Actual source code: ex52.c

petsc-3.6.1 2015-07-22
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  2: static char help[] = "Solves a linear system in parallel with KSP. Modified from ex2.c \n\
  3:                       Illustrate how to use external packages MUMPS and SUPERLU \n\
  4: Input parameters include:\n\
  5:   -random_exact_sol : use a random exact solution vector\n\
  6:   -view_exact_sol   : write exact solution vector to stdout\n\
  7:   -m <mesh_x>       : number of mesh points in x-direction\n\
  8:   -n <mesh_n>       : number of mesh points in y-direction\n\n";

 10: #include <petscksp.h>

 14: int main(int argc,char **args)
 15: {
 16:   Vec            x,b,u;    /* approx solution, RHS, exact solution */
 17:   Mat            A,F;
 18:   KSP            ksp;      /* linear solver context */
 19:   PC             pc;
 20:   PetscRandom    rctx;     /* random number generator context */
 21:   PetscReal      norm;     /* norm of solution error */
 22:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 24:   PetscBool      flg,flg_ilu,flg_ch;
 25: #if defined(PETSC_HAVE_MUMPS)
 26:   PetscBool      flg_mumps,flg_mumps_ch;
 27: #endif
 28: #if defined(PETSC_HAVE_SUPERLU) || defined(PETSC_HAVE_SUPERLU_DIST)
 29:   PetscBool      flg_superlu;
 30: #endif
 31:   PetscScalar    v;
 32:   PetscMPIInt    rank,size;
 33: #if defined(PETSC_USE_LOG)
 34:   PetscLogStage  stage;
 35: #endif

 37:   PetscInitialize(&argc,&args,(char*)0,help);
 38:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 39:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 40:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 41:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 42:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43:          Compute the matrix and right-hand-side vector that define
 44:          the linear system, Ax = b.
 45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 46:   MatCreate(PETSC_COMM_WORLD,&A);
 47:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 48:   MatSetFromOptions(A);
 49:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 50:   MatSeqAIJSetPreallocation(A,5,NULL);
 51:   MatSetUp(A);

 53:   /*
 54:      Currently, all PETSc parallel matrix formats are partitioned by
 55:      contiguous chunks of rows across the processors.  Determine which
 56:      rows of the matrix are locally owned.
 57:   */
 58:   MatGetOwnershipRange(A,&Istart,&Iend);

 60:   /*
 61:      Set matrix elements for the 2-D, five-point stencil in parallel.
 62:       - Each processor needs to insert only elements that it owns
 63:         locally (but any non-local elements will be sent to the
 64:         appropriate processor during matrix assembly).
 65:       - Always specify global rows and columns of matrix entries.

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

 72:    */
 73:   PetscLogStageRegister("Assembly", &stage);
 74:   PetscLogStagePush(stage);
 75:   for (Ii=Istart; Ii<Iend; Ii++) {
 76:     v = -1.0; i = Ii/n; j = Ii - i*n;
 77:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 78:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 79:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 80:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 81:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 82:   }

 84:   /*
 85:      Assemble matrix, using the 2-step process:
 86:        MatAssemblyBegin(), MatAssemblyEnd()
 87:      Computations can be done while messages are in transition
 88:      by placing code between these two statements.
 89:   */
 90:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 91:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 92:   PetscLogStagePop();

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

 97:   /*
 98:      Create parallel vectors.
 99:       - We form 1 vector from scratch and then duplicate as needed.
100:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
101:         in this example, we specify only the
102:         vector's global dimension; the parallel partitioning is determined
103:         at runtime.
104:       - When solving a linear system, the vectors and matrices MUST
105:         be partitioned accordingly.  PETSc automatically generates
106:         appropriately partitioned matrices and vectors when MatCreate()
107:         and VecCreate() are used with the same communicator.
108:       - The user can alternatively specify the local vector and matrix
109:         dimensions when more sophisticated partitioning is needed
110:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
111:         below).
112:   */
113:   VecCreate(PETSC_COMM_WORLD,&u);
114:   VecSetSizes(u,PETSC_DECIDE,m*n);
115:   VecSetFromOptions(u);
116:   VecDuplicate(u,&b);
117:   VecDuplicate(b,&x);

