partitioning is determined at runtime. 
 81:         - Note: We form 1 vector from scratch and then duplicate as needed.
 82:   */
 83:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&C1);
 84:   MatSetFromOptions(C1);
 85:   MatGetOwnershipRange(C1,&Istart,&Iend);
 86:   VecCreate(PETSC_COMM_WORLD,&u);
 87:   VecSetSizes(u,PETSC_DECIDE,m*n);
 88:   VecSetFromOptions(u);
 89:   VecDuplicate(u,&b1);
 90:   VecDuplicate(u,&x1);

 92:   /*
 93:      Create first linear solver context.
 94:      Set runtime options (e.g., -pc_type <type>).
 95:      Note that the first linear system uses the default option
 96:      names, while the second linear systme uses a different
 97:      options prefix.
 98:   */
 99:   SLESCreate(PETSC_COMM_WORLD,&sles1);
100:   SLESSetFromOptions(sles1);

102:   /* 
103:      Set user-defined monitoring routine for first linear system.
104:   */
105:   SLESGetKSP(sles1,&ksp1);
106:   PetscOptionsHasName(PETSC_NULL,"-my_ksp_monitor",&flg);
107:   if (flg) {KSPSetMonitor(ksp1,MyKSPMonitor,PETSC_NULL,0);}

109:   /*
110:      Create data structures for second linear system.
111:   */
112:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&C2);
113:   MatSetFromOptions(C2);
114:   MatGetOwnershipRange(C2,&Istart2,&Iend2);
115:   VecDuplicate(u,&b2);
116:   VecDuplicate(u,&x2);

118:   /*
119:      Create second linear solver context
120:   */
121:   SLESCreate(PETSC_COMM_WORLD,&sles2);

123:   /* 
124:      Set different options prefix for second linear system.
125:      Set runtime options (e.g., -s2_pc_type <type>)
126:   */
127:   SLESAppendOptionsPrefix(sles2,"s2_");
128:   SLESSetFromOptions(sles2);

130:   /* 
131:      Assemble exact solution vector in parallel.  Note that each
132:      processor needs to set only its local part of the vector.
133:   */
134:   VecGetLocalSize(u,&ldim);
135:   VecGetOwnershipRange(u,&low,&high);
136:   for (i=0; i<ldim; i++) {
137:     iglobal = i + low;
138:     v = (PetscScalar)(i + 100*rank);
139:     VecSetValues(u,1,&iglobal,&v,ADD_VALUES);
140:   }
141:   VecAssemblyBegin(u);
142:   VecAssemblyEnd(u);

144:   /* 
145:      Log the number of flops for computing vector entries
146:   */
147:   PetscLogFlops(2*ldim);

149:   /*
150:      End curent profiling stage
151:   */
152:   PetscLogStagePop();

154:   /* -------------------------------------------------------------- 
155:                         Linear solver loop:
156:       Solve 2 different linear systems several times in succession 
157:      -------------------------------------------------------------- */

159:   for (t=0; t<ntimes; t++) {

161:     /* - - - - - - - - - - - - Stage 1: - - - - - - - - - - - - - -
162:                  Assemble and solve first linear system            
163:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

165:     /*
166:        Begin profiling stage #1
167:     */
168:     PetscLogStagePush(stages[1]);

170:     /* 
171:        Initialize all matrix entries to zero.  MatZeroEntries() retains
172:        the nonzero structure of the matrix for sparse formats.
173:     */
174:     MatZeroEntries(C1);

176:     /* 
177:        Set matrix entries in parallel.  Also, log the number of flops
178:        for computing matrix entries.
179:         - Each processor needs to insert only elements that it owns
180:           locally (but any non-local elements will be sent to the
181:           appropriate processor during matrix assembly). 
182:         - Always specify global row and columns of matrix entries.
183:     */
184:     for (I=Istart; I<Iend; I++) {
185:       v = -1.0; i = I/n; j = I - i*n;
186:       if (i>0)   {J = I - n; MatSetValues(C1,1,&I,1,&J,&v,ADD_VALUES);}
187:       if (i<m-1) {J = I + n; MatSetValues(C1,1,&I,1,&J,&v,ADD_VALUES);}
188:       if (j>0)   {J = I - 1; MatSetValues(C1,1,&I,1,&J,&v,ADD_VALUES);}
189:       if (j<n-1) {J = I + 1; MatSetValues(C1,1,&I,1,&J,&v,ADD_VALUES);}
190:       v = 4.0; MatSetValues(C1,1,&I,1,&I,&v,ADD_VALUES);
191:     }
192:     for (I=Istart; I<Iend; I++) { /* Make matrix nonsymmetric */
193:       v = -1.0*(t+0.5); i = I/n;
194:       if (i>0)   {J = I - n; MatSetValues(C1,1,&I,1,&J,&v,ADD_VALUES);}
195:     }
196:     PetscLogFlops(2*(Istart-Iend));

