Actual source code: ex2.c
2: /* Program usage: mpiexec -n <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: petscsys.h - base PETSc routines petscvec.h - vectors
22: 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 = PETSC_FALSE;
40: PetscScalar v,one = 1.0,neg_one = -1.0;
41: #if defined(PETSC_USE_LOG)
42: PetscLogStage stage;
43: #endif
45: PetscInitialize(&argc,&args,(char *)0,help);
46: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
47: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
48: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: Compute the matrix and right-hand-side vector that define
50: the linear system, Ax = b.
51: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
52: /*
53: Create parallel matrix, specifying only its global dimensions.
54: When using MatCreate(), the matrix format can be specified at
55: runtime. Also, the parallel partitioning of the matrix is
56: determined by PETSc at runtime.
58: Performance tuning note: For problems of substantial size,
59: preallocation of matrix memory is crucial for attaining good
60: performance. See the matrix chapter of the users manual for details.
61: */
62: MatCreate(PETSC_COMM_WORLD,&A);
63: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
64: MatSetFromOptions(A);
65: MatMPIAIJSetPreallocation(A,5,PETSC_NULL,5,PETSC_NULL);
66: MatSeqAIJSetPreallocation(A,5,PETSC_NULL);
68: /*
69: Currently, all PETSc parallel matrix formats are partitioned by
70: contiguous chunks of rows across the processors. Determine which
71: rows of the matrix are locally owned.
72: */
73: MatGetOwnershipRange(A,&Istart,&Iend);
75: /*
76: Set matrix elements for the 2-D, five-point stencil in parallel.
77: - Each processor needs to insert only elements that it owns
78: locally (but any non-local elements will be sent to the
79: appropriate processor during matrix assembly).
80: - Always specify global rows and columns of matrix entries.
82: Note: this uses the less common natural ordering that orders first
83: all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
84: instead of J = I +- m as you might expect. The more standard ordering
85: would first do all variables for y = h, then y = 2h etc.
87: */
88: PetscLogStageRegister("Assembly", &stage);
89: PetscLogStagePush(stage);
90: for (Ii=Istart; Ii<Iend; Ii++) {
91: v = -1.0; i = Ii/n; j = Ii - i*n;
92: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
93: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
94: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
95: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
96: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&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);
107: PetscLogStagePop();
109: /*
110: Create parallel vectors.
111: - We form 1 vector from scratch and then duplicate as needed.
112: - When using VecCreate(), VecSetSizes and VecSetFromOptions()
113: in this example, we specify only the
114: vector's global dimension; the parallel partitioning is determined
115: at runtime.
116: - When solving a linear system, the vectors and matrices MUST
117: be partitioned accordingly. PETSc automatically generates
118: appropriately partitioned matrices and vectors when MatCreate()
119: and VecCreate() are used with the same communicator.
120: - The user can alternatively specify the local vector and matrix
121: dimensions when more sophisticated partitioning is needed
122: (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
123: below).
124: */
125: VecCreate(PETSC_COMM_WORLD,&u);
126: VecSetSizes(u,PETSC_DECIDE,m*n);
127: VecSetFromOptions(u);
128: VecDuplicate(u,&b);
129: VecDuplicate(b,&x);
131: /*
132: Set exact solution; then compute right-hand-side vector.
133: By default we use an exact solution of a vector with all
134: elements of 1.0; Alternatively, using the runtime option
135: -random_sol forms a solution vector with random components.
136: */
137: PetscOptionsGetTruth(PETSC_NULL,"-random_exact_sol",&flg,PETSC_NULL);
138: if (flg) {
139: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
140: PetscRandomSetFromOptions(rctx);
141: VecSetRandom(u,rctx);
142: PetscRandomDestroy(rctx);
143: } else {
144: VecSet(u,one);
145: }
146: MatMult(A,u,b);
148: /*
149: View the exact solution vector if desired
150: */
151: flg = PETSC_FALSE;
152: PetscOptionsGetTruth(PETSC_NULL,"-view_exact_sol",&flg,PETSC_NULL);
153: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Create the linear solver and set various options
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
159: /*
160: Create linear solver context
161: */
162: KSPCreate(PETSC_COMM_WORLD,&ksp);
164: /*
165: Set operators. Here the matrix that defines the linear system
166: also serves as the preconditioning matrix.
167: */
168: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
170: /*
171: Set linear solver defaults for this problem (optional).
172: - By extracting the KSP and PC contexts from the KSP context,
173: we can then directly call any KSP and PC routines to set
174: various options.
175: - The following two statements are optional; all of these
176: parameters could alternatively be specified at runtime via
177: KSPSetFromOptions(). All of these defaults can be
178: overridden at runtime, as indicated below.
179: */
180: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
181: PETSC_DEFAULT);
183: /*
184: Set runtime options, e.g.,
185: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
186: These options will override those specified above as long as
187: KSPSetFromOptions() is called _after_ any other customization
188: routines.
189: */
190: KSPSetFromOptions(ksp);
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Solve the linear system
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: KSPSolve(ksp,b,x);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Check solution and clean up
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: /*
203: Check the error
204: */
205: VecAXPY(x,neg_one,u);
206: VecNorm(x,NORM_2,&norm);
207: KSPGetIterationNumber(ksp,&its);
208: /* Scale the norm */
209: /* norm *= sqrt(1.0/((m+1)*(n+1))); */
211: /*
212: Print convergence information. PetscPrintf() produces a single
213: print statement from all processes that share a communicator.
214: An alternative is PetscFPrintf(), which prints to a file.
215: */
216: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
217: norm,its);
219: /*
220: Free work space. All PETSc objects should be destroyed when they
221: are no longer needed.
222: */
223: KSPDestroy(ksp);
224: VecDestroy(u); VecDestroy(x);
225: VecDestroy(b); MatDestroy(A);
227: /*
228: Always call PetscFinalize() before exiting a program. This routine
229: - finalizes the PETSc libraries as well as MPI
230: - provides summary and diagnostic information if certain runtime
231: options are chosen (e.g., -log_summary).
232: */
233: PetscFinalize();
234: return 0;
235: }