Actual source code: ex23.c
2: static char help[] = "Solves a tridiagonal linear system.\n\n";
4: /*T
5: Concepts: KSP^basic parallel example;
6: Processors: n
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 uniprocessor example is ex1.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,tol=1000.*PETSC_MACHINE_EPSILON; /* norm of solution error */
29: PetscInt i,n = 10,col[3],its,rstart,rend,nlocal;
30: PetscScalar one = 1.0,value[3];
32: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
33: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
35: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
36: Compute the matrix and right-hand-side vector that define
37: the linear system, Ax = b.
38: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
40: /*
41: Create vectors. Note that we form 1 vector from scratch and
42: then duplicate as needed. For this simple case let PETSc decide how
43: many elements of the vector are stored on each processor. The second
44: argument to VecSetSizes() below causes PETSc to decide.
45: */
46: VecCreate(PETSC_COMM_WORLD,&x);
47: VecSetSizes(x,PETSC_DECIDE,n);
48: VecSetFromOptions(x);
49: VecDuplicate(x,&b);
50: VecDuplicate(x,&u);
52: /* Identify the starting and ending mesh points on each
53: processor for the interior part of the mesh. We let PETSc decide
54: above. */
56: VecGetOwnershipRange(x,&rstart,&rend);
57: VecGetLocalSize(x,&nlocal);
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.
67: We pass in nlocal as the "local" size of the matrix to force it
68: to have the same parallel layout as the vector created above.
69: */
70: MatCreate(PETSC_COMM_WORLD,&A);
71: MatSetSizes(A,nlocal,nlocal,n,n);
72: MatSetFromOptions(A);
73: MatSetUp(A);
75: /*
76: Assemble matrix.
78: The linear system is distributed across the processors by
79: chunks of contiguous rows, which correspond to contiguous
80: sections of the mesh on which the problem is discretized.
81: For matrix assembly, each processor contributes entries for
82: the part that it owns locally.
83: */
85: if (!rstart) {
86: rstart = 1;
87: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
88: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
89: }
90: if (rend == n) {
91: rend = n-1;
92: i = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
93: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
94: }
96: /* Set entries corresponding to the mesh interior */
97: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
98: for (i=rstart; i<rend; i++) {
99: col[0] = i-1; col[1] = i; col[2] = i+1;
100: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
101: }
103: /* Assemble the matrix */
104: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
105: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
107: /*
108: Set exact solution; then compute right-hand-side vector.
109: */
110: VecSet(u,one);
111: MatMult(A,u,b);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Create the linear solver and set various options
115: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116: /*
117: Create linear solver context
118: */
119: KSPCreate(PETSC_COMM_WORLD,&ksp);
121: /*
122: Set operators. Here the matrix that defines the linear system
123: also serves as the preconditioning matrix.
124: */
125: KSPSetOperators(ksp,A,A);
127: /*
128: Set linear solver defaults for this problem (optional).
129: - By extracting the KSP and PC contexts from the KSP context,
130: we can then directly call any KSP and PC routines to set
131: various options.
132: - The following four statements are optional; all of these
133: parameters could alternatively be specified at runtime via
134: KSPSetFromOptions();
135: */
136: KSPGetPC(ksp,&pc);
137: PCSetType(pc,PCJACOBI);
138: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
140: /*
141: Set runtime options, e.g.,
142: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
143: These options will override those specified above as long as
144: KSPSetFromOptions() is called _after_ any other customization
145: routines.
146: */
147: KSPSetFromOptions(ksp);
149: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: Solve the linear system
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: /*
153: Solve linear system
154: */
155: KSPSolve(ksp,b,x);
157: /*
158: View solver info; we could instead use the option -ksp_view to
159: print this info to the screen at the conclusion of KSPSolve().
160: */
161: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
163: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: Check solution and clean up
165: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166: /*
167: Check the error
168: */
169: VecAXPY(x,-1.0,u);
170: VecNorm(x,NORM_2,&norm);
171: KSPGetIterationNumber(ksp,&its);
172: if (norm > tol) {
173: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
174: }
176: /*
177: Free work space. All PETSc objects should be destroyed when they
178: are no longer needed.
179: */
180: VecDestroy(&x); VecDestroy(&u);
181: VecDestroy(&b); MatDestroy(&A);
182: KSPDestroy(&ksp);
184: /*
185: Always call PetscFinalize() before exiting a program. This routine
186: - finalizes the PETSc libraries as well as MPI
187: - provides summary and diagnostic information if certain runtime
188: options are chosen (e.g., -log_view).
189: */
190: PetscFinalize();
191: return ierr;
192: }
194: /*TEST
196: build:
197: requires: !complex !single
199: test:
200: args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
202: test:
203: suffix: 2
204: nsize: 3
205: args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
207: test:
208: suffix: 3
209: nsize: 2
210: args: -ksp_monitor_short -ksp_rtol 1e-6 -ksp_type pipefgmres
212: TEST*/