Actual source code: ex1.c
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 petscpc.h - preconditioners
14: petscis.h - index sets
15: petscviewer.h - viewers
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 */
28: PetscInt i,n = 10,col[3],its;
29: PetscMPIInt size;
30: PetscScalar value[3];
32: PetscInitialize(&argc,&args,(char*)0,help);
33: MPI_Comm_size(PETSC_COMM_WORLD,&size);
35: PetscOptionsGetInt(NULL,NULL,"-n",&n,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: Set exact solution; then compute right-hand-side vector.
83: */
84: VecSet(u,1.0);
85: MatMult(A,u,b);
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Create the linear solver and set various options
89: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
90: KSPCreate(PETSC_COMM_WORLD,&ksp);
92: /*
93: Set operators. Here the matrix that defines the linear system
94: also serves as the matrix that defines the preconditioner.
95: */
96: KSPSetOperators(ksp,A,A);
98: /*
99: Set linear solver defaults for this problem (optional).
100: - By extracting the KSP and PC contexts from the KSP context,
101: we can then directly call any KSP and PC routines to set
102: various options.
103: - The following four statements are optional; all of these
104: parameters could alternatively be specified at runtime via
105: KSPSetFromOptions();
106: */
107: KSPGetPC(ksp,&pc);
108: PCSetType(pc,PCJACOBI);
109: KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
111: /*
112: Set runtime options, e.g.,
113: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
114: These options will override those specified above as long as
115: KSPSetFromOptions() is called _after_ any other customization
116: routines.
117: */
118: KSPSetFromOptions(ksp);
120: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121: Solve the linear system
122: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123: KSPSolve(ksp,b,x);
125: /*
126: View solver info; we could instead use the option -ksp_view to
127: print this info to the screen at the conclusion of KSPSolve().
128: */
129: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Check the solution and clean up
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: VecAXPY(x,-1.0,u);
135: VecNorm(x,NORM_2,&norm);
136: KSPGetIterationNumber(ksp,&its);
137: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
139: /*
140: Free work space. All PETSc objects should be destroyed when they
141: are no longer needed.
142: */
143: VecDestroy(&x)); PetscCall(VecDestroy(&u);
144: VecDestroy(&b)); PetscCall(MatDestroy(&A);
145: KSPDestroy(&ksp);
147: /*
148: Always call PetscFinalize() before exiting a program. This routine
149: - finalizes the PETSc libraries as well as MPI
150: - provides summary and diagnostic information if certain runtime
151: options are chosen (e.g., -log_view).
152: */
153: PetscFinalize();
154: return 0;
155: }
157: /*TEST
159: test:
160: args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
162: test:
163: suffix: 2
164: args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
166: test:
167: suffix: 2_aijcusparse
168: requires: cuda
169: args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
171: test:
172: suffix: 3
173: args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
175: test:
176: suffix: 3_aijcusparse
177: requires: cuda
178: args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
180: test:
181: suffix: aijcusparse
182: requires: cuda
183: args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
184: output_file: output/ex1_1_aijcusparse.out
186: TEST*/