Actual source code: ex52.c

petsc-3.4.4 2014-03-13
  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: #if defined(PETSC_USE_LOG)
 26:   PetscLogStage stage;
 27: #endif

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

 42:   /*
 43:      Currently, all PETSc parallel matrix formats are partitioned by
 44:      contiguous chunks of rows across the processors.  Determine which
 45:      rows of the matrix are locally owned.
 46:   */
 47:   MatGetOwnershipRange(A,&Istart,&Iend);

 49:   /*
 50:      Set matrix elements for the 2-D, five-point stencil in parallel.
 51:       - Each processor needs to insert only elements that it owns
 52:         locally (but any non-local elements will be sent to the
 53:         appropriate processor during matrix assembly).
 54:       - Always specify global rows and columns of matrix entries.

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

 61:    */
 62:   PetscLogStageRegister("Assembly", &stage);
 63:   PetscLogStagePush(stage);
 64:   for (Ii=Istart; Ii<Iend; Ii++) {
 65:     v = -1.0; i = Ii/n; j = Ii - i*n;
 66:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 67:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 68:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 69:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 70:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 71:   }

 73:   /*
 74:      Assemble matrix, using the 2-step process:
 75:        MatAssemblyBegin(), MatAssemblyEnd()
 76:      Computations can be done while messages are in transition
 77:      by placing code between these two statements.
 78:   */
 79:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 80:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 81:   PetscLogStagePop();

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

 86:   /*
 87:      Create parallel vectors.
 88:       - We form 1 vector from scratch and then duplicate as needed.
 89:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
 90:         in this example, we specify only the
 91:         vector's global dimension; the parallel partitioning is determined
 92:         at runtime.
 93:       - When solving a linear system, the vectors and matrices MUST
 94:         be partitioned accordingly.  PETSc automatically generates
 95:         appropriately partitioned matrices and vectors when MatCreate()
 96:         and VecCreate() are used with the same communicator.
 97:       - The user can alternatively specify the local vector and matrix
 98:         dimensions when more sophisticated partitioning is needed
 99:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
100:         below).
101:   */
102:   VecCreate(PETSC_COMM_WORLD,&u);
103:   VecSetSizes(u,PETSC_DECIDE,m*n);
104:   VecSetFromOptions(u);
105:   VecDuplicate(u,&b);
106:   VecDuplicate(b,&x);

108:   /*
109:      Set exact solution; then compute right-hand-side vector.
110:      By default we use an exact solution of a vector with all
111:      elements of 1.0;  Alternatively, using the runtime option
112:      -random_sol forms a solution vector with random components.
113:   */
114:   PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);
115:   if (flg) {
116:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
117:     PetscRandomSetFromOptions(rctx);
118:     VecSetRandom(u,rctx);
119:     PetscRandomDestroy(&rctx);
120:   } else {
121:     VecSet(u,1.0);
122:   }
123:   MatMult(A,u,b);

125:   /*
126:      View the exact solution vector if desired
127:   */
128:   flg  = PETSC_FALSE;
129:   PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);
130:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:                 Create the linear solver and set various options
134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

136:   /*
137:      Create linear solver context
138:   */
139:   KSPCreate(PETSC_COMM_WORLD,&ksp);
140:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

142:   /*
143:     Example of how to use external package MUMPS
144:     Note: runtime options
145:           '-ksp_type preonly -pc_type lu -pc_factor_mat_solver_package mumps -mat_mumps_icntl_7 2 -mat_mumps_icntl_1 0.0'
146:           are equivalent to these procedural calls
147:   */
148: #if defined(PETSC_HAVE_MUMPS)
149:   flg    = PETSC_FALSE;
150:   flg_ch = PETSC_FALSE;
151:   PetscOptionsGetBool(NULL,"-use_mumps_lu",&flg,NULL);
152:   PetscOptionsGetBool(NULL,"-use_mumps_ch",&flg_ch,NULL);
153:   if (flg || flg_ch) {
154:     KSPSetType(ksp,KSPPREONLY);
155:     PC        pc;
156:     Mat       F;
157:     PetscInt  ival,icntl;
158:     PetscReal val;
159:     KSPGetPC(ksp,&pc);
160:     if (flg) {
161:       PCSetType(pc,PCLU);
162:     } else if (flg_ch) {
163:       MatSetOption(A,MAT_SPD,PETSC_TRUE); /* set MUMPS id%SYM=1 */
164:       PCSetType(pc,PCCHOLESKY);
165:     }
166:     PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);
167:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
168:     PCFactorGetMatrix(pc,&F);
169:     icntl = 7; ival = 2;
170:     MatMumpsSetIcntl(F,icntl,ival);
171:     icntl = 1; val = 0.0;
172:     MatMumpsSetCntl(F,icntl,val);
173:   }
174: #endif