198:     /* 
199:        Assemble matrix, using the 2-step process:
200:          MatAssemblyBegin(), MatAssemblyEnd()
201:        Computations can be done while messages are in transition
202:        by placing code between these two statements.
203:     */
204:     MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
205:     MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);

207:     /* 
208:        Indicate same nonzero structure of successive linear system matrices
209:     */
210:     MatSetOption(C1,MAT_NO_NEW_NONZERO_LOCATIONS);

212:     /* 
213:        Compute right-hand-side vector
214:     */
215:     MatMult(C1,u,b1);

217:     /* 
218:        Set operators. Here the matrix that defines the linear system
219:        also serves as the preconditioning matrix.
220:         - The flag SAME_NONZERO_PATTERN indicates that the
221:           preconditioning matrix has identical nonzero structure
222:           as during the last linear solve (although the values of
223:           the entries have changed). Thus, we can save some
224:           work in setting up the preconditioner (e.g., no need to
225:           redo symbolic factorization for ILU/ICC preconditioners).
226:         - If the nonzero structure of the matrix is different during
227:           the second linear solve, then the flag DIFFERENT_NONZERO_PATTERN
228:           must be used instead.  If you are unsure whether the
229:           matrix structure has changed or not, use the flag
230:           DIFFERENT_NONZERO_PATTERN.
231:         - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
232:           believes your assertion and does not check the structure
233:           of the matrix.  If you erroneously claim that the structure
234:           is the same when it actually is not, the new preconditioner
235:           will not function correctly.  Thus, use this optimization
236:           feature with caution!
237:     */
238:     SLESSetOperators(sles1,C1,C1,SAME_NONZERO_PATTERN);

240:     /* 
241:        Use the previous solution of linear system #1 as the initial
242:        guess for the next solve of linear system #1.  The user MUST
243:        call KSPSetInitialGuessNonzero() in indicate use of an initial
244:        guess vector; otherwise, an initial guess of zero is used.
245:     */
246:     if (t>0) {
247:       KSPSetInitialGuessNonzero(ksp1,PETSC_TRUE);
248:     }

250:     /* 
251:        Solve the first linear system.  Here we explicitly call
252:        SLESSetUp() for more detailed performance monitoring of
253:        certain preconditioners, such as ICC and ILU.  This call
254:        is optional, ase SLESSetUp() will automatically be called
255:        within SLESSolve() if it hasn't been called already.
256:     */
257:     SLESSetUp(sles1,b1,x1);
258:     SLESSolve(sles1,b1,x1,&its);

260:     /*
261:        Check error of solution to first linear system
262:     */
263:     CheckError(u,x1,b1,its,CHECK_ERROR);

265:     /* - - - - - - - - - - - - Stage 2: - - - - - - - - - - - - - -
266:                  Assemble and solve second linear system            
267:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

269:     /*
270:        Conclude profiling stage #1; begin profiling stage #2
271:     */
272:     PetscLogStagePop();
273:     PetscLogStagePush(stages[2]);

275:     /*
276:        Initialize all matrix entries to zero
277:     */
278:     MatZeroEntries(C2);

280:    /* 
281:       Assemble matrix in parallel. Also, log the number of flops
282:       for computing matrix entries.
283:        - To illustrate the features of parallel matrix assembly, we
284:          intentionally set the values differently from the way in
285:          which the matrix is distributed across the processors.  Each
286:          entry that is not owned locally will be sent to the appropriate
287:          processor during MatAssemblyBegin() and MatAssemblyEnd().
288:        - For best efficiency the user should strive to set as many
289:          entries locally as possible.
290:     */
291:     for (i=0; i<m; i++) {
292:       for (j=2*rank; j<2*rank+2; j++) {
293:         v = -1.0;  I = j + n*i;
294:         if (i>0)   {J = I - n; MatSetValues(C2,1,&I,1,&J,&v,ADD_VALUES);}
295:         if (i<m-1) {J = I + n; MatSetValues(C2,1,&I,1,&J,&v,ADD_VALUES);}
296:         if (j>0)   {J = I - 1; MatSetValues(C2,1,&I,1,&J,&v,ADD_VALUES);}
297:         if (j<n-1) {J = I + 1; MatSetValues(C2,1,&I,1,&J,&v,ADD_VALUES);}
298:         v = 6.0 + t*0.5; MatSetValues(C2,1,&I,1,&I,&v,ADD_VALUES);
299:       }
300:     }
301:     for (I=Istart2; I<Iend2; I++) { /* Make matrix nonsymmetric */
302:       v = -1.0*(t+0.5); i = I/n;
303:       if (i>0)   {J = I - n; MatSetValues(C2,1,&I,1,&J,&v,ADD_VALUES);}
304:     }
305:     MatAssemblyBegin(C2,MAT_FINAL_ASSEMBLY);
306:     MatAssemblyEnd(C2,MAT_FINAL_ASSEMBLY);
307:     PetscLogFlops(2*(Istart-Iend));

