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: macro __FUNCT__ to define routine names for use in error handling.\n\
5: Input parameters include:\n\
6: -user_defined_pc : Activate a user-defined preconditioner\n\n";
8: /*T
9: Concepts: KSP^basic parallel example
10: Concepts: PC^setting a user-defined shell preconditioner
11: Concepts: error handling^Using the macro __FUNCT__ to define routine names;
12: Processors: n
13: T*/
15: /*
16: Include "petscksp.h" so that we can use KSP solvers. Note that this file
17: automatically includes:
18: petsc.h - base PETSc routines petscvec.h - vectors
19: petscsys.h - system routines petscmat.h - matrices
20: petscis.h - index sets petscksp.h - Krylov subspace methods
21: petscviewer.h - viewers petscpc.h - preconditioners
22: */
23: #include petscksp.h
25: /* Define context for user-provided preconditioner */
26: typedef struct {
27: Vec diag;
28: } SampleShellPC;
30: /* Declare routines for user-provided preconditioner */
36: /*
37: User-defined routines. Note that immediately before each routine below,
38: we define the macro __FUNCT__ to be a string containing the routine name.
39: If defined, this macro is used in the PETSc error handlers to provide a
40: complete traceback of routine names. All PETSc library routines use this
41: macro, and users can optionally employ it as well in their application
42: codes. Note that users can get a traceback of PETSc errors regardless of
43: whether they define __FUNCT__ in application codes; this macro merely
44: provides the added traceback detail of the application routine names.
45: */
49: int main(int argc,char **args)
50: {
51: Vec x,b,u; /* approx solution, RHS, exact solution */
52: Mat A; /* linear system matrix */
53: KSP ksp; /* linear solver context */
54: PC pc; /* preconditioner context */
55: PetscReal norm; /* norm of solution error */
56: SampleShellPC *shell; /* user-defined preconditioner context */
57: PetscScalar v,one = 1.0,none = -1.0;
58: PetscInt i,j,I,J,Istart,Iend,m = 8,n = 7,its;
60: PetscTruth user_defined_pc;
62: PetscInitialize(&argc,&args,(char *)0,help);
63: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
64: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
66: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: Compute the matrix and right-hand-side vector that define
68: the linear system, Ax = b.
69: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
70: /*
71: Create parallel matrix, specifying only its global dimensions.
72: When using MatCreate(), the matrix format can be specified at
73: runtime. Also, the parallel partioning of the matrix is
74: determined by PETSc at runtime.
75: */
76: MatCreate(PETSC_COMM_WORLD,&A);
77: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
78: MatSetFromOptions(A);
80: /*
81: Currently, all PETSc parallel matrix formats are partitioned by
82: contiguous chunks of rows across the processors. Determine which
83: rows of the matrix are locally owned.
84: */
85: MatGetOwnershipRange(A,&Istart,&Iend);
87: /*
88: Set matrix elements for the 2-D, five-point stencil in parallel.
89: - Each processor needs to insert only elements that it owns
90: locally (but any non-local elements will be sent to the
91: appropriate processor during matrix assembly).
92: - Always specify global rows and columns of matrix entries.
93: */
94: for (I=Istart; I<Iend; I++) {
95: v = -1.0; i = I/n; j = I - i*n;
96: if (i>0) {J = I - n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
97: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
98: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
99: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
100: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_VALUES);
101: }
103: /*
104: Assemble matrix, using the 2-step process:
105: MatAssemblyBegin(), MatAssemblyEnd()
106: Computations can be done while messages are in transition
107: by placing code between these two statements.
108: */
109: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
110: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
112: /*
113: Create parallel vectors.
114: - When using VecCreate() VecSetSizes() and VecSetFromOptions(),
115: we specify only the vector's global
116: dimension; the parallel partitioning is determined at runtime.
117: - Note: We form 1 vector from scratch and then duplicate as needed.
118: */
119: VecCreate(PETSC_COMM_WORLD,&u);
120: VecSetSizes(u,PETSC_DECIDE,m*n);
121: VecSetFromOptions(u);
122: VecDuplicate(u,&b);
123: VecDuplicate(b,&x);
125: /*
126: Set exact solution; then compute right-hand-side vector.
127: */
128: VecSet(u,one);
129: MatMult(A,u,b);
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Create the linear solver and set various options
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: /*
136: Create linear solver context
137: */
138: KSPCreate(PETSC_COMM_WORLD,&ksp);
140: /*
141: Set operators. Here the matrix that defines the linear system
142: also serves as the preconditioning matrix.
