Actual source code: ex5.c

  1: /*$Id: ex5.c,v 1.93 2001/09/11 16:33:29 bsmith Exp $*/

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

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

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

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

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

 46:   /*
 47:      Set flag if we are doing a nonsymmetric problem; the default is symmetric.
 48:   */
 49:   PetscOptionsHasName(PETSC_NULL,"-mat_nonsym",&mat_nonsymmetric);

 51:   /*
 52:      Register two stages for separate profiling of the two linear solves.
 53:      Use the runtime option -log_summary for a printout of performance
 54:      statistics at the program's conlusion.
 55:   */
 56:   PetscLogStageRegister(&stages[0],"Original Solve");
 57:   PetscLogStageRegister(&stages[1],"Second Solve");

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

 65:   /* 
 66:      Create parallel matrix, specifying only its global dimensions.
 67:      When using MatCreate(), the matrix format can be specified at
 68:      runtime. Also, the parallel partitioning of the matrix is
 69:      determined by PETSc at runtime.
 70:   */
 71:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&C);
 72:   MatSetFromOptions(C);

 74:   /* 
 75:      Currently, all PETSc parallel matrix formats are partitioned by
 76:      contiguous chunks of rows across the processors.  Determine which
 77:      rows of the matrix are locally owned. 
 78:   */
 79:   MatGetOwnershipRange(C,&Istart,&Iend);

 81:   /* 
 82:      Set matrix entries matrix in parallel.
 83:       - Each processor needs to insert only elements that it owns
 84:         locally (but any non-local elements will be sent to the
 85:         appropriate processor during matrix assembly). 
 86:       - Always specify global row and columns of matrix entries.
 87:   */
 88:   for (I=Istart; I<Iend; I++) {
 89:     v = -1.0; i = I/n; j = I - i*n;
 90:     if (i>0)   {J = I - n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 91:     if (i<m-1) {J = I + n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 92:     if (j>0)   {J = I - 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 93:     if (j<n-1) {J = I + 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
 94:     v = 4.0; MatSetValues(C,1,&I,1,&I,&v,ADD_VALUES);
 95:   }

 97:   /*
 98:      Make the matrix nonsymmetric if desired
 99:   */
100:   if (mat_nonsymmetric) {
101:     for (I=Istart; I<Iend; I++) {
102:       v = -1.5; i = I/n;
103:       if (i>1)   {J = I-n-1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
104:     }
105:   } else {
106:     MatSetOption(C,MAT_SYMMETRIC);
107:   }

109:   /* 
110:      Assemble matrix, using the 2-step process:
111:        MatAssemblyBegin(), MatAssemblyEnd()
112:      Computations can be done while messages are in transition
113:      by placing code between these two statements.
114:   */
115:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
116:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

118:   /* 
119:      Create parallel vectors.
120:       - When using VecSetSizes(), we specify only the vector's global
121:         dimension; the parallel partitioning is determined at runtime. 
122:       - Note: We form 1 vector from scratch and then duplicate as needed.
123:   */
124:   VecCreate(PETSC_COMM_WORLD,&u);
125:   VecSetSizes(u,PETSC_DECIDE,m*n);
126:   VecSetFromOptions(u);
127:   VecDuplicate(u,&b);
128:   VecDuplicate(b,&x);

130:   /* 
131:      Currently, all parallel PETSc vectors are partitioned by
132:      contiguous chunks across the processors.  Determine which
133:      range of entries are locally owned.
134:   */
135:   VecGetOwnershipRange(x,&low,&high);

137:   /*
138:     Set elements within the exact solution vector in parallel.
139:      - Each processor needs to insert only elements that it owns
140:        locally (but any non-local entries will be sent to the
141:        appropriate processor during vector assembly).
142:      - Always specify global locations of vector entries.
143:   */
144:   VecGetLocalSize(x,&ldim);
145:   for (i=0; i<ldim; i++) {
146:     iglobal = i + low;
147:     v = (PetscScalar)(i + 100*rank);
148:     VecSetValues(u,1,&iglobal,&v,INSERT_VALUES);
149:   }

151:   /* 
152:      Assemble vector, using the 2-step process:
153:        VecAssemblyBegin(), VecAssemblyEnd()
154:      Computations can be done while messages are in transition,
155:      by placing code between these two statements.
156:   */
157:   VecAssemblyBegin(u);
158:   VecAssemblyEnd(u);

160:   /* 
161:      Compute right-hand-side vector
162:   */
163:   MatMult(C,u,b);
164: 
165:   /* 
166:     Create linear solver context
167:   */
168:   SLESCreate(PETSC_COMM_WORLD,&sles);

