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: }