Actual source code: ex2.c


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

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

 15: /*
 16:   Include "petscksp.h" so that we can use KSP solvers.
 17: */
 18: #include <petscksp.h>

 20: int main(int argc,char **args)
 21: {
 22:   Vec            x,b,u;    /* approx solution, RHS, exact solution */
 23:   Mat            A;        /* linear system matrix */
 24:   KSP            ksp;      /* linear solver context */
 25:   PetscReal      norm;     /* norm of solution error */
 26:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 27:   PetscBool      flg;
 28:   PetscScalar    v;

 30:   PetscInitialize(&argc,&args,(char*)0,help);
 31:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 33:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 34:          Compute the matrix and right-hand-side vector that define
 35:          the linear system, Ax = b.
 36:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 37:   /*
 38:      Create parallel matrix, specifying only its global dimensions.
 39:      When using MatCreate(), the matrix format can be specified at
 40:      runtime. Also, the parallel partitioning of the matrix is
 41:      determined by PETSc at runtime.

 43:      Performance tuning note:  For problems of substantial size,
 44:      preallocation of matrix memory is crucial for attaining good
 45:      performance. See the matrix chapter of the users manual for details.
 46:   */
 47:   MatCreate(PETSC_COMM_WORLD,&A);
 48:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 49:   MatSetFromOptions(A);
 50:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 51:   MatSeqAIJSetPreallocation(A,5,NULL);
 52:   MatSeqSBAIJSetPreallocation(A,1,5,NULL);
 53:   MatMPISBAIJSetPreallocation(A,1,5,NULL,5,NULL);
 54:   MatMPISELLSetPreallocation(A,5,NULL,5,NULL);
 55:   MatSeqSELLSetPreallocation(A,5,NULL);

 57:   /*
 58:      Currently, all PETSc parallel matrix formats are partitioned by
 59:      contiguous chunks of rows across the processors.  Determine which
 60:      rows of the matrix are locally owned.
 61:   */
 62:   MatGetOwnershipRange(A,&Istart,&Iend);

 64:   /*
 65:      Set matrix elements for the 2-D, five-point stencil in parallel.
 66:       - Each processor needs to insert only elements that it owns
 67:         locally (but any non-local elements will be sent to the
 68:         appropriate processor during matrix assembly).
 69:       - Always specify global rows and columns of matrix entries.

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

 76:    */
 77:   for (Ii=Istart; Ii<Iend; Ii++) {
 78:     v = -1.0; i = Ii/n; j = Ii - i*n;
 79:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 80:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 81:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 82:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 83:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
 84:   }

 86:   /*
 87:      Assemble matrix, using the 2-step process:
 88:        MatAssemblyBegin(), MatAssemblyEnd()
 89:      Computations can be done while messages are in transition
 90:      by placing code between these two statements.
 91:   */
 92:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 93:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

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

 98:   /*
 99:      Create parallel vectors.
100:       - We form 1 vector from scratch and then duplicate as needed.
101:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
102:         in this example, we specify only the
103:         vector's global dimension; the parallel partitioning is determined
104:         at runtime.
105:       - When solving a linear system, the vectors and matrices MUST
106:         be partitioned accordingly.  PETSc automatically generates
107:         appropriately partitioned matrices and vectors when MatCreate()
108:         and VecCreate() are used with the same communicator.
109:       - The user can alternatively specify the local vector and matrix
110:         dimensions when more sophisticated partitioning is needed
111:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
112:         below).
113:   */
114:   VecCreate(PETSC_COMM_WORLD,&u);
115:   VecSetSizes(u,PETSC_DECIDE,m*n);
116:   VecSetFromOptions(u);
117:   VecDuplicate(u,&b);
118:   VecDuplicate(b,&x);

120:   /*
121:      Set exact solution; then compute right-hand-side vector.
122:      By default we use an exact solution of a vector with all
123:      elements of 1.0;
124:   */
125:   VecSet(u,1.0);
126:   MatMult(A,u,b);

128:   /*
129:      View the exact solution vector if desired
130:   */
131:   flg  = PETSC_FALSE;
132:   PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
133:   if (flg) VecView(u,PETSC_VIEWER_STDOUT_WORLD);

135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136:                 Create the linear solver and set various options
137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138:   KSPCreate(PETSC_COMM_WORLD,&ksp);

140:   /*
141:      Set operators. Here the matrix that defines the linear system
142:      also serves as the preconditioning matrix.
143:   */
144:   KSPSetOperators(ksp,A,A);

146:   /*
147:      Set linear solver defaults for this problem (optional).
148:      - By extracting the KSP and PC contexts from the KSP context,
149:        we can then directly call any KSP and PC routines to set
150:        various options.
151:      - The following two statements are optional; all of these
152:        parameters could alternatively be specified at runtime via
153:        KSPSetFromOptions().  All of these defaults can be
154:        overridden at runtime, as indicated below.
155:   */
156:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,PETSC_DEFAULT);

158:   /*
159:     Set runtime options, e.g.,
160:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
161:     These options will override those specified above as long as
162:     KSPSetFromOptions() is called _after_ any other customization
163:     routines.
164:   */
165:   KSPSetFromOptions(ksp);

167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168:                       Solve the linear system
169:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

171:   KSPSolve(ksp,b,x);

173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174:                       Check the solution and clean up
175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
176:   VecAXPY(x,-1.0,u);
177:   VecNorm(x,NORM_2,&norm);
178:   KSPGetIterationNumber(ksp,&its);

180:   /*
181:      Print convergence information.  PetscPrintf() produces a single
182:      print statement from all processes that share a communicator.
183:      An alternative is PetscFPrintf(), which prints to a file.
184:   */
185:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

