Actual source code: ex2.c
1: /*$Id: ex2.c,v 1.94 2001/08/07 21:30:54 bsmith Exp $*/
3: /* Program usage: mpirun -np <procs> ex2 [-help] [all PETSc options] */
5: static char help[] = "Solves a linear system in parallel with SLES.n
6: Input parameters include:n
7: -random_exact_sol : use a random exact solution vectorn
8: -view_exact_sol : write exact solution vector to stdoutn
9: -m <mesh_x> : number of mesh points in x-directionn
10: -n <mesh_n> : number of mesh points in y-directionnn";
12: /*T
13: Concepts: SLES^basic parallel example;
14: Concepts: SLES^Laplacian, 2d
15: Concepts: Laplacian, 2d
16: Processors: n
17: T*/
19: /*
20: Include "petscsles.h" so that we can use SLES solvers. Note that this file
21: automatically includes:
22: petsc.h - base PETSc routines petscvec.h - vectors
23: petscsys.h - system routines petscmat.h - matrices
24: petscis.h - index sets petscksp.h - Krylov subspace methods
25: petscviewer.h - viewers petscpc.h - preconditioners
26: */
27: #include petscsles.h
29: #undef __FUNCT__
31: int main(int argc,char **args)
32: {
33: Vec x,b,u; /* approx solution, RHS, exact solution */
34: Mat A; /* linear system matrix */
35: SLES sles; /* linear solver context */
36: PetscRandom rctx; /* random number generator context */
37: PetscReal norm; /* norm of solution error */
38: int i,j,I,J,Istart,Iend,ierr,m = 8,n = 7,its;
39: PetscTruth flg;
40: PetscScalar v,one = 1.0,neg_one = -1.0;
41: KSP ksp;
43: PetscInitialize(&argc,&args,(char *)0,help);
44: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
45: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
47: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
48: Compute the matrix and right-hand-side vector that define
49: the linear system, Ax = b.
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51: /*
52: Create parallel matrix, specifying only its global dimensions.
53: When using MatCreate(), the matrix format can be specified at
54: runtime. Also, the parallel partitioning of the matrix is
55: determined by PETSc at runtime.
57: Performance tuning note: For problems of substantial size,
58: preallocation of matrix memory is crucial for attaining good
59: performance. Since preallocation is not possible via the generic
60: matrix creation routine MatCreate(), we recommend for practical
61: problems instead to use the creation routine for a particular matrix
62: format, e.g.,
63: MatCreateMPIAIJ() - parallel AIJ (compressed sparse row)
64: MatCreateMPIBAIJ() - parallel block AIJ
65: See the matrix chapter of the users manual for details.
66: */
67: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
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(rctx,u);
140: PetscRandomDestroy(rctx);
141: } else {
142: VecSet(&one,u);
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: SLESCreate(PETSC_COMM_WORLD,&sles);
161: /*
162: Set operators. Here the matrix that defines the linear system
163: also serves as the preconditioning matrix.
164: */
165: SLESSetOperators(sles,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 SLES 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: SLESSetFromOptions(). All of these defaults can be
175: overridden at runtime, as indicated below.
176: */
178: SLESGetKSP(sles,&ksp);
179: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,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: SLESSetFromOptions() is called _after_ any other customization
186: routines.
187: */
188: SLESSetFromOptions(sles);
190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Solve the linear system
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
194: SLESSolve(sles,b,x,&its);
196: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197: Check solution and clean up
198: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: /*
201: Check the error
202: */
203: VecAXPY(&neg_one,u,x);
204: VecNorm(x,NORM_2,&norm);
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 %dn",norm,its);
216: /*
217: Free work space. All PETSc objects should be destroyed when they
218: are no longer needed.
219: */
220: SLESDestroy(sles);
221: VecDestroy(u); VecDestroy(x);
222: VecDestroy(b); MatDestroy(A);
224: /*
225: Always call PetscFinalize() before exiting a program. This routine
226: - finalizes the PETSc libraries as well as MPI
227: - provides summary and diagnostic information if certain runtime
228: options are chosen (e.g., -log_summary).
229: */
230: PetscFinalize();
231: return 0;
232: }