Actual source code: ex1.c
petsc-3.7.5 2017-01-01
2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";
4: /*T
5: Concepts: KSP^solving a system of linear equations
6: Processors: 1
7: T*/
9: /*
10: Include "petscksp.h" so that we can use KSP solvers. Note that this file
11: automatically includes:
12: petscsys.h - base PETSc routines petscvec.h - vectors
13: petscmat.h - matrices
14: petscis.h - index sets petscksp.h - Krylov subspace methods
15: petscviewer.h - viewers petscpc.h - preconditioners
17: Note: The corresponding parallel example is ex23.c
18: */
19: #include <petscksp.h>
23: int main(int argc,char **args)
24: {
25: Vec x, b, u; /* approx solution, RHS, exact solution */
26: Mat A; /* linear system matrix */
27: KSP ksp; /* linear solver context */
28: PC pc; /* preconditioner context */
29: PetscReal norm; /* norm of solution error */
31: PetscInt i,n = 10,col[3],its;
32: PetscMPIInt size;
33: PetscScalar neg_one = -1.0,one = 1.0,value[3];
34: PetscBool nonzeroguess = PETSC_FALSE;
36: PetscInitialize(&argc,&args,(char*)0,help);
37: MPI_Comm_size(PETSC_COMM_WORLD,&size);
38: if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
39: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
40: PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);
43: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44: Compute the matrix and right-hand-side vector that define
45: the linear system, Ax = b.
46: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
48: /*
49: Create vectors. Note that we form 1 vector from scratch and
50: then duplicate as needed.
51: */
52: VecCreate(PETSC_COMM_WORLD,&x);
53: PetscObjectSetName((PetscObject) x, "Solution");
54: VecSetSizes(x,PETSC_DECIDE,n);
55: VecSetFromOptions(x);
56: VecDuplicate(x,&b);
57: VecDuplicate(x,&u);
59: /*
60: Create matrix. When using MatCreate(), the matrix format can
61: be specified at runtime.
63: Performance tuning note: For problems of substantial size,
64: preallocation of matrix memory is crucial for attaining good
65: performance. See the matrix chapter of the users manual for details.
66: */
67: MatCreate(PETSC_COMM_WORLD,&A);
68: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
69: MatSetFromOptions(A);
70: MatSetUp(A);
72: /*
73: Assemble matrix
74: */
75: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
76: for (i=1; i<n-1; i++) {
77: col[0] = i-1; col[1] = i; col[2] = i+1;
78: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
79: }
80: i = n - 1; col[0] = n - 2; col[1] = n - 1;
81: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
82: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
83: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
84: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
85: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
87: /*
88: Set exact solution; then compute right-hand-side vector.
89: */
90: VecSet(u,one);
91: MatMult(A,u,b);
93: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94: Create the linear solver and set various options
95: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
96: /*
97: Create linear solver context
98: */
99: KSPCreate(PETSC_COMM_WORLD,&ksp);
101: /*
102: Set operators. Here the matrix that defines the linear system
103: also serves as the preconditioning matrix.
104: */
105: KSPSetOperators(ksp,A,A);
107: /*
108: Set linear solver defaults for this problem (optional).
109: - By extracting the KSP and PC contexts from the KSP context,
110: we can then directly call any KSP and PC routines to set
111: various options.
112: - The following four statements are optional; all of these
113: parameters could alternatively be specified at runtime via
114: KSPSetFromOptions();
115: */
116: KSPGetPC(ksp,&pc);
117: PCSetType(pc,PCJACOBI);
118: KSPSetTolerances(ksp,1.e-5,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: KSPSetFromOptions() is called _after_ any other customization
125: routines.
126: */
127: KSPSetFromOptions(ksp);
129: if (nonzeroguess) {
130: PetscScalar p = .5;
131: VecSet(x,p);
132: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
133: }
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Solve the linear system
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: /*
139: Solve linear system
140: */
141: KSPSolve(ksp,b,x);
143: /*
144: View solver info; we could instead use the option -ksp_view to
145: print this info to the screen at the conclusion of KSPSolve().
146: */
147: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
149: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: Check solution and clean up
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: /*
153: Check the error
154: */
155: VecAXPY(x,neg_one,u);
156: VecNorm(x,NORM_2,&norm);
157: KSPGetIterationNumber(ksp,&its);
158: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
160: /*
161: Free work space. All PETSc objects should be destroyed when they
162: are no longer needed.
163: */
164: VecDestroy(&x); VecDestroy(&u);
165: VecDestroy(&b); MatDestroy(&A);
166: KSPDestroy(&ksp);
168: /*
169: Always call PetscFinalize() before exiting a program. This routine
170: - finalizes the PETSc libraries as well as MPI
171: - provides summary and diagnostic information if certain runtime
172: options are chosen (e.g., -log_summary).
173: */
174: PetscFinalize();
175: return 0;
176: }