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: #undef __FUNCT__
26: int main(int argc,char **args)
27: {
28: Vec x, b, u; /* approx solution, RHS, exact solution */
29: Mat A; /* linear system matrix */
30: SLES sles; /* linear solver context */
31: PC pc; /* preconditioner context */
32: KSP ksp; /* Krylov subspace method context */
33: PetscReal norm; /* norm of solution error */
34: int ierr,i,n = 10,col[3],its,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,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);
73: MatSetFromOptions(A);
75: /*
76: Assemble matrix
77: */
78: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
79: for (i=1; i<n-1; i++) {
80: col[0] = i-1; col[1] = i; col[2] = i+1;
81: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
82: }
83: i = n - 1; col[0] = n - 2; col[1] = n - 1;
84: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
85: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
86: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
87: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
88: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
90: /*
91: Set exact solution; then compute right-hand-side vector.
92: */
93: VecSet(&one,u);
94: MatMult(A,u,b);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Create the linear solver and set various options
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
99: /*
100: Create linear solver context
101: */
102: SLESCreate(PETSC_COMM_WORLD,&sles);
104: /*
105: Set operators. Here the matrix that defines the linear system
106: also serves as the preconditioning matrix.
107: */
108: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
110: /*
111: Set linear solver defaults for this problem (optional).
112: - By extracting the KSP and PC contexts from the SLES context,
113: we can then directly call any KSP and PC routines to set
114: various options.
115: - The following four statements are optional; all of these
116: parameters could alternatively be specified at runtime via
117: SLESSetFromOptions();
118: */
119: SLESGetKSP(sles,&ksp);
120: SLESGetPC(sles,&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: SLESSetFromOptions() is called _after_ any other customization
129: routines.
130: */
131: SLESSetFromOptions(sles);
132:
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Solve the linear system
135: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136: /*
137: Solve linear system
138: */
139: SLESSolve(sles,b,x,&its);
141: /*
142: View solver info; we could instead use the option -sles_view to
143: print this info to the screen at the conclusion of SLESSolve().
144: */
145: SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Check solution and clean up
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: /*
151: Check the error
152: */
153: VecAXPY(&neg_one,u,x);
154: ierr = VecNorm(x,NORM_2,&norm);
155: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",norm,its);
156: /*
157: Free work space. All PETSc objects should be destroyed when they
158: are no longer needed.
159: */
160: VecDestroy(x); VecDestroy(u);
161: VecDestroy(b); MatDestroy(A);
162: SLESDestroy(sles);
164: /*
165: Always call PetscFinalize() before exiting a program. This routine
166: - finalizes the PETSc libraries as well as MPI
167: - provides summary and diagnostic information if certain runtime
168: options are chosen (e.g., -log_summary).
169: */
170: PetscFinalize();
171: return 0;
172: }