Actual source code: ex2.c

petsc-master 2018-11-21
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  2: static char help[] = "Solves a linear system in parallel with KSP.\n\
  3: Input parameters include:\n\
  4:   -random_exact_sol : use a random exact solution vector\n\
  5:   -view_exact_sol   : write exact solution vector to stdout\n\
  6:   -m <mesh_x>       : number of mesh points in x-direction\n\
  7:   -n <mesh_n>       : number of mesh points in y-direction\n\n";

  9: /*T
 10:    Concepts: KSP^basic parallel example;
 11:    Concepts: KSP^Laplacian, 2d
 12:    Concepts: Laplacian, 2d
 13:    Processors: n
 14: T*/



 18: /*
 19:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 20:   automatically includes:
 21:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 22:      petscmat.h - matrices
 23:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 24:      petscviewer.h - viewers               petscpc.h  - preconditioners
 25: */
 26:  #include <petscksp.h>

 28: int main(int argc,char **args)
 29: {
 30:   Vec            x,b,u;    /* approx solution, RHS, exact solution */
 31:   Mat            A;        /* linear system matrix */
 32:   KSP            ksp;      /* linear solver context */
 33:   PetscRandom    rctx;     /* random number generator context */
 34:   PetscReal      norm;     /* norm of solution error */
 35:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 37:   PetscBool      flg = PETSC_FALSE;
 38:   PetscScalar    v;
 39: #if defined(PETSC_USE_LOG)
 40:   PetscLogStage stage;
 41: #endif

 43:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 44:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 47:          Compute the matrix and right-hand-side vector that define
 48:          the linear system, Ax = b.
 49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 50:   /*
 51:      Create parallel matrix, specifying only its global dimensions.
 52:      When using MatCreate(), the matrix format can be specified at
 53:      runtime. Also, the parallel partitioning of the matrix is
 54:      determined by PETSc at runtime.

 56:      Performance tuning note:  For problems of substantial size,
 57:      preallocation of matrix memory is crucial for attaining good
 58:      performance. See the matrix chapter of the users manual for details.
 59:   */
 60:   MatCreate(PETSC_COMM_WORLD,&A);
 61:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 62:   MatSetFromOptions(A);
 63:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 64:   MatSeqAIJSetPreallocation(A,5,NULL);
 65:   MatSeqSBAIJSetPreallocation(A,1,5,NULL);
 66:   MatMPISBAIJSetPreallocation(A,1,5,NULL,5,NULL);
 67:   MatMPISELLSetPreallocation(A,5,NULL,5,NULL);
 68:   MatSeqSELLSetPreallocation(A,5,NULL);

 70:   /*
 71:      Currently, all PETSc parallel matrix formats are partitioned by
 72:      contiguous chunks of rows across the processors.  Determine which
 73:      rows of the matrix are locally owned.
 74:   */
 75:   MatGetOwnershipRange(A,&Istart,&Iend);

 77:   /*
 78:      Set matrix elements for the 2-D, five-point stencil in parallel.
 79:       - Each processor needs to insert only elements that it owns
 80:         locally (but any non-local elements will be sent to the
 81:         appropriate processor during matrix assembly).
 82:       - Always specify global rows and columns of matrix entries.

 84:      Note: this uses the less common natural ordering that orders first
 85:      all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
 86:      instead of J = I +- m as you might expect. The more standard ordering
 87:      would first do all variables for y = h, then y = 2h etc.

 89:    */
 90:   PetscLogStageRegister("Assembly", &stage);
 91:   PetscLogStagePush(stage);
 92:   for (Ii=Istart; Ii<Iend; Ii++) {
 93:     v = -1.0; i = Ii/n; j = Ii - i*n;
 94:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 95:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 96:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 97:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 98:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
 99:   }

101:   /*
102:      Assemble matrix, using the 2-step process:
103:        MatAssemblyBegin(), MatAssemblyEnd()
104:      Computations can be done while messages are in transition
105:      by placing code between these two statements.
106:   */
107:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
108:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
109:   PetscLogStagePop();

