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. See the matrix chapter of the users manual for details.
59: */
60: MatCreate(PETSC_COMM_WORLD,&A);
61: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
62: MatSetFromOptions(A);
64: /*
65: Currently, all PETSc parallel matrix formats are partitioned by
66: contiguous chunks of rows across the processors. Determine which
67: rows of the matrix are locally owned.
68: */
69: MatGetOwnershipRange(A,&Istart,&Iend);
71: /*
72: Set matrix elements for the 2-D, five-point stencil in parallel.
73: - Each processor needs to insert only elements that it owns
74: locally (but any non-local elements will be sent to the
75: appropriate processor during matrix assembly).
76: - Always specify global rows and columns of matrix entries.
78: Note: this uses the less common natural ordering that orders first
79: all the unknowns for x = h then for x = 2h etc; Hence you see J = I +- n
80: instead of J = I +- m as you might expect. The more standard ordering
81: would first do all variables for y = h, then y = 2h etc.
83: */
84: for (I=Istart; I<Iend; I++) {
85: v = -1.0; i = I/n; j = I - i*n;
86: if (i>0) {J = I - n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
87: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
88: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
89: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
90: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_VALUES);
91: }
93: /*
94: Assemble matrix, using the 2-step process:
95: MatAssemblyBegin(), MatAssemblyEnd()
96: Computations can be done while messages are in transition
97: by placing code between these two statements.
98: */
99: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
100: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
102: /*
103: Create parallel vectors.
104: - We form 1 vector from scratch and then duplicate as needed.
105: - When using VecCreate(), VecSetSizes and VecSetFromOptions()
106: in this example, we specify only the
107: vector's global dimension; the parallel partitioning is determined
108: at runtime.
109: - When solving a linear system, the vectors and matrices MUST
110: be partitioned accordingly. PETSc automatically generates
111: appropriately partitioned matrices and vectors when MatCreate()
112: and VecCreate() are used with the same communicator.
113: - The user can alternatively specify the local vector and matrix
114: dimensions when more sophisticated partitioning is needed
115: (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
116: below).
117: */
118: VecCreate(PETSC_COMM_WORLD,&u);
119: VecSetSizes(u,PETSC_DECIDE,m*n);
120: VecSetFromOptions(u);
121: VecDuplicate(u,&b);
122: VecDuplicate(b,&x);
124: /*
125: Set exact solution; then compute right-hand-side vector.
126: By default we use an exact solution of a vector with all
127: elements of 1.0; Alternatively, using the runtime option
128: -random_sol forms a solution vector with random components.
129: */
130: PetscOptionsHasName(PETSC_NULL,"-random_exact_sol",&flg);
131: if (flg) {
132: PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
133: VecSetRandom(u,rctx);
134: PetscRandomDestroy(rctx);
135: } else {
136: VecSet(u,one);
137: }
138: MatMult(A,u,b);
140: /*
141: View the exact solution vector if desired
142: */
143: PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
144: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Create the linear solver and set various options
148: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: /*
151: Create linear solver context
152: */
153: KSPCreate(PETSC_COMM_WORLD,&ksp);
155: /*
156: Set operators. Here the matrix that defines the linear system
157: also serves as the preconditioning matrix.
158: */
159: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
161: /*
162: Set linear solver defaults for this problem (optional).
163: - By extracting the KSP and PC contexts from the KSP context,
164: we can then directly call any KSP and PC routines to set
165: various options.
166: - The following two statements are optional; all of these
167: parameters could alternatively be specified at runtime via
168: KSPSetFromOptions(). All of these defaults can be
169: overridden at runtime, as indicated below.
170: */
172: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
173: PETSC_DEFAULT);
175: /*
176: Set runtime options, e.g.,
177: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
178: These options will override those specified above as long as
179: KSPSetFromOptions() is called _after_ any other customization
180: routines.
181: */
182: KSPSetFromOptions(ksp);
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Solve the linear system
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: KSPSolve(ksp,b,x);
190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Check solution and clean up
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
194: /*
195: Check the error
196: */
197: VecAXPY(x,neg_one,u);
198: VecNorm(x,NORM_2,&norm);
199: KSPGetIterationNumber(ksp,&its);
200: /* Scale the norm */
201: /* norm *= sqrt(1.0/((m+1)*(n+1))); */
203: /*
204: Print convergence information. PetscPrintf() produces a single
205: print statement from all processes that share a communicator.
206: An alternative is PetscFPrintf(), which prints to a file.
207: */
208: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
209: norm,its);
211: /*
212: Free work space. All PETSc objects should be destroyed when they
213: are no longer needed.
214: */
215: KSPDestroy(ksp);
216: VecDestroy(u); VecDestroy(x);
217: VecDestroy(b); MatDestroy(A);
219: /*
220: Always call PetscFinalize() before exiting a program. This routine
221: - finalizes the PETSc libraries as well as MPI
222: - provides summary and diagnostic information if certain runtime
223: options are chosen (e.g., -log_summary).
224: */
225: PetscFinalize();
226: return 0;
227: }