Actual source code: ex15.c
2: static char help[] = "Solves a linear system in parallel with KSP. Also\n\
3: illustrates setting a user-defined shell preconditioner and using the\n\
4: Input parameters include:\n\
5: -user_defined_pc : Activate a user-defined preconditioner\n\n";
7: /*
8: Include "petscksp.h" so that we can use KSP solvers. Note that this file
9: automatically includes:
10: petscsys.h - base PETSc routines petscvec.h - vectors
11: petscmat.h - matrices
12: petscis.h - index sets petscksp.h - Krylov subspace methods
13: petscviewer.h - viewers petscpc.h - preconditioners
14: */
15: #include <petscksp.h>
17: /* Define context for user-provided preconditioner */
18: typedef struct {
19: Vec diag;
20: } SampleShellPC;
22: /* Declare routines for user-provided preconditioner */
23: extern PetscErrorCode SampleShellPCCreate(SampleShellPC **);
24: extern PetscErrorCode SampleShellPCSetUp(PC, Mat, Vec);
25: extern PetscErrorCode SampleShellPCApply(PC, Vec x, Vec y);
26: extern PetscErrorCode SampleShellPCDestroy(PC);
28: /*
29: User-defined routines. Note that immediately before each routine below,
30: If defined, this macro is used in the PETSc error handlers to provide a
31: complete traceback of routine names. All PETSc library routines use this
32: macro, and users can optionally employ it as well in their application
33: codes. Note that users can get a traceback of PETSc errors regardless of
34: provides the added traceback detail of the application routine names.
35: */
37: int main(int argc, char **args)
38: {
39: Vec x, b, u; /* approx solution, RHS, exact solution */
40: Mat A; /* linear system matrix */
41: KSP ksp; /* linear solver context */
42: PC pc; /* preconditioner context */
43: PetscReal norm; /* norm of solution error */
44: SampleShellPC *shell; /* user-defined preconditioner context */
45: PetscScalar v, one = 1.0, none = -1.0;
46: PetscInt i, j, Ii, J, Istart, Iend, m = 8, n = 7, its;
47: PetscBool user_defined_pc = PETSC_FALSE;
50: PetscInitialize(&argc, &args, (char *)0, help);
51: PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL);
52: PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL);
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Compute the matrix and right-hand-side vector that define
56: the linear system, Ax = b.
57: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: /*
59: Create parallel matrix, specifying only its global dimensions.
60: When using MatCreate(), the matrix format can be specified at
61: runtime. Also, the parallel partioning of the matrix is
62: determined by PETSc at runtime.
63: */
64: MatCreate(PETSC_COMM_WORLD, &A);
65: MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, m * n, m * n);
66: MatSetFromOptions(A);
67: MatSetUp(A);
69: /*
70: Currently, all PETSc parallel matrix formats are partitioned by
71: contiguous chunks of rows across the processors. Determine which
72: rows of the matrix are locally owned.
73: */
74: MatGetOwnershipRange(A, &Istart, &Iend);
76: /*
77: Set matrix elements for the 2-D, five-point stencil in parallel.
78: - Each processor needs to insert only elements that it owns
79: locally (but any non-local elements will be sent to the
80: appropriate processor during matrix assembly).
81: - Always specify global rows and columns of matrix entries.
82: */
83: for (Ii = Istart; Ii < Iend; Ii++) {
84: v = -1.0;
85: i = Ii / n;
86: j = Ii - i * n;
87: if (i > 0) {
88: J = Ii - n;
89: MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
90: }
91: if (i < m - 1) {
92: J = Ii + n;
93: MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
94: }
95: if (j > 0) {
96: J = Ii - 1;
97: MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
98: }
99: if (j < n - 1) {
100: J = Ii + 1;
101: MatSetValues(A, 1, &Ii, 1, &J, &v, INSERT_VALUES);
102: }
103: v = 4.0;
104: MatSetValues(A, 1, &Ii, 1, &Ii, &v, INSERT_VALUES);
105: }
107: /*
108: Assemble matrix, using the 2-step process:
109: MatAssemblyBegin(), MatAssemblyEnd()
110: Computations can be done while messages are in transition
111: by placing code between these two statements.
112: */
113: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
114: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
116: /*
117: Create parallel vectors.
118: - When using VecCreate() VecSetSizes() and VecSetFromOptions(),
119: we specify only the vector's global
120: dimension; the parallel partitioning is determined at runtime.
121: - Note: We form 1 vector from scratch and then duplicate as needed.
122: */
123: VecCreate(PETSC_COMM_WORLD, &u);
124: VecSetSizes(u, PETSC_DECIDE, m * n);
125: VecSetFromOptions(u);
126: VecDuplicate(u, &b);
127: VecDuplicate(b, &x);
129: /*
130: Set exact solution; then compute right-hand-side vector.
131: */
132: VecSet(u, one);
133: MatMult(A, u, b);
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Create the linear solver and set various options
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: /*
140: Create linear solver context
141: */
142: KSPCreate(PETSC_COMM_WORLD, &ksp);
144: /*
145: Set operators. Here the matrix that defines the linear system
146: also serves as the preconditioning matrix.
147: */
148: KSPSetOperators(ksp, A, A);
150: /*
151: Set linear solver defaults for this problem (optional).
152: - By extracting the KSP and PC contexts from the KSP context,
153: we can then directly call any KSP and PC routines
154: to set various options.
