Actual source code: ex1.c
1: /*$Id: ex1.c,v 1.90 2001/08/07 21:30:54 bsmith 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: PetscReal norm; /* norm of solution error */
32: int ierr,i,n = 10,col[3],its,size;
33: PetscScalar 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,&x);
50: PetscObjectSetName((PetscObject) x, "Solution");
51: VecSetSizes(x,PETSC_DECIDE,n);
52: VecSetFromOptions(x);
53: VecDuplicate(x,&b);
54: VecDuplicate(x,&u);
56: /*
57: Create matrix. When using MatCreate(), the matrix format can
58: be specified at runtime.
60: Performance tuning note: For problems of substantial size,
61: preallocation of matrix memory is crucial for attaining good
62: performance. Since preallocation is not possible via the generic
63: matrix creation routine MatCreate(), we recommend for practical
64: problems instead to use the creation routine for a particular matrix
65: format, e.g.,
66: MatCreateSeqAIJ() - sequential AIJ (compressed sparse row)
67: MatCreateSeqBAIJ() - block AIJ
68: See the matrix chapter of the users manual for details.
69: */
70: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);
71: MatSetFromOptions(A);
73: /*
74: Assemble matrix
75: */
76: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
77: for (i=1; i<n-1; i++) {
78: col[0] = i-1; col[1] = i; col[2] = i+1;
79: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
80: }
81: i = n - 1; col[0] = n - 2; col[1] = n - 1;
82: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
83: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
84: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
85: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
88: /*
89: Set exact solution; then compute right-hand-side vector.
90: */
91: VecSet(&one,u);
92: MatMult(A,u,b);
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Create the linear solver and set various options
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
97: /*
98: Create linear solver context
99: */
100: SLESCreate(PETSC_COMM_WORLD,&sles);
102: /*
103: Set operators. Here the matrix that defines the linear system
104: also serves as the preconditioning matrix.
105: */
106: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
108: /*
109: Set linear solver defaults for this problem (optional).
110: - By extracting the KSP and PC contexts from the SLES context,
111: we can then directly call any KSP and PC routines to set
112: various options.
113: - The following four statements are optional; all of these
114: parameters could alternatively be specified at runtime via
115: SLESSetFromOptions();
116: */
117: SLESGetKSP(sles,&ksp);
118: SLESGetPC(sles,&pc);
119: PCSetType(pc,PCJACOBI);
120: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
122: /*
123: Set runtime options, e.g.,
124: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
125: These options will override those specified above as long as
126: SLESSetFromOptions() is called _after_ any other customization
127: routines.
128: */
129: SLESSetFromOptions(sles);
130:
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Solve the linear system
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: /*
135: Solve linear system
136: */
137: SLESSolve(sles,b,x,&its);
139: /*
140: View solver info; we could instead use the option -sles_view to
141: print this info to the screen at the conclusion of SLESSolve().
142: */
143: SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);
145: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146: Check solution and clean up
147: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148: /*
149: Check the error
150: */
151: VecAXPY(&neg_one,u,x);
152: ierr = VecNorm(x,NORM_2,&norm);
153: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",norm,its);
154: /*
155: Free work space. All PETSc objects should be destroyed when they
156: are no longer needed.
157: */
158: VecDestroy(x); VecDestroy(u);
159: VecDestroy(b); MatDestroy(A);
160: SLESDestroy(sles);
162: /*
163: Always call PetscFinalize() before exiting a program. This routine
164: - finalizes the PETSc libraries as well as MPI
165: - provides summary and diagnostic information if certain runtime
166: options are chosen (e.g., -log_summary).
167: */
168: PetscFinalize();
169: return 0;
170: }