111:   /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
112:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);

114:   /*
115:      Create parallel vectors.
116:       - We form 1 vector from scratch and then duplicate as needed.
117:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
118:         in this example, we specify only the
119:         vector's global dimension; the parallel partitioning is determined
120:         at runtime.
121:       - When solving a linear system, the vectors and matrices MUST
122:         be partitioned accordingly.  PETSc automatically generates
123:         appropriately partitioned matrices and vectors when MatCreate()
124:         and VecCreate() are used with the same communicator.
125:       - The user can alternatively specify the local vector and matrix
126:         dimensions when more sophisticated partitioning is needed
127:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
128:         below).
129:   */
130:   VecCreate(PETSC_COMM_WORLD,&u);
131:   VecSetSizes(u,PETSC_DECIDE,m*n);
132:   VecSetFromOptions(u);
133:   VecDuplicate(u,&b);
134:   VecDuplicate(b,&x);

136:   /*
137:      Set exact solution; then compute right-hand-side vector.
138:      By default we use an exact solution of a vector with all
139:      elements of 1.0;  Alternatively, using the runtime option
140:      -random_sol forms a solution vector with random components.
141:   */
142:   PetscOptionsGetBool(NULL,NULL,"-random_exact_sol",&flg,NULL);
143:   if (flg) {
144:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
145:     PetscRandomSetFromOptions(rctx);
146:     VecSetRandom(u,rctx);
147:     PetscRandomDestroy(&rctx);
148:   } else {
149:     VecSet(u,1.0);
150:   }
151:   MatMult(A,u,b);

153:   /*
154:      View the exact solution vector if desired
155:   */
156:   flg  = PETSC_FALSE;
157:   PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
158:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161:                 Create the linear solver and set various options
162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

164:   /*
165:      Create linear solver context
166:   */
167:   KSPCreate(PETSC_COMM_WORLD,&ksp);

169:   /*
170:      Set operators. Here the matrix that defines the linear system
171:      also serves as the preconditioning matrix.
172:   */
173:   KSPSetOperators(ksp,A,A);

175:   /*
176:      Set linear solver defaults for this problem (optional).
177:      - By extracting the KSP and PC contexts from the KSP context,
178:        we can then directly call any KSP and PC routines to set
179:        various options.
180:      - The following two statements are optional; all of these
181:        parameters could alternatively be specified at runtime via
182:        KSPSetFromOptions().  All of these defaults can be
183:        overridden at runtime, as indicated below.
184:   */
185:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
186:                           PETSC_DEFAULT);

188:   /*
189:     Set runtime options, e.g.,
190:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
191:     These options will override those specified above as long as
192:     KSPSetFromOptions() is called _after_ any other customization
193:     routines.
194:   */
195:   KSPSetFromOptions(ksp);

197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:                       Solve the linear system
199:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

201:   KSPSolve(ksp,b,x);

203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204:                       Check solution and clean up
205:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

207:   /*
208:      Check the error
209:   */
210:   VecAXPY(x,-1.0,u);
211:   VecNorm(x,NORM_2,&norm);
212:   KSPGetIterationNumber(ksp,&its);

214:   /*
215:      Print convergence information.  PetscPrintf() produces a single
216:      print statement from all processes that share a communicator.
217:      An alternative is PetscFPrintf(), which prints to a file.
218:   */
219:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

221:   /*
222:      Free work space.  All PETSc objects should be destroyed when they
223:      are no longer needed.
224:   */
225:   KSPDestroy(&ksp);
226:   VecDestroy(&u);  VecDestroy(&x);
227:   VecDestroy(&b);  MatDestroy(&A);

229:   /*
230:      Always call PetscFinalize() before exiting a program.  This routine
231:        - finalizes the PETSc libraries as well as MPI
232:        - provides summary and diagnostic information if certain runtime
233:          options are chosen (e.g., -log_view).
234:   */
235:   PetscFinalize();
236:   return ierr;
237: }


