Actual source code: ex58.c
petsc-3.3-p7 2013-05-11
2: /* Program usage: mpiexec ex1 [-help] [all PETSc options] */
4: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";
6: /*T
7: Concepts: KSP^solving a system of linear equations
8: Processors: 1
9: T*/
11: /*
12: Modified from ex1.c for testing matrix operations when matrix structure is changed.
13: Contributed by Jose E. Roman, Feb. 2012.
14: */
15: #include <petscksp.h>
19: int main(int argc,char **args)
20: {
21: Vec x, b, u; /* approx solution, RHS, exact solution */
22: Mat A,B,C; /* linear system matrix */
23: KSP ksp; /* linear solver context */
24: PC pc; /* preconditioner context */
25: PetscReal norm; /* norm of solution error */
27: PetscInt i,n = 20,col[3],its;
28: PetscMPIInt size;
29: PetscScalar neg_one = -1.0,one = 1.0,value[3];
30: PetscBool nonzeroguess = PETSC_FALSE;
32: PetscInitialize(&argc,&args,(char *)0,help);
33: MPI_Comm_size(PETSC_COMM_WORLD,&size);
34: if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
35: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
36: PetscOptionsGetBool(PETSC_NULL,"-nonzero_guess",&nonzeroguess,PETSC_NULL);
39: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: Compute the matrix and right-hand-side vector that define
41: the linear system, Ax = b.
42: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
44: /*
45: Create vectors. Note that we form 1 vector from scratch and
46: then duplicate as needed.
47: */
48: VecCreate(PETSC_COMM_WORLD,&x);
49: PetscObjectSetName((PetscObject) x, "Solution");
50: VecSetSizes(x,PETSC_DECIDE,n);
51: VecSetFromOptions(x);
52: VecDuplicate(x,&b);
53: VecDuplicate(x,&u);
55: /*
56: Create matrix. When using MatCreate(), the matrix format can
57: be specified at runtime.
59: Performance tuning note: For problems of substantial size,
60: preallocation of matrix memory is crucial for attaining good
61: performance. See the matrix chapter of the users manual for details.
62: */
63: MatCreate(PETSC_COMM_WORLD,&A);
64: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
65: MatSetFromOptions(A);
66: MatSetUp(A);
68: /*
69: Assemble matrix
70: */
71: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
72: for (i=1; i<n-1; i++) {
73: col[0] = i-1; col[1] = i; col[2] = i+1;
74: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
75: }
76: i = n - 1; col[0] = n - 2; col[1] = n - 1;
77: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
78: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
79: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
80: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
81: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
83: /*
84: jroman: added matrices
85: */
86: MatCreate(PETSC_COMM_WORLD,&B);
87: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
88: MatSetFromOptions(B);
89: MatSetUp(B);
90: for (i=0; i<n; i++) {
91: MatSetValue(B,i,i,value[1],INSERT_VALUES);
92: if (n-i+n/3<n) {
93: MatSetValue(B,n-i+n/3,i,value[0],INSERT_VALUES);
94: MatSetValue(B,i,n-i+n/3,value[0],INSERT_VALUES);
95: }
96: }
97: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
98: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
99: MatDuplicate(A,MAT_COPY_VALUES,&C);
100: MatAXPY(C,2.0,B,DIFFERENT_NONZERO_PATTERN);
102: /*
103: Set exact solution; then compute right-hand-side vector.
104: */
105: VecSet(u,one);
106: MatMult(C,u,b);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Create the linear solver and set various options
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111: /*
112: Create linear solver context
113: */
114: KSPCreate(PETSC_COMM_WORLD,&ksp);
116: /*
117: Set operators. Here the matrix that defines the linear system
118: also serves as the preconditioning matrix.
119: */
120: KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
122: /*
123: Set linear solver defaults for this problem (optional).
124: - By extracting the KSP and PC contexts from the KSP context,
125: we can then directly call any KSP and PC routines to set
126: various options.
127: - The following four statements are optional; all of these
128: parameters could alternatively be specified at runtime via
129: KSPSetFromOptions();
130: */
131: KSPGetPC(ksp,&pc);
132: PCSetType(pc,PCJACOBI);
133: KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
135: /*
136: Set runtime options, e.g.,
137: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
138: These options will override those specified above as long as
139: KSPSetFromOptions() is called _after_ any other customization
140: routines.
141: */
142: KSPSetFromOptions(ksp);
144: if (nonzeroguess) {
145: PetscScalar p = .5;
146: VecSet(x,p);
147: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
148: }
149:
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Solve the linear system
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: /*
154: Solve linear system
155: */
156: KSPSolve(ksp,b,x);
158: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: Check solution and clean up
160: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
161: /*
162: Check the error
163: */
164: VecAXPY(x,neg_one,u);
165: VecNorm(x,NORM_2,&norm);
166: KSPGetIterationNumber(ksp,&its);
167: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G, Iterations %D\n",
168: norm,its);
170: /*
171: Free work space. All PETSc objects should be destroyed when they
172: are no longer needed.
173: */
174: VecDestroy(&x); VecDestroy(&u);
175: VecDestroy(&b); MatDestroy(&A);
176: MatDestroy(&B);
177: MatDestroy(&C);
178: KSPDestroy(&ksp);
180: /*
181: Always call PetscFinalize() before exiting a program. This routine
182: - finalizes the PETSc libraries as well as MPI
183: - provides summary and diagnostic information if certain runtime
184: options are chosen (e.g., -log_summary).
185: */
186: PetscFinalize();
187: return 0;
188: }