170:   /* 
171:      Set operators. Here the matrix that defines the linear system
172:      also serves as the preconditioning matrix.
173:   */
174:   SLESSetOperators(sles,C,C,DIFFERENT_NONZERO_PATTERN);

176:   /* 
177:      Set runtime options (e.g., -ksp_type <type> -pc_type <type>)
178:   */

180:   SLESSetFromOptions(sles);

182:   /* 
183:      Solve linear system.  Here we explicitly call SLESSetUp() for more
184:      detailed performance monitoring of certain preconditioners, such
185:      as ICC and ILU.  This call is optional, as SLESSetUp() will
186:      automatically be called within SLESSolve() if it hasn't been
187:      called already.
188:   */
189:   SLESSetUp(sles,b,x);
190:   SLESSolve(sles,b,x,&its);
191: 
192:   /* 
193:      Check the error
194:   */
195:   VecAXPY(&none,u,x);
196:   VecNorm(x,NORM_2,&norm);
197:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",norm,its);

199:   /* -------------- Stage 1: Solve Second System ---------------------- */
200:   /* 
201:      Solve another linear system with the same method.  We reuse the SLES
202:      context, matrix and vector data structures, and hence save the
203:      overhead of creating new ones.

205:      Indicate to PETSc profiling that we're concluding the first
206:      stage with PetscLogStagePop(), and beginning the second stage with
207:      PetscLogStagePush().
208:   */
209:   PetscLogStagePop();
210:   PetscLogStagePush(stages[1]);

212:   /* 
213:      Initialize all matrix entries to zero.  MatZeroEntries() retains the
214:      nonzero structure of the matrix for sparse formats.
215:   */
216:   MatZeroEntries(C);

218:   /* 
219:      Assemble matrix again.  Note that we retain the same matrix data
220:      structure and the same nonzero pattern; we just change the values
221:      of the matrix entries.
222:   */
223:   for (i=0; i<m; i++) {
224:     for (j=2*rank; j<2*rank+2; j++) {
225:       v = -1.0;  I = j + n*i;
226:       if (i>0)   {J = I - n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
227:       if (i<m-1) {J = I + n; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
228:       if (j>0)   {J = I - 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
229:       if (j<n-1) {J = I + 1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
230:       v = 6.0; MatSetValues(C,1,&I,1,&I,&v,ADD_VALUES);
231:     }
232:   }
233:   if (mat_nonsymmetric) {
234:     for (I=Istart; I<Iend; I++) {
235:       v = -1.5; i = I/n;
236:       if (i>1)   {J = I-n-1; MatSetValues(C,1,&I,1,&J,&v,ADD_VALUES);}
237:     }
238:   }
239:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
240:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

242:   /* 
243:      Compute another right-hand-side vector
244:   */
245:   MatMult(C,u,b);

247:   /* 
248:      Set operators. Here the matrix that defines the linear system
249:      also serves as the preconditioning matrix.
250:       - The flag SAME_NONZERO_PATTERN indicates that the
251:         preconditioning matrix has identical nonzero structure
252:         as during the last linear solve (although the values of
253:         the entries have changed). Thus, we can save some
254:         work in setting up the preconditioner (e.g., no need to
255:         redo symbolic factorization for ILU/ICC preconditioners).
256:       - If the nonzero structure of the matrix is different during
257:         the second linear solve, then the flag DIFFERENT_NONZERO_PATTERN
258:         must be used instead.  If you are unsure whether the
259:         matrix structure has changed or not, use the flag
260:         DIFFERENT_NONZERO_PATTERN.
261:       - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
262:         believes your assertion and does not check the structure
263:         of the matrix.  If you erroneously claim that the structure
264:         is the same when it actually is not, the new preconditioner
265:         will not function correctly.  Thus, use this optimization
266:         feature with caution!
267:   */
268:   SLESSetOperators(sles,C,C,SAME_NONZERO_PATTERN);

270:   /* 
271:      Solve linear system
272:   */
273:   SLESSetUp(sles,b,x);
274:   SLESSolve(sles,b,x,&its);

276:   /* 
277:      Check the error
278:   */
279:   VecAXPY(&none,u,x);
280:   VecNorm(x,NORM_2,&norm);
281:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",norm,its);

283:   /* 
284:      Free work space.  All PETSc objects should be destroyed when they
285:      are no longer needed.
286:   */
287:   SLESDestroy(sles);
288:   VecDestroy(u);
289:   VecDestroy(x);
290:   VecDestroy(b);
291:   MatDestroy(C);

293:   /*
294:      Indicate to PETSc profiling that we're concluding the second stage 
295:   */
296:   PetscLogStagePop();

298:   PetscFinalize();
299:   return 0;
300: }