119:   /*
120:      Set exact solution; then compute right-hand-side vector.
121:      By default we use an exact solution of a vector with all
122:      elements of 1.0;  Alternatively, using the runtime option
123:      -random_sol forms a solution vector with random components.
124:   */
125:   PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);
126:   if (flg) {
127:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
128:     PetscRandomSetFromOptions(rctx);
129:     VecSetRandom(u,rctx);
130:     PetscRandomDestroy(&rctx);
131:   } else {
132:     VecSet(u,1.0);
133:   }
134:   MatMult(A,u,b);

136:   /*
137:      View the exact solution vector if desired
138:   */
139:   flg  = PETSC_FALSE;
140:   PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);
141:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:                 Create the linear solver and set various options
145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

147:   /*
148:      Create linear solver context
149:   */
150:   KSPCreate(PETSC_COMM_WORLD,&ksp);
151:   KSPSetOperators(ksp,A,A);

153:   /*
154:     Example of how to use external package MUMPS
155:     Note: runtime options
156:           '-ksp_type preonly -pc_type lu -pc_factor_mat_solver_package mumps -mat_mumps_icntl_7 2 -mat_mumps_icntl_1 0.0'
157:           are equivalent to these procedural calls
158:   */
159: #if defined(PETSC_HAVE_MUMPS)
160:   flg_mumps    = PETSC_FALSE;
161:   flg_mumps_ch = PETSC_FALSE;
162:   PetscOptionsGetBool(NULL,"-use_mumps_lu",&flg_mumps,NULL);
163:   PetscOptionsGetBool(NULL,"-use_mumps_ch",&flg_mumps_ch,NULL);
164:   if (flg_mumps || flg_mumps_ch) {
165:     KSPSetType(ksp,KSPPREONLY);
166:     PetscInt  ival,icntl;
167:     PetscReal val;
168:     KSPGetPC(ksp,&pc);
169:     if (flg_mumps) {
170:       PCSetType(pc,PCLU);
171:     } else if (flg_mumps_ch) {
172:       MatSetOption(A,MAT_SPD,PETSC_TRUE); /* set MUMPS id%SYM=1 */
173:       PCSetType(pc,PCCHOLESKY);
174:     }
175:     PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);
176:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
177:     PCFactorGetMatrix(pc,&F);

179:     /* sequential ordering */
180:     icntl = 7; ival = 2;
181:     MatMumpsSetIcntl(F,icntl,ival);

183:     /* threshhold for row pivot detection */
184:     MatMumpsSetIcntl(F,24,1);
185:     icntl = 3; val = 1.e-6;
186:     MatMumpsSetCntl(F,icntl,val);

188:     /* compute determinant of A */
189:     MatMumpsSetIcntl(F,33,1);
190:   }
191: #endif

193:   /*
194:     Example of how to use external package SuperLU
195:     Note: runtime options
196:           '-ksp_type preonly -pc_type ilu -pc_factor_mat_solver_package superlu -mat_superlu_ilu_droptol 1.e-8'
197:           are equivalent to these procedual calls
198:   */
199: #if defined(PETSC_HAVE_SUPERLU) || defined(PETSC_HAVE_SUPERLU_DIST)
200:   flg_ilu     = PETSC_FALSE;
201:   flg_superlu = PETSC_FALSE;
202:   PetscOptionsGetBool(NULL,"-use_superlu_lu",&flg_superlu,NULL);
203:   PetscOptionsGetBool(NULL,"-use_superlu_ilu",&flg_ilu,NULL);
204:   if (flg_superlu || flg_ilu) {
205:     KSPSetType(ksp,KSPPREONLY);
206:     KSPGetPC(ksp,&pc);
207:     if (flg_superlu) {
208:       PCSetType(pc,PCLU);
209:     } else if (flg_ilu) {
210:       PCSetType(pc,PCILU);
211:     }
212:     if (size == 1) {
213: #if !defined(PETSC_HAVE_SUPERLU)
214:       SETERRQ(PETSC_COMM_WORLD,1,"This test requires SUPERLU");
215: #endif
216:       PCFactorSetMatSolverPackage(pc,MATSOLVERSUPERLU);
217:     } else {
218: #if !defined(PETSC_HAVE_SUPERLU_DIST)
219:       SETERRQ(PETSC_COMM_WORLD,1,"This test requires SUPERLU_DIST");
220: #endif
221:       PCFactorSetMatSolverPackage(pc,MATSOLVERSUPERLU_DIST);
222:     }
223:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
224:     PCFactorGetMatrix(pc,&F);
225: #if defined(PETSC_HAVE_SUPERLU)
226:     if (size == 1) {
227:       MatSuperluSetILUDropTol(F,1.e-8);
228:     }
229: #endif
230:   }
231: #endif

