Actual source code: ex52.c

petsc-3.5.2 2014-09-08
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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;        /* linear system matrix */
 18:   KSP            ksp;      /* linear solver context */
 19:   PetscRandom    rctx;     /* random number generator context */
 20:   PetscReal      norm;     /* norm of solution error */
 21:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 23:   PetscBool      flg,flg_ilu,flg_ch;
 24:   PetscScalar    v;
 25:   PetscMPIInt    rank;
 26: #if defined(PETSC_USE_LOG)
 27:   PetscLogStage stage;
 28: #endif

 30:   PetscInitialize(&argc,&args,(char*)0,help);
 31:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 32:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 33:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 34:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35:          Compute the matrix and right-hand-side vector that define
 36:          the linear system, Ax = b.
 37:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 38:   MatCreate(PETSC_COMM_WORLD,&A);
 39:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 40:   MatSetFromOptions(A);
 41:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 42:   MatSeqAIJSetPreallocation(A,5,NULL);
 43:   MatSetUp(A);

 45:   /*
 46:      Currently, all PETSc parallel matrix formats are partitioned by
 47:      contiguous chunks of rows across the processors.  Determine which
 48:      rows of the matrix are locally owned.
 49:   */
 50:   MatGetOwnershipRange(A,&Istart,&Iend);

 52:   /*
 53:      Set matrix elements for the 2-D, five-point stencil in parallel.
 54:       - Each processor needs to insert only elements that it owns
 55:         locally (but any non-local elements will be sent to the
 56:         appropriate processor during matrix assembly).
 57:       - Always specify global rows and columns of matrix entries.

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

 64:    */
 65:   PetscLogStageRegister("Assembly", &stage);
 66:   PetscLogStagePush(stage);
 67:   for (Ii=Istart; Ii<Iend; Ii++) {
 68:     v = -1.0; i = Ii/n; j = Ii - i*n;
 69:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 70:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 71:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 72:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 73:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 74:   }

 76:   /*
 77:      Assemble matrix, using the 2-step process:
 78:        MatAssemblyBegin(), MatAssemblyEnd()
 79:      Computations can be done while messages are in transition
 80:      by placing code between these two statements.
 81:   */
 82:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 83:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 84:   PetscLogStagePop();

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

 89:   /*
 90:      Create parallel vectors.
 91:       - We form 1 vector from scratch and then duplicate as needed.
 92:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
 93:         in this example, we specify only the
 94:         vector's global dimension; the parallel partitioning is determined
 95:         at runtime.
 96:       - When solving a linear system, the vectors and matrices MUST
 97:         be partitioned accordingly.  PETSc automatically generates
 98:         appropriately partitioned matrices and vectors when MatCreate()
 99:         and VecCreate() are used with the same communicator.
100:       - The user can alternatively specify the local vector and matrix
101:         dimensions when more sophisticated partitioning is needed
102:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
103:         below).
104:   */
105:   VecCreate(PETSC_COMM_WORLD,&u);
106:   VecSetSizes(u,PETSC_DECIDE,m*n);
107:   VecSetFromOptions(u);
108:   VecDuplicate(u,&b);
109:   VecDuplicate(b,&x);

111:   /*
112:      Set exact solution; then compute right-hand-side vector.
113:      By default we use an exact solution of a vector with all
114:      elements of 1.0;  Alternatively, using the runtime option
115:      -random_sol forms a solution vector with random components.
116:   */
117:   PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);
118:   if (flg) {
119:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
120:     PetscRandomSetFromOptions(rctx);
121:     VecSetRandom(u,rctx);
122:     PetscRandomDestroy(&rctx);
123:   } else {
124:     VecSet(u,1.0);
125:   }
126:   MatMult(A,u,b);

128:   /*
129:      View the exact solution vector if desired
130:   */
131:   flg  = PETSC_FALSE;
132:   PetscOptionsGetBool(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:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

139:   /*
140:      Create linear solver context
141:   */
142:   KSPCreate(PETSC_COMM_WORLD,&ksp);
143:   KSPSetOperators(ksp,A,A);

145:   /*
146:     Example of how to use external package MUMPS
147:     Note: runtime options
148:           '-ksp_type preonly -pc_type lu -pc_factor_mat_solver_package mumps -mat_mumps_icntl_7 2 -mat_mumps_icntl_1 0.0'
149:           are equivalent to these procedural calls
150:   */
151: #if defined(PETSC_HAVE_MUMPS)
152:   Mat       F;
153:   flg    = PETSC_FALSE;
154:   flg_ch = PETSC_FALSE;
155:   PetscOptionsGetBool(NULL,"-use_mumps_lu",&flg,NULL);
156:   PetscOptionsGetBool(NULL,"-use_mumps_ch",&flg_ch,NULL);
157:   if (flg || flg_ch) {
158:     KSPSetType(ksp,KSPPREONLY);
159:     PC        pc;
160:     PetscInt  ival,icntl;
161:     PetscReal val;
162:     KSPGetPC(ksp,&pc);
163:     if (flg) {
164:       PCSetType(pc,PCLU);
165:     } else if (flg_ch) {
166:       MatSetOption(A,MAT_SPD,PETSC_TRUE); /* set MUMPS id%SYM=1 */
167:       PCSetType(pc,PCCHOLESKY);
168:     }
169:     PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);
170:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
171:     PCFactorGetMatrix(pc,&F);

173:     /* sequential ordering */
174:     icntl = 7; ival = 2;
175:     MatMumpsSetIcntl(F,icntl,ival);

