Actual source code: ex48.c
2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";
4: /*
5: Test example that demonstrates how MINRES can produce a dp of zero
6: but still converge.
8: Provided by: Mark Filipiak <mjf@staffmail.ed.ac.uk>
9: */
10: #include <petscksp.h>
12: int main(int argc,char **args)
13: {
14: Vec x, b, u; /* approx solution, RHS, exact solution */
15: Mat A; /* linear system matrix */
16: KSP ksp; /* linear solver context */
17: PC pc; /* preconditioner context */
18: PetscReal norm;
19: PetscInt i,n = 2,col[3],its;
20: PetscMPIInt size;
21: PetscScalar one = 1.0,value[3];
22: PetscBool nonzeroguess = PETSC_FALSE;
24: PetscInitialize(&argc,&args,(char*)0,help);
25: MPI_Comm_size(PETSC_COMM_WORLD,&size);
27: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
28: PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);
30: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
31: Compute the matrix and right-hand-side vector that define
32: the linear system, Ax = b.
33: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
35: /*
36: Create vectors. Note that we form 1 vector from scratch and
37: then duplicate as needed.
38: */
39: VecCreate(PETSC_COMM_WORLD,&x);
40: PetscObjectSetName((PetscObject) x, "Solution");
41: VecSetSizes(x,PETSC_DECIDE,n);
42: VecSetFromOptions(x);
43: VecDuplicate(x,&b);
44: VecDuplicate(x,&u);
46: /*
47: Create matrix. When using MatCreate(), the matrix format can
48: be specified at runtime.
50: Performance tuning note: For problems of substantial size,
51: preallocation of matrix memory is crucial for attaining good
52: performance. See the matrix chapter of the users manual for details.
53: */
54: MatCreate(PETSC_COMM_WORLD,&A);
55: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
56: MatSetFromOptions(A);
57: MatSetUp(A);
59: /*
60: Assemble matrix
61: */
62: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
63: for (i=1; i<n-1; i++) {
64: col[0] = i-1; col[1] = i; col[2] = i+1;
65: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
66: }
67: i = n - 1; col[0] = n - 2; col[1] = n - 1;
68: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
69: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
70: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
71: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
72: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
74: /*
75: Set constant right-hand-side vector.
76: */
77: VecSet(b,one);
78: /*
79: Solution = RHS for the matrix [[2 -1] [-1 2]] and RHS [1 1]
80: */
81: VecSet(u,one);
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Create the linear solver and set various options
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: /*
87: Create linear solver context
88: */
89: KSPCreate(PETSC_COMM_WORLD,&ksp);
91: /*
92: Set operators. Here the matrix that defines the linear system
93: also serves as the preconditioning matrix.
94: */
95: KSPSetOperators(ksp,A,A);
97: /*
98: Set linear solver defaults for this problem (optional).
99: - By extracting the KSP and PC contexts from the KSP context,
100: we can then directly call any KSP and PC routines to set
101: various options.
102: - The following four statements are optional; all of these
103: parameters could alternatively be specified at runtime via
104: KSPSetFromOptions();
105: */
106: KSPGetPC(ksp,&pc);
107: PCSetType(pc,PCJACOBI);
108: KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
110: /*
111: Set runtime options, e.g.,
112: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
113: These options will override those specified above as long as
114: KSPSetFromOptions() is called _after_ any other customization
115: routines.
116: */
117: KSPSetFromOptions(ksp);
119: if (nonzeroguess) {
120: PetscScalar p = .5;
121: VecSet(x,p);
122: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
123: }
125: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126: Solve the linear system
127: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128: /*
129: Solve linear system
130: */
131: KSPSolve(ksp,b,x);
133: /*
134: View solver info; we could instead use the option -ksp_view to
135: print this info to the screen at the conclusion of KSPSolve().
136: */
137: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Check solution and clean up
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142: /*
143: Check the error
144: */
145: VecAXPY(x,-1.0,u);
146: VecNorm(x,NORM_2,&norm);
147: KSPGetIterationNumber(ksp,&its);
148: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
150: /*
151: Free work space. All PETSc objects should be destroyed when they
152: are no longer needed.
153: */
154: VecDestroy(&x)); PetscCall(VecDestroy(&u);
155: VecDestroy(&b)); PetscCall(MatDestroy(&A);
156: KSPDestroy(&ksp);
158: /*
159: Always call PetscFinalize() before exiting a program. This routine
160: - finalizes the PETSc libraries as well as MPI
161: - provides summary and diagnostic information if certain runtime
162: options are chosen (e.g., -log_view).
163: */
164: PetscFinalize();
165: return 0;
166: }
168: /*TEST
170: test:
171: args: -ksp_monitor_short -ksp_converged_reason -ksp_type minres -pc_type jacobi -ksp_error_if_not_converged
173: TEST*/