Actual source code: ex1.c
2: /* Program usage: mpiexec 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: petscsys.h - base PETSc routines petscvec.h - vectors
15: 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. See the matrix chapter of the users manual for details.
65: */
66: MatCreate(PETSC_COMM_WORLD,&A);
67: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
68: MatSetFromOptions(A);
70: /*
71: Assemble matrix
72: */
73: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
74: for (i=1; i<n-1; i++) {
75: col[0] = i-1; col[1] = i; col[2] = i+1;
76: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
77: }
78: i = n - 1; col[0] = n - 2; col[1] = n - 1;
79: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
80: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
81: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
82: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
83: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
85: /*
86: Set exact solution; then compute right-hand-side vector.
87: */
88: VecSet(u,one);
89: MatMult(A,u,b);
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Create the linear solver and set various options
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: /*
95: Create linear solver context
96: */
97: KSPCreate(PETSC_COMM_WORLD,&ksp);
99: /*
100: Set operators. Here the matrix that defines the linear system
101: also serves as the preconditioning matrix.
102: */
103: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
105: /*
106: Set linear solver defaults for this problem (optional).
107: - By extracting the KSP and PC contexts from the KSP context,
108: we can then directly call any KSP and PC routines to set
109: various options.
110: - The following four statements are optional; all of these
111: parameters could alternatively be specified at runtime via
112: KSPSetFromOptions();
113: */
114: KSPGetPC(ksp,&pc);
115: PCSetType(pc,PCJACOBI);
116: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
118: /*
119: Set runtime options, e.g.,
120: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
121: These options will override those specified above as long as
122: KSPSetFromOptions() is called _after_ any other customization
123: routines.
124: */
125: KSPSetFromOptions(ksp);
126:
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Solve the linear system
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130: /*
131: Solve linear system
132: */
133: KSPSolve(ksp,b,x);
135: /*
136: View solver info; we could instead use the option -ksp_view to
137: print this info to the screen at the conclusion of KSPSolve().
138: */
139: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Check solution and clean up
143: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144: /*
145: Check the error
146: */
147: VecAXPY(x,neg_one,u);
148: VecNorm(x,NORM_2,&norm);
149: KSPGetIterationNumber(ksp,&its);
150: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %D\n",
151: norm,its);
152: /*
153: Free work space. All PETSc objects should be destroyed when they
154: are no longer needed.
155: */
156: VecDestroy(x); VecDestroy(u);
157: VecDestroy(b); MatDestroy(A);
158: KSPDestroy(ksp);
160: /*
161: Always call PetscFinalize() before exiting a program. This routine
162: - finalizes the PETSc libraries as well as MPI
163: - provides summary and diagnostic information if certain runtime
164: options are chosen (e.g., -log_summary).
165: */
166: PetscFinalize();
167: return 0;
168: }