187:   /*
188:      Free work space.  All PETSc objects should be destroyed when they
189:      are no longer needed.
190:   */
191:   KSPDestroy(&ksp);
192:   VecDestroy(&u));  PetscCall(VecDestroy(&x);
193:   VecDestroy(&b));  PetscCall(MatDestroy(&A);

195:   /*
196:      Always call PetscFinalize() before exiting a program.  This routine
197:        - finalizes the PETSc libraries as well as MPI
198:        - provides summary and diagnostic information if certain runtime
199:          options are chosen (e.g., -log_view).
200:   */
201:   PetscFinalize();
202:   return 0;
203: }

205: /*TEST

207:    build:
208:       requires: !single

210:    test:
211:       suffix: chebyest_1
212:       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

214:    test:
215:       suffix: chebyest_2
216:       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

218:    test:
219:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

221:    test:
222:       suffix: 2
223:       nsize: 2
224:       args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always

226:    test:
227:       suffix: 3
228:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

230:    test:
231:       suffix: 4
232:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

234:    test:
235:       suffix: 5
236:       nsize: 2
237:       args: -ksp_monitor_short -m 5 -n 5 -mat_view draw -ksp_gmres_cgs_refinement_type refine_always -nox
238:       output_file: output/ex2_2.out

240:    test:
241:       suffix: bjacobi
242:       nsize: 4
243:       args: -pc_type bjacobi -pc_bjacobi_blocks 1 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

245:    test:
246:       suffix: bjacobi_2
247:       nsize: 4
248:       args: -pc_type bjacobi -pc_bjacobi_blocks 2 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres -ksp_view

250:    test:
251:       suffix: bjacobi_3
252:       nsize: 4
253:       args: -pc_type bjacobi -pc_bjacobi_blocks 4 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres

255:    test:
256:       suffix: qmrcgs
257:       args: -ksp_type qmrcgs -pc_type ilu
258:       output_file: output/ex2_fbcgs.out

260:    test:
261:       suffix: qmrcgs_2
262:       nsize: 3
263:       args: -ksp_type qmrcgs -pc_type bjacobi
264:       output_file: output/ex2_fbcgs_2.out

266:    test:
267:       suffix: fbcgs
268:       args: -ksp_type fbcgs -pc_type ilu

270:    test:
271:       suffix: fbcgs_2
272:       nsize: 3
273:       args: -ksp_type fbcgsr -pc_type bjacobi

275:    test:
276:       suffix: groppcg
277:       args: -ksp_monitor_short -ksp_type groppcg -m 9 -n 9

279:    test:
280:       suffix: mkl_pardiso_cholesky
281:       requires: mkl_pardiso
282:       args: -ksp_type preonly -pc_type cholesky -mat_type sbaij -pc_factor_mat_solver_type mkl_pardiso

284:    test:
285:       suffix: mkl_pardiso_lu
286:       requires: mkl_pardiso
287:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mkl_pardiso

289:    test:
290:       suffix: pipebcgs
291:       args: -ksp_monitor_short -ksp_type pipebcgs -m 9 -n 9

293:    test:
294:       suffix: pipecg
295:       args: -ksp_monitor_short -ksp_type pipecg -m 9 -n 9

297:    test:
298:       suffix: pipecgrr
299:       args: -ksp_monitor_short -ksp_type pipecgrr -m 9 -n 9

301:    test:
302:       suffix: pipecr
303:       args: -ksp_monitor_short -ksp_type pipecr -m 9 -n 9

305:    test:
306:       suffix: pipelcg
307:       args: -ksp_monitor_short -ksp_type pipelcg -m 9 -n 9 -pc_type none -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmax 2
308:       filter: grep -v "sqrt breakdown in iteration"

310:    test:
311:       suffix: sell
312:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -m 9 -n 9 -mat_type sell

314:    test:
315:       requires: mumps
316:       suffix: sell_mumps
317:       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

319:    test:
320:       suffix: telescope
321:       nsize: 4
322:       args: -m 100 -n 100 -ksp_converged_reason -pc_type telescope -pc_telescope_reduction_factor 4 -telescope_pc_type bjacobi

324:    test:
325:       suffix: umfpack
326:       requires: suitesparse
327:       args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type umfpack

329:    test:
330:       suffix: spqr
331:       requires: suitesparse
332:       args: -ksp_type preonly -pc_type qr -pc_factor_mat_solver_type spqr

334:    test:
335:      suffix: pc_symmetric
336:      args: -m 10 -n 9 -ksp_converged_reason -ksp_type gmres -ksp_pc_side symmetric -pc_type cholesky

338:    test:
339:       suffix: pipeprcg
340:       args: -ksp_monitor_short -ksp_type pipeprcg -m 9 -n 9

342:    test:
343:       suffix: pipeprcg_rcw
344:       args: -ksp_monitor_short -ksp_type pipeprcg -recompute_w false -m 9 -n 9

346:    test:
347:       suffix: pipecg2
348:       args: -ksp_monitor_short -ksp_type pipecg2 -m 9 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}

350:    test:
351:       suffix: pipecg2_2
352:       nsize: 4
353:       args: -ksp_monitor_short -ksp_type pipecg2 -m 15 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}

355:    test:
356:       suffix: hpddm
357:       nsize: 4
358:       requires: hpddm
359:       filter: sed -e "s/ iterations 9/ iterations 8/g"
360:       args: -ksp_converged_reason -ksp_type hpddm -ksp_hpddm_precision {{single double}shared output} -ksp_pc_side {{left right}shared output}

362:  TEST*/