176:   /*
177:     Example of how to use external package SuperLU
178:     Note: runtime options
179:           '-ksp_type preonly -pc_type ilu -pc_factor_mat_solver_package superlu -mat_superlu_ilu_droptol 1.e-8'
180:           are equivalent to these procedual calls
181:   */
182: #if defined(PETSC_HAVE_SUPERLU)
183:   flg_ilu = PETSC_FALSE;
184:   flg     = PETSC_FALSE;
185:   PetscOptionsGetBool(NULL,"-use_superlu_lu",&flg,NULL);
186:   PetscOptionsGetBool(NULL,"-use_superlu_ilu",&flg_ilu,NULL);
187:   if (flg || flg_ilu) {
188:     KSPSetType(ksp,KSPPREONLY);
189:     PC  pc;
190:     Mat F;
191:     KSPGetPC(ksp,&pc);
192:     if (flg) {
193:       PCSetType(pc,PCLU);
194:     } else if (flg_ilu) {
195:       PCSetType(pc,PCILU);
196:     }
197:     PCFactorSetMatSolverPackage(pc,MATSOLVERSUPERLU);
198:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
199:     PCFactorGetMatrix(pc,&F);
200:     MatSuperluSetILUDropTol(F,1.e-8);
201:   }
202: #endif

204:   /*
205:     Example of how to use procedural calls that are equivalent to
206:           '-ksp_type preonly -pc_type lu/ilu -pc_factor_mat_solver_package petsc'
207:   */
208:   flg     = PETSC_FALSE;
209:   flg_ilu = PETSC_FALSE;
210:   flg_ch  = PETSC_FALSE;
211:   PetscOptionsGetBool(NULL,"-use_petsc_lu",&flg,NULL);
212:   PetscOptionsGetBool(NULL,"-use_petsc_ilu",&flg_ilu,NULL);
213:   PetscOptionsGetBool(NULL,"-use_petsc_ch",&flg_ch,NULL);
214:   if (flg || flg_ilu || flg_ch) {
215:     KSPSetType(ksp,KSPPREONLY);
216:     PC  pc;
217:     Mat F;
218:     KSPGetPC(ksp,&pc);
219:     if (flg) {
220:       PCSetType(pc,PCLU);
221:     } else if (flg_ilu) {
222:       PCSetType(pc,PCILU);
223:     } else if (flg_ch) {
224:       PCSetType(pc,PCCHOLESKY);
225:     }
226:     PCFactorSetMatSolverPackage(pc,MATSOLVERPETSC);
227:     PCFactorSetUpMatSolverPackage(pc); /* call MatGetFactor() to create F */
228:     PCFactorGetMatrix(pc,&F);

230:     /* Test MatGetDiagonal() */
231:     Vec diag;
232:     KSPSetUp(ksp);
233:     MatView(F,PETSC_VIEWER_STDOUT_WORLD);
234:     VecDuplicate(x,&diag);
235:     MatGetDiagonal(F,diag);
236:     VecView(diag,PETSC_VIEWER_STDOUT_WORLD);
237:     VecDestroy(&diag);
238:   }

240:   KSPSetFromOptions(ksp);

242:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243:                       Solve the linear system
244:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

246:   KSPSolve(ksp,b,x);

248:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
249:                       Check solution and clean up
250:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

252:   /*
253:      Check the error
254:   */
255:   VecAXPY(x,-1.0,u);
256:   VecNorm(x,NORM_2,&norm);
257:   KSPGetIterationNumber(ksp,&its);

259:   /*
260:      Print convergence information.  PetscPrintf() produces a single
261:      print statement from all processes that share a communicator.
262:      An alternative is PetscFPrintf(), which prints to a file.
263:   */
264:   if (norm < 1.e-12) {
265:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",norm,its);
266:   } else {
267:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G iterations %D\n",
268:                      norm,its);
269:  }

271:   /*
272:      Free work space.  All PETSc objects should be destroyed when they
273:      are no longer needed.
274:   */
275:   KSPDestroy(&ksp);
276:   VecDestroy(&u);  VecDestroy(&x);
277:   VecDestroy(&b);  MatDestroy(&A);

279:   /*
280:      Always call PetscFinalize() before exiting a program.  This routine
281:        - finalizes the PETSc libraries as well as MPI
282:        - provides summary and diagnostic information if certain runtime
283:          options are chosen (e.g., -log_summary).
284:   */
285:   PetscFinalize();
286:   return 0;
287: }