Actual source code: ex5.c

  2: static char help[] = "Solves two linear systems in parallel with KSP.  The code\n\
  3: illustrates repeated solution of linear systems with the same preconditioner\n\
  4: method but different matrices (having the same nonzero structure).  The code\n\
  5: also uses multiple profiling stages.  Input arguments are\n\
  6:   -m <size> : problem size\n\
  7:   -mat_nonsym : use nonsymmetric matrix (default is symmetric)\n\n";

  9: /*T
 10:    Concepts: KSP^repeatedly solving linear systems;
 11:    Concepts: PetscLog^profiling multiple stages of code;
 12:    Processors: n
 13: T*/

 15: /* 
 16:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 17:   automatically includes:
 18:      petsc.h       - base PETSc routines   petscvec.h - vectors
 19:      petscsys.h    - system routines       petscmat.h - matrices
 20:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 21:      petscviewer.h - viewers               petscpc.h  - preconditioners
 22: */
 23:  #include petscksp.h

 27: int main(int argc,char **args)
 28: {
 29:   KSP            ksp;             /* linear solver context */
 30:   Mat            C;                /* matrix */
 31:   Vec            x,u,b;          /* approx solution, RHS, exact solution */
 32:   PetscReal      norm;             /* norm of solution error */
 33:   PetscScalar    v,none = -1.0;
 34:   PetscInt       I,J,ldim,low,high,iglobal,Istart,Iend;
 36:   PetscInt       i,j,m = 3,n = 2,its;
 37:   PetscMPIInt    size,rank;
 38:   PetscTruth     mat_nonsymmetric;
 39:   int            stages[2];

 41:   PetscInitialize(&argc,&args,(char *)0,help);
 42:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 43:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 44:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 45:   n = 2*size;

 47:   /*
 48:      Set flag if we are doing a nonsymmetric problem; the default is symmetric.
 49:   */
 50:   PetscOptionsHasName(PETSC_NULL,"-mat_nonsym",&mat_nonsymmetric);

 52:   /*
 53:      Register two stages for separate profiling of the two linear solves.
 54:      Use the runtime option -log_summary for a printout of performance
 55:      statistics at the program's conlusion.
 56:   */
 57:   PetscLogStageRegister(&stages[0],"Original Solve");
 58:   PetscLogStageRegister(&stages[1],"Second Solve");

 60:   /* -------------- Stage 0: Solve Original System ---------------------- */
 61:   /* 
 62:      Indicate to PETSc profiling that we're beginning the first stage
 63:   */
 64:   PetscLogStagePush(stages[0]);

 66:   /* 
 67:      Create parallel matrix, specifying only its global dimensions.
 68:      When using MatCreate(), the matrix format can be specified at
 69:      runtime. Also, the parallel partitioning of the matrix is
 70:      determined by PETSc at runtime.
 71:   */
 72:   MatCreate(PETSC_COMM_WORLD,&C);
 73:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 74:   MatSetFromOptions(C);

 76:   /* 
 77:      Currently, all PETSc parallel matrix formats are partitioned by
 78:      contiguous chunks of rows across the processors.  Determine which
 79:      rows of the matrix are locally owned. 
 80:   */
 81:   MatGetOwnershipRange(C,&Istart,&Iend);

 83:   /* 
 84:      Set matrix entries matrix in parallel.
 85:       - Each processor needs to insert only elements that it owns
 86:         locally (but any non-local elements will be sent to the
 87:         appropriate processor during matrix assembly). 
 88:       - Always specify global row and columns of matrix entries.
 89:   */
 90:   for (I=Istart; I<Iend; I++) {
 91:     v = -1.0; i = I/n; j = I - i*n;
 92:     if (i>0)   {J = I - n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 93:     if (i<m-1) {J = I + n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 94:     if (j>0)   {J = I - 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 95:     if (j<n-1) {J = I + 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 96:     v = 4.0; MatSetValues(C,1,&I,1,&I,&v,ADD_VALUES);
 97:   }

 99:   /*
100:      Make the matrix nonsymmetric if desired
101:   */
102:   if (mat_nonsymmetric) {
103:     for (I=Istart; I<Iend; I++) {
104:       v = -1.5; i = I/n;
105:       if (i>1)   {J = I-n-1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
106:     }
107:   } else {
108:     MatSetOption(C,MAT_SYMMETRIC);
109:     MatSetOption(C,MAT_SYMMETRY_ETERNAL);
110:   }

112:   /* 
113:      Assemble matrix, using the 2-step process:
114:        MatAssemblyBegin(), MatAssemblyEnd()
115:      Computations can be done while messages are in transition
116:      by placing code between these two statements.
117:   */
118:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
119:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

121:   /* 
122:      Create parallel vectors.
123:       - When using VecSetSizes(), we specify only the vector's global
124:         dimension; the parallel partitioning is determined at runtime. 
125:       - Note: We form 1 vector from scratch and then duplicate as needed.
126:   */
127:   VecCreate(PETSC_COMM_WORLD,&u);
128:   VecSetSizes(u,PETSC_DECIDE,m*n);
129:   VecSetFromOptions(u);
130:   VecDuplicate(u,&b);
131:   VecDuplicate(b,&x);

133:   /* 
134:      Currently, all parallel PETSc vectors are partitioned by
135:      contiguous chunks across the processors.  Determine which
136:      range of entries are locally owned.
137:   */
138:   VecGetOwnershipRange(x,&low,&high);

