Actual source code: ex1.c
2: /* Program usage: mpirun ex1 [-help] [all PETSc options] */
4: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";
6: /*T
7: Concepts: KSP^solving a system of linear equations
8: Processors: 1
9: T*/
11: /*
12: Include "petscksp.h" so that we can use KSP solvers. Note that this file
13: automatically includes:
14: petsc.h - base PETSc routines petscvec.h - vectors
15: petscsys.h - system routines petscmat.h - matrices
16: petscis.h - index sets petscksp.h - Krylov subspace methods
17: petscviewer.h - viewers petscpc.h - preconditioners
19: Note: The corresponding parallel example is ex23.c
20: */
21: #include petscksp.h
25: int main(int argc,char **args)
26: {
27: Vec x, b, u; /* approx solution, RHS, exact solution */
28: Mat A; /* linear system matrix */
29: KSP ksp; /* linear solver context */
30: PC pc; /* preconditioner context */
31: PetscReal norm; /* norm of solution error */
33: PetscInt i,n = 10,col[3],its;
34: PetscMPIInt size;
35: PetscScalar neg_one = -1.0,one = 1.0,value[3];
37: PetscInitialize(&argc,&args,(char *)0,help);
38: MPI_Comm_size(PETSC_COMM_WORLD,&size);
39: if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");
40: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
42: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: Compute the matrix and right-hand-side vector that define
44: the linear system, Ax = b.
45: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
47: /*
48: Create vectors. Note that we form 1 vector from scratch and
49: then duplicate as needed.
50: */
51: VecCreate(PETSC_COMM_WORLD,&x);
52: PetscObjectSetName((PetscObject) x, "Solution");
53: VecSetSizes(x,PETSC_DECIDE,n);
54: VecSetFromOptions(x);
55: VecDuplicate(x,&b);
56: VecDuplicate(x,&u);
58: /*
59: Create matrix. When using MatCreate(), the matrix format can
60: be specified at runtime.
62: Performance tuning note: For problems of substantial size,
63: preallocation of matrix memory is crucial for attaining good
64: performance. Since preallocation is not possible via the generic
65: matrix creation routine MatCreate(), we recommend for practical
66: problems instead to use the creation routine for a particular matrix
67: format, e.g.,
68: MatCreateSeqAIJ() - sequential AIJ (compressed sparse row)
69: MatCreateSeqBAIJ() - block AIJ
70: See the matrix chapter of the users manual for details.
71: */
72: MatCreate(PETSC_COMM_WORLD,&A);
73: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
74: MatSetFromOptions(A);
76: /*
77: Assemble matrix
78: */
79: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
80: for (i=1; i<n-1; i++) {
81: col[0] = i-1; col[1] = i; col[2] = i+1;
82: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
83: }
84: i = n - 1; col[0] = n - 2; col[1] = n - 1;
85: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
86: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
87: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
88: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
89: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
91: /*
92: Set exact solution; then compute right-hand-side vector.
93: */
94: VecSet(u,one);
95: MatMult(A,u,b);
97: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98: Create the linear solver and set various options
99: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: /*
101: Create linear solver context
102: */
103: KSPCreate(PETSC_COMM_WORLD,&ksp);
105: /*
106: Set operators. Here the matrix that defines the linear system
107: also serves as the preconditioning matrix.
108: */
109: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
111: /*
112: Set linear solver defaults for this problem (optional).
113: - By extracting the KSP and PC contexts from the KSP context,
114: we can then directly call any KSP and PC routines to set
115: various options.
116: - The following four statements are optional; all of these
117: parameters could alternatively be specified at runtime via
118: KSPSetFromOptions();
119: */
120: KSPGetPC(ksp,&pc);
121: PCSetType(pc,PCJACOBI);
122: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
124: /*
125: Set runtime options, e.g.,
126: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
127: These options will override those specified above as long as
128: KSPSetFromOptions() is called _after_ any other customization
129: routines.
130: */
131: KSPSetFromOptions(ksp);
132:
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Solve the linear system
135: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136: /*
137: Solve linear system
138: */
139: KSPSolve(ksp,b,x);
141: /*
142: View solver info; we could instead use the option -ksp_view to
143: print this info to the screen at the conclusion of KSPSolve().
144: */
145: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Check solution and clean up
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: /*
151: Check the error
152: */
153: VecAXPY(x,neg_one,u);
154: VecNorm(x,NORM_2,&norm);
155: KSPGetIterationNumber(ksp,&its);
156: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %D\n",
157: norm,its);
158: /*
159: Free work space. All PETSc objects should be destroyed when they
160: are no longer needed.
161: */
162: VecDestroy(x); VecDestroy(u);
163: VecDestroy(b); MatDestroy(A);
164: KSPDestroy(ksp);
166: /*
167: Always call PetscFinalize() before exiting a program. This routine
168: - finalizes the PETSc libraries as well as MPI
169: - provides summary and diagnostic information if certain runtime
170: options are chosen (e.g., -log_summary).
171: */
172: PetscFinalize();
173: return 0;
174: }