Actual source code: ex58.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: Modified from ex1.c for testing matrix operations when matrix structure is changed.
11: Contributed by Jose E. Roman, Feb. 2012.
12: */
13: #include <petscksp.h>
17: int main(int argc,char **args)
18: {
19: Vec x, b, u; /* approx solution, RHS, exact solution */
20: Mat A,B,C; /* linear system matrix */
21: KSP ksp; /* linear solver context */
22: PC pc; /* preconditioner context */
23: PetscReal norm; /* norm of solution error */
25: PetscInt i,n = 20,col[3],its;
26: PetscMPIInt size;
27: PetscScalar neg_one = -1.0,one = 1.0,value[3];
28: PetscBool nonzeroguess = PETSC_FALSE;
30: PetscInitialize(&argc,&args,(char*)0,help);
31: MPI_Comm_size(PETSC_COMM_WORLD,&size);
32: if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
33: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
34: PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);
37: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
38: Compute the matrix and right-hand-side vector that define
39: the linear system, Ax = b.
40: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
42: /*
43: Create vectors. Note that we form 1 vector from scratch and
44: then duplicate as needed.
45: */
46: VecCreate(PETSC_COMM_WORLD,&x);
47: PetscObjectSetName((PetscObject) x, "Solution");
48: VecSetSizes(x,PETSC_DECIDE,n);
49: VecSetFromOptions(x);
50: VecDuplicate(x,&b);
51: VecDuplicate(x,&u);
53: /*
54: Create matrix. When using MatCreate(), the matrix format can
55: be specified at runtime.
57: Performance tuning note: For problems of substantial size,
58: preallocation of matrix memory is crucial for attaining good
59: performance. See the matrix chapter of the users manual for details.
60: */
61: MatCreate(PETSC_COMM_WORLD,&A);
62: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
63: MatSetFromOptions(A);
64: MatSetUp(A);
66: /*
67: Assemble matrix
68: */
69: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
70: for (i=1; i<n-1; i++) {
71: col[0] = i-1; col[1] = i; col[2] = i+1;
72: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
73: }
74: i = n - 1; col[0] = n - 2; col[1] = n - 1;
75: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
76: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
77: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
78: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
79: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
81: /*
82: jroman: added matrices
83: */
84: MatCreate(PETSC_COMM_WORLD,&B);
85: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
86: MatSetFromOptions(B);
87: MatSetUp(B);
88: for (i=0; i<n; i++) {
89: MatSetValue(B,i,i,value[1],INSERT_VALUES);
90: if (n-i+n/3<n) {
91: MatSetValue(B,n-i+n/3,i,value[0],INSERT_VALUES);
92: MatSetValue(B,i,n-i+n/3,value[0],INSERT_VALUES);
93: }
94: }
95: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
96: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
97: MatDuplicate(A,MAT_COPY_VALUES,&C);
98: MatAXPY(C,2.0,B,DIFFERENT_NONZERO_PATTERN);
100: /*
101: Set exact solution; then compute right-hand-side vector.
102: */
103: VecSet(u,one);
104: MatMult(C,u,b);
106: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107: Create the linear solver and set various options
108: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109: /*
110: Create linear solver context
111: */
112: KSPCreate(PETSC_COMM_WORLD,&ksp);
114: /*
115: Set operators. Here the matrix that defines the linear system
116: also serves as the preconditioning matrix.
117: */
118: KSPSetOperators(ksp,C,C);
120: /*
121: Set linear solver defaults for this problem (optional).
122: - By extracting the KSP and PC contexts from the KSP context,
123: we can then directly call any KSP and PC routines to set
124: various options.
125: - The following four statements are optional; all of these
126: parameters could alternatively be specified at runtime via
127: KSPSetFromOptions();
128: */
129: KSPGetPC(ksp,&pc);
130: PCSetType(pc,PCJACOBI);
131: KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
133: /*
134: Set runtime options, e.g.,
135: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
136: These options will override those specified above as long as
137: KSPSetFromOptions() is called _after_ any other customization
138: routines.
139: */
140: KSPSetFromOptions(ksp);
142: if (nonzeroguess) {
143: PetscScalar p = .5;
144: VecSet(x,p);
145: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
146: }
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Solve the linear system
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151: /*
152: Solve linear system
153: */
154: KSPSolve(ksp,b,x);
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: Check solution and clean up
158: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
159: /*
160: Check the error
161: */
162: VecAXPY(x,neg_one,u);
163: VecNorm(x,NORM_2,&norm);
164: KSPGetIterationNumber(ksp,&its);
165: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
167: /*
168: Free work space. All PETSc objects should be destroyed when they
169: are no longer needed.
170: */
171: VecDestroy(&x); VecDestroy(&u);
172: VecDestroy(&b); MatDestroy(&A);
173: MatDestroy(&B);
174: MatDestroy(&C);
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_summary).
182: */
183: PetscFinalize();
184: return 0;
185: }