Actual source code: ex1.c
1: /*$Id: ex1.c,v 1.88 2001/03/23 23:23:55 balay Exp $*/
3: /* Program usage: mpirun ex1 [-help] [all PETSc options] */
5: static char help[] = "Solves a tridiagonal linear system with SLES.nn";
7: /*T
8: Concepts: SLES^solving a system of linear equations
9: Processors: 1
10: T*/
12: /*
13: Include "petscsles.h" so that we can use SLES solvers. Note that this file
14: automatically includes:
15: petsc.h - base PETSc routines petscvec.h - vectors
16: petscsys.h - system routines petscmat.h - matrices
17: petscis.h - index sets petscksp.h - Krylov subspace methods
18: petscviewer.h - viewers petscpc.h - preconditioners
20: Note: The corresponding parallel example is ex23.c
21: */
22: #include petscsles.h
24: int main(int argc,char **args)
25: {
26: Vec x, b, u; /* approx solution, RHS, exact solution */
27: Mat A; /* linear system matrix */
28: SLES sles; /* linear solver context */
29: PC pc; /* preconditioner context */
30: KSP ksp; /* Krylov subspace method context */
31: double norm; /* norm of solution error */
32: int ierr,i,n = 10,col[3],its,size;
33: Scalar neg_one = -1.0,one = 1.0,value[3];
35: PetscInitialize(&argc,&args,(char *)0,help);
36: MPI_Comm_size(PETSC_COMM_WORLD,&size);
37: if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");
38: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
40: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: Compute the matrix and right-hand-side vector that define
42: the linear system, Ax = b.
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45: /*
46: Create vectors. Note that we form 1 vector from scratch and
47: then duplicate as needed.
48: */
49: VecCreate(PETSC_COMM_WORLD,PETSC_DECIDE,n,&x);
50: VecSetFromOptions(x);
51: VecDuplicate(x,&b);
52: VecDuplicate(x,&u);
54: /*
55: Create matrix. When using MatCreate(), the matrix format can
56: be specified at runtime.
58: Performance tuning note: For problems of substantial size,
59: preallocation of matrix memory is crucial for attaining good
60: performance. Since preallocation is not possible via the generic
61: matrix creation routine MatCreate(), we recommend for practical
62: problems instead to use the creation routine for a particular matrix
63: format, e.g.,
64: MatCreateSeqAIJ() - sequential AIJ (compressed sparse row)
65: MatCreateSeqBAIJ() - block AIJ
66: See the matrix chapter of the users manual for details.
67: */
68: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);
69: MatSetFromOptions(A);
71: /*
72: Assemble matrix
73: */
74: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
75: for (i=1; i<n-1; i++) {
76: col[0] = i-1; col[1] = i; col[2] = i+1;
77: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
78: }
79: i = n - 1; col[0] = n - 2; col[1] = n - 1;
80: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
81: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
82: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
83: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
86: /*
87: Set exact solution; then compute right-hand-side vector.
88: */
89: VecSet(&one,u);
90: MatMult(A,u,b);
92: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
93: Create the linear solver and set various options
94: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
95: /*
96: Create linear solver context
97: */
98: SLESCreate(PETSC_COMM_WORLD,&sles);
100: /*
101: Set operators. Here the matrix that defines the linear system
102: also serves as the preconditioning matrix.
103: */
104: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
106: /*
107: Set linear solver defaults for this problem (optional).
108: - By extracting the KSP and PC contexts from the SLES context,
109: we can then directly call any KSP and PC routines to set
110: various options.
111: - The following four statements are optional; all of these
112: parameters could alternatively be specified at runtime via
113: SLESSetFromOptions();
114: */
115: SLESGetKSP(sles,&ksp);
116: SLESGetPC(sles,&pc);
117: PCSetType(pc,PCJACOBI);
118: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
120: /*
121: Set runtime options, e.g.,
122: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
123: These options will override those specified above as long as
124: SLESSetFromOptions() is called _after_ any other customization
125: routines.
126: */
127: SLESSetFromOptions(sles);
128:
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Solve the linear system
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: /*
133: Solve linear system
134: */
135: SLESSolve(sles,b,x,&its);
137: /*
138: View solver info; we could instead use the option -sles_view to
139: print this info to the screen at the conclusion of SLESSolve().
140: */
141: SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);
143: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: Check solution and clean up
145: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: /*
147: Check the error
148: */
149: VecAXPY(&neg_one,u,x);
150: ierr = VecNorm(x,NORM_2,&norm);
151: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",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: SLESDestroy(sles);
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: }