155: */
156: KSPGetPC(ksp, &pc);
157: KSPSetTolerances(ksp, 1.e-7, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
159: /*
160: Set a user-defined "shell" preconditioner if desired
161: */
162: PetscOptionsGetBool(NULL, NULL, "-user_defined_pc", &user_defined_pc, NULL);
163: if (user_defined_pc) {
164: /* (Required) Indicate to PETSc that we're using a "shell" preconditioner */
165: PCSetType(pc, PCSHELL);
167: /* (Optional) Create a context for the user-defined preconditioner; this
168: context can be used to contain any application-specific data. */
169: SampleShellPCCreate(&shell);
171: /* (Required) Set the user-defined routine for applying the preconditioner */
172: PCShellSetApply(pc, SampleShellPCApply);
173: PCShellSetContext(pc, shell);
175: /* (Optional) Set user-defined function to free objects used by custom preconditioner */
176: PCShellSetDestroy(pc, SampleShellPCDestroy);
178: /* (Optional) Set a name for the preconditioner, used for PCView() */
179: PCShellSetName(pc, "MyPreconditioner");
181: /* (Optional) Do any setup required for the preconditioner */
182: /* Note: This function could be set with PCShellSetSetUp and it would be called when necessary */
183: SampleShellPCSetUp(pc, A, x);
185: } else {
186: PCSetType(pc, PCJACOBI);
187: }
189: /*
190: Set runtime options, e.g.,
191: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
192: These options will override those specified above as long as
193: KSPSetFromOptions() is called _after_ any other customization
194: routines.
195: */
196: KSPSetFromOptions(ksp);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Solve the linear system
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: KSPSolve(ksp, b, x);
204: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: Check solution and clean up
206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
208: /*
209: Check the error
210: */
211: VecAXPY(x, none, u);
212: VecNorm(x, NORM_2, &norm);
213: KSPGetIterationNumber(ksp, &its);
214: PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g iterations %" PetscInt_FMT "\n", (double)norm, its);
216: /*
217: Free work space. All PETSc objects should be destroyed when they
218: are no longer needed.
219: */
220: KSPDestroy(&ksp);
221: VecDestroy(&u);
222: VecDestroy(&x);
223: VecDestroy(&b);
224: MatDestroy(&A);
226: PetscFinalize();
227: return 0;
228: }
230: /***********************************************************************/
231: /* Routines for a user-defined shell preconditioner */
232: /***********************************************************************/
234: /*
235: SampleShellPCCreate - This routine creates a user-defined
236: preconditioner context.
238: Output Parameter:
239: . shell - user-defined preconditioner context
240: */
241: PetscErrorCode SampleShellPCCreate(SampleShellPC **shell)
242: {
243: SampleShellPC *newctx;
245: PetscNew(&newctx);
246: newctx->diag = 0;
247: *shell = newctx;
248: return 0;
249: }
250: /* ------------------------------------------------------------------- */
251: /*
252: SampleShellPCSetUp - This routine sets up a user-defined
253: preconditioner context.
255: Input Parameters:
256: . pc - preconditioner object
257: . pmat - preconditioner matrix
258: . x - vector
260: Output Parameter:
261: . shell - fully set up user-defined preconditioner context
263: Notes:
264: In this example, we define the shell preconditioner to be Jacobi's
265: method. Thus, here we create a work vector for storing the reciprocal
266: of the diagonal of the preconditioner matrix; this vector is then
267: used within the routine SampleShellPCApply().
268: */
269: PetscErrorCode SampleShellPCSetUp(PC pc, Mat pmat, Vec x)
270: {
271: SampleShellPC *shell;
272: Vec diag;
274: PCShellGetContext(pc, &shell);
275: VecDuplicate(x, &diag);
276: MatGetDiagonal(pmat, diag);
277: VecReciprocal(diag);
279: shell->diag = diag;
280: return 0;
281: }
282: /* ------------------------------------------------------------------- */
283: /*
284: SampleShellPCApply - This routine demonstrates the use of a
285: user-provided preconditioner.
287: Input Parameters:
288: + pc - preconditioner object
289: - x - input vector
291: Output Parameter:
292: . y - preconditioned vector
294: Notes:
295: This code implements the Jacobi preconditioner, merely as an
296: example of working with a PCSHELL. Note that the Jacobi method
297: is already provided within PETSc.
298: */
299: PetscErrorCode SampleShellPCApply(PC pc, Vec x, Vec y)
300: {
301: SampleShellPC *shell;
303: PCShellGetContext(pc, &shell);
304: VecPointwiseMult(y, x, shell->diag);
306: return 0;
307: }
308: /* ------------------------------------------------------------------- */
309: /*
310: SampleShellPCDestroy - This routine destroys a user-defined
311: preconditioner context.
313: Input Parameter:
314: . shell - user-defined preconditioner context
315: */
316: PetscErrorCode SampleShellPCDestroy(PC pc)
317: {
318: SampleShellPC *shell;
320: PCShellGetContext(pc, &shell);
321: VecDestroy(&shell->diag);
322: PetscFree(shell);
324: return 0;
325: }
327: /*TEST
329: build:
330: requires: !complex !single
332: test:
333: nsize: 2
334: args: -ksp_view -user_defined_pc -ksp_gmres_cgs_refinement_type refine_always
336: test:
337: suffix: tsirm
338: args: -m 60 -n 60 -ksp_type tsirm -pc_type ksp -ksp_monitor_short -ksp_ksp_type fgmres -ksp_ksp_rtol 1e-10 -ksp_pc_type mg -ksp_ksp_max_it 30
339: timeoutfactor: 4
341: TEST*/