140:   /*
141:     Set elements within the exact solution vector in parallel.
142:      - Each processor needs to insert only elements that it owns
143:        locally (but any non-local entries will be sent to the
144:        appropriate processor during vector assembly).
145:      - Always specify global locations of vector entries.
146:   */
147:   VecGetLocalSize(x,&ldim);
148:   for (i=0; i<ldim; i++) {
149:     iglobal = i + low;
150:     v = (PetscScalar)(i + 100*rank);
151:     VecSetValues(u,1,&iglobal,&v,INSERT_VALUES);
152:   }

154:   /* 
155:      Assemble vector, using the 2-step process:
156:        VecAssemblyBegin(), VecAssemblyEnd()
157:      Computations can be done while messages are in transition,
158:      by placing code between these two statements.
159:   */
160:   VecAssemblyBegin(u);
161:   VecAssemblyEnd(u);

163:   /* 
164:      Compute right-hand-side vector
165:   */
166:   MatMult(C,u,b);
167: 
168:   /* 
169:     Create linear solver context
170:   */
171:   KSPCreate(PETSC_COMM_WORLD,&ksp);

173:   /* 
174:      Set operators. Here the matrix that defines the linear system
175:      also serves as the preconditioning matrix.
176:   */
177:   KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);

179:   /* 
180:      Set runtime options (e.g., -ksp_type <type> -pc_type <type>)
181:   */

183:   KSPSetFromOptions(ksp);

185:   /* 
186:      Solve linear system.  Here we explicitly call KSPSetUp() for more
187:      detailed performance monitoring of certain preconditioners, such
188:      as ICC and ILU.  This call is optional, as KSPSetUp() will
189:      automatically be called within KSPSolve() if it hasn't been
190:      called already.
191:   */
192:   KSPSetUp(ksp);
193:   KSPSolve(ksp,b,x);
194: 
195:   /* 
196:      Check the error
197:   */
198:   VecAXPY(x,none,u);
199:   VecNorm(x,NORM_2,&norm);
200:   KSPGetIterationNumber(ksp,&its);
201:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %D\n",norm,its);

203:   /* -------------- Stage 1: Solve Second System ---------------------- */
204:   /* 
205:      Solve another linear system with the same method.  We reuse the KSP
206:      context, matrix and vector data structures, and hence save the
207:      overhead of creating new ones.

209:      Indicate to PETSc profiling that we're concluding the first
210:      stage with PetscLogStagePop(), and beginning the second stage with
211:      PetscLogStagePush().
212:   */
213:   PetscLogStagePop();
214:   PetscLogStagePush(stages[1]);

216:   /* 
217:      Initialize all matrix entries to zero.  MatZeroEntries() retains the
218:      nonzero structure of the matrix for sparse formats.
219:   */
220:   MatZeroEntries(C);

222:   /* 
223:      Assemble matrix again.  Note that we retain the same matrix data
224:      structure and the same nonzero pattern; we just change the values
225:      of the matrix entries.
226:   */
227:   for (i=0; i<m; i++) {
228:     for (j=2*rank; j<2*rank+2; j++) {
229:       v = -1.0;  I = j + n*i;
230:       if (i>0)   {J = I - n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
231:       if (i<m-1) {J = I + n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
232:       if (j>0)   {J = I - 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
233:       if (j<n-1) {J = I + 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
234:       v = 6.0; MatSetValues(C,1,&I,1,&I,&v,ADD_VALUES);
235:     }
236:   }
237:   if (mat_nonsymmetric) {
238:     for (I=Istart; I<Iend; I++) {
239:       v = -1.5; i = I/n;
240:       if (i>1)   {J = I-n-1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
241:     }
242:   }
243:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
244:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

246:   /* 
247:      Compute another right-hand-side vector
248:   */
249:   MatMult(C,u,b);

251:   /* 
252:      Set operators. Here the matrix that defines the linear system
253:      also serves as the preconditioning matrix.
254:       - The flag SAME_NONZERO_PATTERN indicates that the
255:         preconditioning matrix has identical nonzero structure
256:         as during the last linear solve (although the values of
257:         the entries have changed). Thus, we can save some
258:         work in setting up the preconditioner (e.g., no need to
259:         redo symbolic factorization for ILU/ICC preconditioners).
260:       - If the nonzero structure of the matrix is different during
261:         the second linear solve, then the flag DIFFERENT_NONZERO_PATTERN
262:         must be used instead.  If you are unsure whether the
263:         matrix structure has changed or not, use the flag
264:         DIFFERENT_NONZERO_PATTERN.
265:       - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
266:         believes your assertion and does not check the structure
267:         of the matrix.  If you erroneously claim that the structure
268:         is the same when it actually is not, the new preconditioner
269:         will not function correctly.  Thus, use this optimization
270:         feature with caution!
271:   */
272:   KSPSetOperators(ksp,C,C,SAME_NONZERO_PATTERN);

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

280:   /* 
281:      Check the error
282:   */
283:   VecAXPY(x,none,u);
284:   VecNorm(x,NORM_2,&norm);
285:   KSPGetIterationNumber(ksp,&its);
286:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %D\n",norm,its);

288:   /* 
289:      Free work space.  All PETSc objects should be destroyed when they
290:      are no longer needed.
291:   */
292:   KSPDestroy(ksp);
293:   VecDestroy(u);
294:   VecDestroy(x);
295:   VecDestroy(b);
296:   MatDestroy(C);

298:   /*
299:      Indicate to PETSc profiling that we're concluding the second stage 
300:   */
301:   PetscLogStagePop();

303:   PetscFinalize();
304:   return 0;
305: }