Actual source code: ex2.c
petsc-3.3-p7 2013-05-11
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: PetscBool flg = PETSC_FALSE;
40: PetscScalar v;
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);
67: MatSetUp(A);
69: /*
70: Currently, all PETSc parallel matrix formats are partitioned by
71: contiguous chunks of rows across the processors. Determine which
72: rows of the matrix are locally owned.
73: */
74: MatGetOwnershipRange(A,&Istart,&Iend);
76: /*
77: Set matrix elements for the 2-D, five-point stencil in parallel.
78: - Each processor needs to insert only elements that it owns
79: locally (but any non-local elements will be sent to the
80: appropriate processor during matrix assembly).
81: - Always specify global rows and columns of matrix entries.
83: Note: this uses the less common natural ordering that orders first
84: all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
85: instead of J = I +- m as you might expect. The more standard ordering
86: would first do all variables for y = h, then y = 2h etc.
88: */
89: PetscLogStageRegister("Assembly", &stage);
90: PetscLogStagePush(stage);
91: for (Ii=Istart; Ii<Iend; Ii++) {
92: v = -1.0; i = Ii/n; j = Ii - i*n;
93: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
94: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
95: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
96: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
97: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
98: }
100: /*
101: Assemble matrix, using the 2-step process:
102: MatAssemblyBegin(), MatAssemblyEnd()
103: Computations can be done while messages are in transition
104: by placing code between these two statements.
105: */
106: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
107: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
108: PetscLogStagePop();
110: /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
111: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
113: /*
114: Create parallel vectors.
115: - We form 1 vector from scratch and then duplicate as needed.
116: - When using VecCreate(), VecSetSizes and VecSetFromOptions()
117: in this example, we specify only the
118: vector's global dimension; the parallel partitioning is determined
119: at runtime.
120: - When solving a linear system, the vectors and matrices MUST
121: be partitioned accordingly. PETSc automatically generates
122: appropriately partitioned matrices and vectors when MatCreate()
123: and VecCreate() are used with the same communicator.
124: - The user can alternatively specify the local vector and matrix
125: dimensions when more sophisticated partitioning is needed
126: (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
127: below).
128: */
129: VecCreate(PETSC_COMM_WORLD,&u);
130: VecSetSizes(u,PETSC_DECIDE,m*n);
131: VecSetFromOptions(u);
132: VecDuplicate(u,&b);
133: VecDuplicate(b,&x);
135: /*
136: Set exact solution; then compute right-hand-side vector.
137: By default we use an exact solution of a vector with all
138: elements of 1.0; Alternatively, using the runtime option
139: -random_sol forms a solution vector with random components.
140: */
141: PetscOptionsGetBool(PETSC_NULL,"-random_exact_sol",&flg,PETSC_NULL);
142: if (flg) {
143: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
144: PetscRandomSetFromOptions(rctx);
145: VecSetRandom(u,rctx);
146: PetscRandomDestroy(&rctx);
147: } else {
148: VecSet(u,1.0);
149: }
150: MatMult(A,u,b);
152: /*
153: View the exact solution vector if desired
154: */
155: flg = PETSC_FALSE;
156: PetscOptionsGetBool(PETSC_NULL,"-view_exact_sol",&flg,PETSC_NULL);
157: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Create the linear solver and set various options
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163: /*
164: Create linear solver context
165: */
166: KSPCreate(PETSC_COMM_WORLD,&ksp);
168: /*
169: Set operators. Here the matrix that defines the linear system
170: also serves as the preconditioning matrix.
171: */
172: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
174: /*
175: Set linear solver defaults for this problem (optional).
176: - By extracting the KSP and PC contexts from the KSP context,
177: we can then directly call any KSP and PC routines to set
178: various options.
179: - The following two statements are optional; all of these
180: parameters could alternatively be specified at runtime via
181: KSPSetFromOptions(). All of these defaults can be
182: overridden at runtime, as indicated below.
183: */
184: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
185: PETSC_DEFAULT);
187: /*
188: Set runtime options, e.g.,
189: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
190: These options will override those specified above as long as
191: KSPSetFromOptions() is called _after_ any other customization
192: routines.
193: */
194: KSPSetFromOptions(ksp);
196: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197: Solve the linear system
198: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: KSPSolve(ksp,b,x);
202: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: Check solution and clean up
204: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206: /*
207: Check the error
208: */
209: VecAXPY(x,-1.0,u);
210: VecNorm(x,NORM_2,&norm);
211: KSPGetIterationNumber(ksp,&its);
212: /* Scale the norm */
213: /* norm *= sqrt(1.0/((m+1)*(n+1))); */
215: /*
216: Print convergence information. PetscPrintf() produces a single
217: print statement from all processes that share a communicator.
218: An alternative is PetscFPrintf(), which prints to a file.
219: */
220: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G iterations %D\n",
221: norm,its);
223: /*
224: Free work space. All PETSc objects should be destroyed when they
225: are no longer needed.
226: */
227: KSPDestroy(&ksp);
228: VecDestroy(&u); VecDestroy(&x);
229: VecDestroy(&b); MatDestroy(&A);
231: /*
232: Always call PetscFinalize() before exiting a program. This routine
233: - finalizes the PETSc libraries as well as MPI
234: - provides summary and diagnostic information if certain runtime
235: options are chosen (e.g., -log_summary).
236: */
237: PetscFinalize();
238: return 0;
239: }