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,Ii,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: MatSetType(A, MATAIJ);
63: MatSetFromOptions(A);
64: MatMPIAIJSetPreallocation(A,5,PETSC_NULL,5,PETSC_NULL);
65: MatSeqAIJSetPreallocation(A,5,PETSC_NULL);
67: /*
68: Currently, all PETSc parallel matrix formats are partitioned by
69: contiguous chunks of rows across the processors. Determine which
70: rows of the matrix are locally owned.
71: */
72: MatGetOwnershipRange(A,&Istart,&Iend);
74: /*
75: Set matrix elements for the 2-D, five-point stencil in parallel.
76: - Each processor needs to insert only elements that it owns
77: locally (but any non-local elements will be sent to the
78: appropriate processor during matrix assembly).
79: - Always specify global rows and columns of matrix entries.
81: Note: this uses the less common natural ordering that orders first
82: all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
83: instead of J = I +- m as you might expect. The more standard ordering
84: would first do all variables for y = h, then y = 2h etc.
86: */
87: for (Ii=Istart; Ii<Iend; Ii++) {
88: v = -1.0; i = Ii/n; j = Ii - i*n;
89: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
90: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
91: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
92: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
93: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
94: }
96: /*
97: Assemble matrix, using the 2-step process:
98: MatAssemblyBegin(), MatAssemblyEnd()
99: Computations can be done while messages are in transition
100: by placing code between these two statements.
101: */
102: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
103: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
105: /*
106: Create parallel vectors.
107: - We form 1 vector from scratch and then duplicate as needed.
108: - When using VecCreate(), VecSetSizes and VecSetFromOptions()
109: in this example, we specify only the
110: vector's global dimension; the parallel partitioning is determined
111: at runtime.
112: - When solving a linear system, the vectors and matrices MUST
113: be partitioned accordingly. PETSc automatically generates
114: appropriately partitioned matrices and vectors when MatCreate()
115: and VecCreate() are used with the same communicator.
116: - The user can alternatively specify the local vector and matrix
117: dimensions when more sophisticated partitioning is needed
118: (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
119: below).
120: */
121: VecCreate(PETSC_COMM_WORLD,&u);
122: VecSetSizes(u,PETSC_DECIDE,m*n);
123: VecSetFromOptions(u);
124: VecDuplicate(u,&b);
125: VecDuplicate(b,&x);
127: /*
128: Set exact solution; then compute right-hand-side vector.
129: By default we use an exact solution of a vector with all
130: elements of 1.0; Alternatively, using the runtime option
131: -random_sol forms a solution vector with random components.
132: */
133: PetscOptionsHasName(PETSC_NULL,"-random_exact_sol",&flg);
134: if (flg) {
135: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
136: PetscRandomSetFromOptions(rctx);
137: VecSetRandom(u,rctx);
138: PetscRandomDestroy(rctx);
139: } else {
140: VecSet(u,one);
141: }
142: MatMult(A,u,b);
144: /*
145: View the exact solution vector if desired
146: */
147: PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
148: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Create the linear solver and set various options
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154: /*
155: Create linear solver context
156: */
157: KSPCreate(PETSC_COMM_WORLD,&ksp);
159: /*
160: Set operators. Here the matrix that defines the linear system
161: also serves as the preconditioning matrix.
162: */
163: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
165: /*
166: Set linear solver defaults for this problem (optional).
167: - By extracting the KSP and PC contexts from the KSP context,
168: we can then directly call any KSP and PC routines to set
169: various options.
170: - The following two statements are optional; all of these
171: parameters could alternatively be specified at runtime via
172: KSPSetFromOptions(). All of these defaults can be
173: overridden at runtime, as indicated below.
174: */
176: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
177: PETSC_DEFAULT);
179: /*
180: Set runtime options, e.g.,
181: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
182: These options will override those specified above as long as
183: KSPSetFromOptions() is called _after_ any other customization
184: routines.
185: */
186: KSPSetFromOptions(ksp);
188: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: Solve the linear system
190: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: KSPSolve(ksp,b,x);
194: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: Check solution and clean up
196: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198: /*
199: Check the error
200: */
201: VecAXPY(x,neg_one,u);
202: VecNorm(x,NORM_2,&norm);
203: KSPGetIterationNumber(ksp,&its);
204: /* Scale the norm */
205: /* norm *= sqrt(1.0/((m+1)*(n+1))); */
207: /*
208: Print convergence information. PetscPrintf() produces a single
209: print statement from all processes that share a communicator.
210: An alternative is PetscFPrintf(), which prints to a file.
211: */
212: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
213: norm,its);
215: /*
216: Free work space. All PETSc objects should be destroyed when they
217: are no longer needed.
218: */
219: KSPDestroy(ksp);
220: VecDestroy(u); VecDestroy(x);
221: VecDestroy(b); MatDestroy(A);
223: /*
224: Always call PetscFinalize() before exiting a program. This routine
225: - finalizes the PETSc libraries as well as MPI
226: - provides summary and diagnostic information if certain runtime
227: options are chosen (e.g., -log_summary).
228: */
229: PetscFinalize();
230: return 0;
231: }