233:   /*
234:     Example of how to use procedural calls that are equivalent to
235:           '-ksp_type preonly -pc_type lu/ilu -pc_factor_mat_solver_package petsc'
236:   */
237:   flg     = PETSC_FALSE;
238:   flg_ilu = PETSC_FALSE;
239:   flg_ch  = PETSC_FALSE;
240:   PetscOptionsGetBool(NULL,"-use_petsc_lu",&flg,NULL);
241:   PetscOptionsGetBool(NULL,"-use_petsc_ilu",&flg_ilu,NULL);
242:   PetscOptionsGetBool(NULL,"-use_petsc_ch",&flg_ch,NULL);
243:   if (flg || flg_ilu || flg_ch) {
244:     KSPSetType(ksp,KSPPREONLY);
245:     KSPGetPC(ksp,&pc);
246:     if (flg) {
247:       PCSetType(pc,PCLU);
248:     } else if (flg_ilu) {
249:       PCSetType(pc,PCILU);
250:     } else if (flg_ch) {
251:       PCSetType(pc,PCCHOLESKY);
252:     }
253:     PCFactorSetMatSolverPackage(pc,MATSOLVERPETSC);
254:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
255:     PCFactorGetMatrix(pc,&F);
256: 
257:     /* Test MatGetDiagonal() */
258:     Vec diag;
259:     KSPSetUp(ksp);
260:     VecDuplicate(x,&diag);
261:     MatGetDiagonal(F,diag);
262:     /* VecView(diag,PETSC_VIEWER_STDOUT_WORLD); */
263:     VecDestroy(&diag);
264:   }

266:   KSPSetFromOptions(ksp);

268:   /* Get info from matrix factors */
269:   KSPSetUp(ksp);

271: #if defined(PETSC_HAVE_MUMPS)
272:   if (flg_mumps || flg_mumps_ch) {
273:     PetscInt  icntl,infog34;
274:     PetscReal cntl,rinfo12,rinfo13;
275:     icntl = 3;
276:     MatMumpsGetCntl(F,icntl,&cntl);
277: 
278:     /* compute determinant */
279:     if (!rank) {
280:       MatMumpsGetInfog(F,34,&infog34);
281:       MatMumpsGetRinfog(F,12,&rinfo12);
282:       MatMumpsGetRinfog(F,13,&rinfo13);
283:       PetscPrintf(PETSC_COMM_SELF,"  Mumps row pivot threshhold = %g\n",cntl);
284:       PetscPrintf(PETSC_COMM_SELF,"  Mumps determinant = (%g, %g) * 2^%D \n",rinfo12,rinfo13,infog34);
285:     }
286:   }
287: #endif

289:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
290:                       Solve the linear system
291:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
292:   KSPSolve(ksp,b,x);

294:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
295:                       Check solution and clean up
296:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
297:   VecAXPY(x,-1.0,u);
298:   VecNorm(x,NORM_2,&norm);
299:   KSPGetIterationNumber(ksp,&its);

301:   /*
302:      Print convergence information.  PetscPrintf() produces a single
303:      print statement from all processes that share a communicator.
304:      An alternative is PetscFPrintf(), which prints to a file.
305:   */
306:   if (norm < 1.e-12) {
307:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",norm,its);
308:   } else {
309:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
310:  }

312:   /*
313:      Free work space.  All PETSc objects should be destroyed when they
314:      are no longer needed.
315:   */
316:   KSPDestroy(&ksp);
317:   VecDestroy(&u);  VecDestroy(&x);
318:   VecDestroy(&b);  MatDestroy(&A);

320:   /*
321:      Always call PetscFinalize() before exiting a program.  This routine
322:        - finalizes the PETSc libraries as well as MPI
323:        - provides summary and diagnostic information if certain runtime
324:          options are chosen (e.g., -log_summary).
325:   */
326:   PetscFinalize();
327:   return 0;
328: }