309:     /* 
310:        Indicate same nonzero structure of successive linear system matrices
311:     */
312:     MatSetOption(C2,MAT_NO_NEW_NONZERO_LOCATIONS);

314:     /*
315:        Compute right-hand-side vector 
316:     */
317:     MatMult(C2,u,b2);

319:     /*
320:        Set operators. Here the matrix that defines the linear system
321:        also serves as the preconditioning matrix.  Indicate same nonzero
322:        structure of successive preconditioner matrices by setting flag
323:        SAME_NONZERO_PATTERN.
324:     */
325:     SLESSetOperators(sles2,C2,C2,SAME_NONZERO_PATTERN);

327:     /* 
328:        Solve the second linear system
329:     */
330:     SLESSetUp(sles2,b2,x2);
331:     SLESSolve(sles2,b2,x2,&its);

333:     /*
334:        Check error of solution to second linear system
335:     */
336:     CheckError(u,x2,b2,its,CHECK_ERROR);

338:     /* 
339:        Conclude profiling stage #2
340:     */
341:     PetscLogStagePop();
342:   }
343:   /* -------------------------------------------------------------- 
344:                        End of linear solver loop
345:      -------------------------------------------------------------- */

347:   /* 
348:      Free work space.  All PETSc objects should be destroyed when they
349:      are no longer needed.
350:   */
351:   SLESDestroy(sles1); SLESDestroy(sles2);
352:   VecDestroy(x1);     VecDestroy(x2);
353:   VecDestroy(b1);     VecDestroy(b2);
354:   MatDestroy(C1);     MatDestroy(C2);
355:   VecDestroy(u);

357:   PetscFinalize();
358:   return 0;
359: }
360: /* ------------------------------------------------------------- */
361: /*
362:     CheckError - Checks the error of the solution.

364:     Input Parameters:
365:     u - exact solution
366:     x - approximate solution
367:     b - work vector
368:     its - number of iterations for convergence
369:     CHECK_ERROR - the event number for error checking
370:                   (for use with profiling)

372:     Notes:
373:     In order to profile this section of code separately from the
374:     rest of the program, we register it as an "event" with
375:     PetscLogEventRegister() in the main program.  Then, we indicate
376:     the start and end of this event by respectively calling
377:         PetscLogEventBegin(CHECK_ERROR,u,x,b,0);
378:         PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
379:     Here, we specify the objects most closely associated with
380:     the event (the vectors u,x,b).  Such information is optional;
381:     we could instead just use 0 instead for all objects.
382: */
383: int CheckError(Vec u,Vec x,Vec b,int its,int CHECK_ERROR)
384: {
385:   PetscScalar none = -1.0;
386:   PetscReal   norm;
387:   int         ierr;

389:   PetscLogEventBegin(CHECK_ERROR,u,x,b,0);

391:   /*
392:      Compute error of the solution, using b as a work vector.
393:   */
394:   VecCopy(x,b);
395:   VecAXPY(&none,u,b);
396:   VecNorm(b,NORM_2,&norm);
397:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",norm,its);
398:   PetscLogEventEnd(CHECK_ERROR,u,x,b,0);
399:   return 0;
400: }
401: /* ------------------------------------------------------------- */
402: /*
403:    MyKSPMonitor - This is a user-defined routine for monitoring
404:    the SLES iterative solvers.

406:    Input Parameters:
407:      ksp   - iterative context
408:      n     - iteration number
409:      rnorm - 2-norm (preconditioned) residual value (may be estimated)
410:      dummy - optional user-defined monitor context (unused here)
411: */
412: int MyKSPMonitor(KSP ksp,int n,PetscReal rnorm,void *dummy)
413: {
414:   Vec      x;
415:   int      ierr;

417:   /* 
418:      Build the solution vector
419:   */
420:   KSPBuildSolution(ksp,PETSC_NULL,&x);

422:   /*
423:      Write the solution vector and residual norm to stdout.
424:       - PetscPrintf() handles output for multiprocessor jobs 
425:         by printing from only one processor in the communicator.
426:       - The parallel viewer PETSC_VIEWER_STDOUT_WORLD handles
427:         data from multiple processors so that the output
428:         is not jumbled.
429:   */
430:   PetscPrintf(PETSC_COMM_WORLD,"iteration %d solution vector:n",n);
431:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);
432:   PetscPrintf(PETSC_COMM_WORLD,"iteration %d KSP Residual norm %14.12e n",n,rnorm);
433:   return 0;
434: }