240: /*TEST

242:    build:
243:       requires: !complex !single

245:    test:
246:       suffix: chebyest_1
247:       args: -m 80 -n 80 -ksp_pc_side right -pc_type ksp -ksp_ksp_type chebyshev -ksp_ksp_max_it 5 -ksp_ksp_chebyshev_esteig 0.9,0,0,1.1 -ksp_monitor_short

249:    test:
250:       suffix: chebyest_2
251:       args: -m 80 -n 80 -ksp_pc_side right -pc_type ksp -ksp_ksp_type chebyshev -ksp_ksp_max_it 5 -ksp_ksp_chebyshev_esteig 0.9,0,0,1.1 -ksp_esteig_ksp_type cg -ksp_monitor_short 

253:    test:
254:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

256:    test:
257:       suffix: 2
258:       nsize: 2
259:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

261:    test:
262:       suffix: 3
263:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

265:    test:
266:       suffix: 4
267:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

269:    test:
270:       suffix: 5
271:       nsize: 2
272:       args: -ksp_monitor_short -m 5 -n 5 -mat_view draw -ksp_gmres_cgs_refinement_type refine_always -nox
273:       output_file: output/ex2_2.out

275:    test:
276:       suffix: bjacobi
277:       nsize: 4
278:       args: -pc_type bjacobi -pc_bjacobi_blocks 1 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

280:    test:
281:       suffix: bjacobi_2
282:       nsize: 4
283:       args: -pc_type bjacobi -pc_bjacobi_blocks 2 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres -ksp_view

285:    test:
286:       suffix: bjacobi_3
287:       nsize: 4
288:       args: -pc_type bjacobi -pc_bjacobi_blocks 4 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

290:    test:
291:       suffix: fbcgs
292:       args: -ksp_type fbcgs -pc_type ilu

294:    test:
295:       suffix: fbcgs_2
296:       nsize: 3
297:       args: -ksp_type fbcgsr -pc_type bjacobi

299:    test:
300:       suffix: groppcg
301:       args: -ksp_monitor_short -ksp_type groppcg -m 9 -n 9

303:    test:
304:       suffix: mkl_pardiso_cholesky
305:       requires: mkl_pardiso
306:       args: -ksp_type preonly -pc_type cholesky -mat_type sbaij -pc_factor_mat_solver_type mkl_pardiso

308:    test:
309:       suffix: mkl_pardiso_lu
310:       requires: mkl_pardiso
311:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mkl_pardiso

313:    test:
314:       suffix: pipebcgs
315:       args: -ksp_monitor_short -ksp_type pipebcgs -m 9 -n 9

317:    test:
318:       suffix: pipecg
319:       args: -ksp_monitor_short -ksp_type pipecg -m 9 -n 9

321:    test:
322:       suffix: pipecgrr
323:       args: -ksp_monitor_short -ksp_type pipecgrr -m 9 -n 9

325:    test:
326:       suffix: pipecr
327:       args: -ksp_monitor_short -ksp_type pipecr -m 9 -n 9

329:    test:
330:       suffix: pipelcg
331:       args: -ksp_monitor_short -ksp_type pipelcg -m 9 -n 9 -pc_type none -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmax 2
332:       filter: grep -v "sqrt breakdown in iteration"

334:    test:
335:       suffix: sell
336:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -m 9 -n 9 -mat_type sell

338:    test:
339:       requires: mumps
340:       suffix: sell_mumps
341:       args: -ksp_type preonly -m 9 -n 12 -mat_type sell -pc_type lu -pc_factor_mat_solver_type mumps -pc_factor_mat_ordering_type natural

343:    test:
344:       suffix: telescope
345:       nsize: 4
346:       args: -m 100 -n 100 -ksp_converged_reason -pc_type telescope -pc_telescope_reduction_factor 4 -telescope_pc_type bjacobi

348:    test:
349:       suffix: umfpack
350:       requires: suitesparse
351:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type umfpack

353:    test:
354:      suffix: pc_symmetric
355:      args: -m 10 -n 9 -ksp_converged_reason -ksp_type gmres -ksp_pc_side symmetric -pc_type cholesky
356: TEST*/