Actual source code: ex2.c
2: /* Program usage: mpirun -np <procs> ex2 [-help] [all PETSc options] */
4: static char help[] = "Solves a linear system in parallel with KSP.\n\
5: Input parameters include:\n\
6: -random_exact_sol : use a random exact solution vector\n\
7: -view_exact_sol : write exact solution vector to stdout\n\
8: -m <mesh_x> : number of mesh points in x-direction\n\
9: -n <mesh_n> : number of mesh points in y-direction\n\n";
11: /*T
12: Concepts: KSP^basic parallel example;
13: Concepts: KSP^Laplacian, 2d
14: Concepts: Laplacian, 2d
15: Processors: n
16: T*/
18: /*
19: Include "petscksp.h" so that we can use KSP solvers. Note that this file
20: automatically includes:
21: petsc.h - base PETSc routines petscvec.h - vectors
22: petscsys.h - system routines petscmat.h - matrices
23: petscis.h - index sets petscksp.h - Krylov subspace methods
24: petscviewer.h - viewers petscpc.h - preconditioners
25: */
26: #include petscksp.h
30: int main(int argc,char **args)
31: {
32: Vec x,b,u; /* approx solution, RHS, exact solution */
33: Mat A; /* linear system matrix */
34: KSP ksp; /* linear solver context */
35: PetscRandom rctx; /* random number generator context */
36: PetscReal norm; /* norm of solution error */
37: PetscInt i,j,I,J,Istart,Iend,m = 8,n = 7,its;
39: PetscTruth flg;
40: PetscScalar v,one = 1.0,neg_one = -1.0;
42: PetscInitialize(&argc,&args,(char *)0,help);
43: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
44: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
46: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47: Compute the matrix and right-hand-side vector that define
48: the linear system, Ax = b.
49: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
50: /*
51: Create parallel matrix, specifying only its global dimensions.
52: When using MatCreate(), the matrix format can be specified at
53: runtime. Also, the parallel partitioning of the matrix is
54: determined by PETSc at runtime.
56: Performance tuning note: For problems of substantial size,
57: preallocation of matrix memory is crucial for attaining good
58: performance. Since preallocation is not possible via the generic
59: matrix creation routine MatCreate(), we recommend for practical
60: problems instead to use the creation routine for a particular matrix
61: format, e.g.,
62: MatCreateMPIAIJ() - parallel AIJ (compressed sparse row)
63: MatCreateMPIBAIJ() - parallel block AIJ
64: See the matrix chapter of the users manual for details.
65: */
66: MatCreate(PETSC_COMM_WORLD,&A);
67: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
68: MatSetFromOptions(A);
70: /*
71: Currently, all PETSc parallel matrix formats are partitioned by
72: contiguous chunks of rows across the processors. Determine which
73: rows of the matrix are locally owned.
74: */
75: MatGetOwnershipRange(A,&Istart,&Iend);
77: /*
78: Set matrix elements for the 2-D, five-point stencil in parallel.
79: - Each processor needs to insert only elements that it owns
80: locally (but any non-local elements will be sent to the
81: appropriate processor during matrix assembly).
82: - Always specify global rows and columns of matrix entries.
84: Note: this uses the less common natural ordering that orders first
85: all the unknowns for x = h then for x = 2h etc; Hence you see J = I +- n
86: instead of J = I +- m as you might expect. The more standard ordering
87: would first do all variables for y = h, then y = 2h etc.
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(A,1,&I,1,&J,&v,INSERT_VALUES);}
93: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
94: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
95: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
96: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_VALUES);
97: }
99: /*
100: Assemble matrix, using the 2-step process:
101: MatAssemblyBegin(), MatAssemblyEnd()
102: Computations can be done while messages are in transition
103: by placing code between these two statements.
104: */
105: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
106: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
108: /*
109: Create parallel vectors.
110: - We form 1 vector from scratch and then duplicate as needed.
111: - When using VecCreate(), VecSetSizes and VecSetFromOptions()
112: in this example, we specify only the
113: vector's global dimension; the parallel partitioning is determined
114: at runtime.
115: - When solving a linear system, the vectors and matrices MUST
116: be partitioned accordingly. PETSc automatically generates
117: appropriately partitioned matrices and vectors when MatCreate()
118: and VecCreate() are used with the same communicator.
119: - The user can alternatively specify the local vector and matrix
120: dimensions when more sophisticated partitioning is needed
121: (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
122: below).
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: Set exact solution; then compute right-hand-side vector.
132: By default we use an exact solution of a vector with all
133: elements of 1.0; Alternatively, using the runtime option
134: -random_sol forms a solution vector with random components.
135: */
136: PetscOptionsHasName(PETSC_NULL,"-random_exact_sol",&flg);
137: if (flg) {
138: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
139: VecSetRandom(u,rctx);
140: PetscRandomDestroy(rctx);
141: } else {
142: VecSet(u,one);
143: }
144: MatMult(A,u,b);
146: /*
147: View the exact solution vector if desired
148: */
149: PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
150: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Create the linear solver and set various options
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156: /*
157: Create linear solver context
158: */
159: KSPCreate(PETSC_COMM_WORLD,&ksp);
161: /*
162: Set operators. Here the matrix that defines the linear system
163: also serves as the preconditioning matrix.
164: */
165: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
167: /*
168: Set linear solver defaults for this problem (optional).
169: - By extracting the KSP and PC contexts from the KSP context,
170: we can then directly call any KSP and PC routines to set
171: various options.
172: - The following two statements are optional; all of these
173: parameters could alternatively be specified at runtime via
174: KSPSetFromOptions(). All of these defaults can be
175: overridden at runtime, as indicated below.
176: */
178: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
179: PETSC_DEFAULT);
181: /*
182: Set runtime options, e.g.,
183: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
184: These options will override those specified above as long as
185: KSPSetFromOptions() is called _after_ any other customization
186: routines.
187: */
188: KSPSetFromOptions(ksp);
190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Solve the linear system
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
194: KSPSolve(ksp,b,x);
196: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197: Check solution and clean up
198: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: /*
201: Check the error
202: */
203: VecAXPY(x,neg_one,u);
204: VecNorm(x,NORM_2,&norm);
205: KSPGetIterationNumber(ksp,&its);
206: /* Scale the norm */
207: /* norm *= sqrt(1.0/((m+1)*(n+1))); */
209: /*
210: Print convergence information. PetscPrintf() produces a single
211: print statement from all processes that share a communicator.
212: An alternative is PetscFPrintf(), which prints to a file.
213: */
214: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
215: norm,its);
217: /*
218: Free work space. All PETSc objects should be destroyed when they
219: are no longer needed.
220: */
221: KSPDestroy(ksp);
222: VecDestroy(u); VecDestroy(x);
223: VecDestroy(b); MatDestroy(A);
225: /*
226: Always call PetscFinalize() before exiting a program. This routine
227: - finalizes the PETSc libraries as well as MPI
228: - provides summary and diagnostic information if certain runtime
229: options are chosen (e.g., -log_summary).
230: */
231: PetscFinalize();
232: return 0;
233: }