Actual source code: ex1.c
petsc-3.8.4 2018-03-24
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>
21: int main(int argc,char **args)
22: {
23: Vec x, b, u; /* approx solution, RHS, exact solution */
24: Mat A; /* linear system matrix */
25: KSP ksp; /* linear solver context */
26: PC pc; /* preconditioner context */
27: PetscReal norm; /* norm of solution error */
29: PetscInt i,n = 10,col[3],its;
30: PetscMPIInt size;
31: PetscScalar one = 1.0,value[3];
32: PetscBool nonzeroguess = PETSC_FALSE,changepcside = PETSC_FALSE;
34: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
35: MPI_Comm_size(PETSC_COMM_WORLD,&size);
36: if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
37: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
38: PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);
41: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42: Compute the matrix and right-hand-side vector that define
43: the linear system, Ax = b.
44: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
46: /*
47: Create vectors. Note that we form 1 vector from scratch and
48: then duplicate as needed.
49: */
50: VecCreate(PETSC_COMM_WORLD,&x);
51: PetscObjectSetName((PetscObject) x, "Solution");
52: VecSetSizes(x,PETSC_DECIDE,n);
53: VecSetFromOptions(x);
54: VecDuplicate(x,&b);
55: VecDuplicate(x,&u);
57: /*
58: Create matrix. When using MatCreate(), the matrix format can
59: be specified at runtime.
61: Performance tuning note: For problems of substantial size,
62: preallocation of matrix memory is crucial for attaining good
63: performance. See the matrix chapter of the users manual for details.
64: */
65: MatCreate(PETSC_COMM_WORLD,&A);
66: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
67: MatSetFromOptions(A);
68: MatSetUp(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);
105: /*
106: Test if you can change the KSP side and type after they have been previously set
107: */
108: PetscOptionsGetBool(NULL,NULL,"-change_pc_side",&changepcside,NULL);
109: if (changepcside) {
110: KSPSetUp(ksp);
111: PetscOptionsInsertString(NULL,"-ksp_norm_type unpreconditioned -ksp_pc_side right");
112: KSPSetFromOptions(ksp);
113: KSPSetUp(ksp);
114: }
116: /*
117: Set linear solver defaults for this problem (optional).
118: - By extracting the KSP and PC contexts from the KSP context,
119: we can then directly call any KSP and PC routines to set
120: various options.
121: - The following four statements are optional; all of these
122: parameters could alternatively be specified at runtime via
123: KSPSetFromOptions();
124: */
125: KSPGetPC(ksp,&pc);
126: PCSetType(pc,PCJACOBI);
127: KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
129: /*
130: Set runtime options, e.g.,
131: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
132: These options will override those specified above as long as
133: KSPSetFromOptions() is called _after_ any other customization
134: routines.
135: */
136: KSPSetFromOptions(ksp);
138: if (nonzeroguess) {
139: PetscScalar p = .5;
140: VecSet(x,p);
141: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
142: }
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Solve the linear system
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: /*
148: Solve linear system
149: */
150: KSPSolve(ksp,b,x);
152: /*
153: View solver info; we could instead use the option -ksp_view to
154: print this info to the screen at the conclusion of KSPSolve().
155: */
156: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
158: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: Check solution and clean up
160: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
161: /*
162: Check the error
163: */
164: VecAXPY(x,-1.0,u);
165: VecNorm(x,NORM_2,&norm);
166: KSPGetIterationNumber(ksp,&its);
167: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
169: /*
170: Free work space. All PETSc objects should be destroyed when they
171: are no longer needed.
172: */
173: VecDestroy(&x); VecDestroy(&u);
174: VecDestroy(&b); MatDestroy(&A);
175: KSPDestroy(&ksp);
177: /*
178: Always call PetscFinalize() before exiting a program. This routine
179: - finalizes the PETSc libraries as well as MPI
180: - provides summary and diagnostic information if certain runtime
181: options are chosen (e.g., -log_view).
182: */
183: PetscFinalize();
184: return ierr;
185: }