177:     /* threshhold for row pivot detection */
178:     MatMumpsSetIcntl(F,24,1);
179:     icntl = 3; val = 1.e-6;
180:     MatMumpsSetCntl(F,icntl,val);

182:     /* compute determinant of A */
183:     MatMumpsSetIcntl(F,33,1);
184:   }
185: #endif

187:   /*
188:     Example of how to use external package SuperLU
189:     Note: runtime options
190:           '-ksp_type preonly -pc_type ilu -pc_factor_mat_solver_package superlu -mat_superlu_ilu_droptol 1.e-8'
191:           are equivalent to these procedual calls
192:   */
193: #if defined(PETSC_HAVE_SUPERLU)
194:   flg_ilu = PETSC_FALSE;
195:   flg     = PETSC_FALSE;
196:   PetscOptionsGetBool(NULL,"-use_superlu_lu",&flg,NULL);
197:   PetscOptionsGetBool(NULL,"-use_superlu_ilu",&flg_ilu,NULL);
198:   if (flg || flg_ilu) {
199:     KSPSetType(ksp,KSPPREONLY);
200:     PC  pc;
201:     Mat F;
202:     KSPGetPC(ksp,&pc);
203:     if (flg) {
204:       PCSetType(pc,PCLU);
205:     } else if (flg_ilu) {
206:       PCSetType(pc,PCILU);
207:     }
208:     PCFactorSetMatSolverPackage(pc,MATSOLVERSUPERLU);
209:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
210:     PCFactorGetMatrix(pc,&F);
211:     MatSuperluSetILUDropTol(F,1.e-8);
212:   }
213: #endif

215:   /*
216:     Example of how to use procedural calls that are equivalent to
217:           '-ksp_type preonly -pc_type lu/ilu -pc_factor_mat_solver_package petsc'
218:   */
219:   flg     = PETSC_FALSE;
220:   flg_ilu = PETSC_FALSE;
221:   flg_ch  = PETSC_FALSE;
222:   PetscOptionsGetBool(NULL,"-use_petsc_lu",&flg,NULL);
223:   PetscOptionsGetBool(NULL,"-use_petsc_ilu",&flg_ilu,NULL);
224:   PetscOptionsGetBool(NULL,"-use_petsc_ch",&flg_ch,NULL);
225:   if (flg || flg_ilu || flg_ch) {
226:     KSPSetType(ksp,KSPPREONLY);
227:     PC  pc;
228:     Mat F;
229:     KSPGetPC(ksp,&pc);
230:     if (flg) {
231:       PCSetType(pc,PCLU);
232:     } else if (flg_ilu) {
233:       PCSetType(pc,PCILU);
234:     } else if (flg_ch) {
235:       PCSetType(pc,PCCHOLESKY);
236:     }
237:     PCFactorSetMatSolverPackage(pc,MATSOLVERPETSC);
238:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
239:     PCFactorGetMatrix(pc,&F);

241:     /* Test MatGetDiagonal() */
242:     Vec diag;
243:     KSPSetUp(ksp);
244:     MatView(F,PETSC_VIEWER_STDOUT_WORLD);
245:     VecDuplicate(x,&diag);
246:     MatGetDiagonal(F,diag);
247:     VecView(diag,PETSC_VIEWER_STDOUT_WORLD);
248:     VecDestroy(&diag);
249:   }

251:   KSPSetFromOptions(ksp);

253:   /* Get info from matrix factors */
254:   KSPSetUp(ksp);

256: #if defined(PETSC_HAVE_MUMPS)
257:   if (flg || flg_ch) {
258:     PetscInt  icntl,infog34;
259:     PetscReal cntl,rinfo12,rinfo13;
260:     icntl = 3;
261:     MatMumpsGetCntl(F,icntl,&cntl);
262: 
263:     /* compute determinant */
264:     if (!rank) {
265:       MatMumpsGetInfog(F,34,&infog34);
266:       MatMumpsGetRinfog(F,12,&rinfo12);
267:       MatMumpsGetRinfog(F,13,&rinfo13);
268:       PetscPrintf(PETSC_COMM_SELF,"  Mumps row pivot threshhold = %g\n",cntl);
269:       PetscPrintf(PETSC_COMM_SELF,"  Mumps determinant = (%g, %g) * 2^%D \n",rinfo12,rinfo13,infog34);
270:     }
271:   }
272: #endif

274:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
275:                       Solve the linear system
276:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
277:   KSPSolve(ksp,b,x);

279:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280:                       Check solution and clean up
281:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
282:   VecAXPY(x,-1.0,u);
283:   VecNorm(x,NORM_2,&norm);
284:   KSPGetIterationNumber(ksp,&its);

286:   /*
287:      Print convergence information.  PetscPrintf() produces a single
288:      print statement from all processes that share a communicator.
289:      An alternative is PetscFPrintf(), which prints to a file.
290:   */
291:   if (norm < 1.e-12) {
292:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",norm,its);
293:   } else {
294:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
295:  }

297:   /*
298:      Free work space.  All PETSc objects should be destroyed when they
299:      are no longer needed.
300:   */
301:   KSPDestroy(&ksp);
302:   VecDestroy(&u);  VecDestroy(&x);
303:   VecDestroy(&b);  MatDestroy(&A);

305:   /*
306:      Always call PetscFinalize() before exiting a program.  This routine
307:        - finalizes the PETSc libraries as well as MPI
308:        - provides summary and diagnostic information if certain runtime
309:          options are chosen (e.g., -log_summary).
310:   */
311:   PetscFinalize();
312:   return 0;
313: }