143: */
144: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
146: /*
147: Set linear solver defaults for this problem (optional).
148: - By extracting the KSP and PC contexts from the KSP context,
149: we can then directly call any KSP and PC routines
150: to set various options.
151: */
152: KSPGetPC(ksp,&pc);
153: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,
154: PETSC_DEFAULT);
156: /*
157: Set a user-defined "shell" preconditioner if desired
158: */
159: PetscOptionsHasName(PETSC_NULL,"-user_defined_pc",&user_defined_pc);
160: if (user_defined_pc) {
161: /* (Required) Indicate to PETSc that we're using a "shell" preconditioner */
162: PCSetType(pc,PCSHELL);
164: /* (Optional) Create a context for the user-defined preconditioner; this
165: context can be used to contain any application-specific data. */
166: SampleShellPCCreate(&shell);
168: /* (Required) Set the user-defined routine for applying the preconditioner */
169: PCShellSetApply(pc,SampleShellPCApply);
170: PCShellSetContext(pc,shell);
172: /* (Optional) Set a name for the preconditioner, used for PCView() */
173: PCShellSetName(pc,"MyPreconditioner");
175: /* (Optional) Do any setup required for the preconditioner */
176: SampleShellPCSetUp(shell,A,x);
178: } else {
179: PCSetType(pc,PCJACOBI);
180: }
182: /*
183: Set runtime options, e.g.,
184: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
185: These options will override those specified above as long as
186: KSPSetFromOptions() is called _after_ any other customization
187: routines.
188: */
189: KSPSetFromOptions(ksp);
191: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192: Solve the linear system
193: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: KSPSolve(ksp,b,x);
197: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: Check solution and clean up
199: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: /*
202: Check the error
203: */
204: VecAXPY(x,none,u);
205: VecNorm(x,NORM_2,&norm);
206: KSPGetIterationNumber(ksp,&its);
207: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",norm,its);
209: /*
210: Free work space. All PETSc objects should be destroyed when they
211: are no longer needed.
212: */
213: KSPDestroy(ksp);
214: VecDestroy(u); VecDestroy(x);
215: VecDestroy(b); MatDestroy(A);
217: if (user_defined_pc) {
218: SampleShellPCDestroy(shell);
219: }
221: PetscFinalize();
222: return 0;
224: }
226: /***********************************************************************/
227: /* Routines for a user-defined shell preconditioner */
228: /***********************************************************************/
232: /*
233: SampleShellPCCreate - This routine creates a user-defined
234: preconditioner context.
236: Output Parameter:
237: . shell - user-defined preconditioner context
238: */
239: PetscErrorCode SampleShellPCCreate(SampleShellPC **shell)
240: {
241: SampleShellPC *newctx;
244: PetscNew(SampleShellPC,&newctx);
245: newctx->diag = 0;
246: *shell = newctx;
247: return 0;
248: }
249: /* ------------------------------------------------------------------- */
252: /*
253: SampleShellPCSetUp - This routine sets up a user-defined
254: preconditioner context.
256: Input Parameters:
257: . shell - user-defined preconditioner context
258: . pmat - preconditioner matrix
259: . x - vector
261: Output Parameter:
262: . shell - fully set up user-defined preconditioner context
264: Notes:
265: In this example, we define the shell preconditioner to be Jacobi's
266: method. Thus, here we create a work vector for storing the reciprocal
267: of the diagonal of the preconditioner matrix; this vector is then
268: used within the routine SampleShellPCApply().
269: */
270: PetscErrorCode SampleShellPCSetUp(SampleShellPC *shell,Mat pmat,Vec x)
271: {
272: Vec diag;
275: VecDuplicate(x,&diag);
276: MatGetDiagonal(pmat,diag);
277: VecReciprocal(diag);
278: shell->diag = diag;
280: return 0;
281: }
282: /* ------------------------------------------------------------------- */
285: /*
286: SampleShellPCApply - This routine demonstrates the use of a
287: user-provided preconditioner.
289: Input Parameters:
290: . ctx - optional user-defined context, as set by PCShellSetContext()
291: . x - input vector
293: Output Parameter:
294: . y - preconditioned vector
296: Notes:
297: Note that the PCSHELL preconditioner passes a void pointer as the
298: first input argument. This can be cast to be the whatever the user
299: has set (via PCSetShellApply()) the application-defined context to be.
301: This code implements the Jacobi preconditioner, merely as an
302: example of working with a PCSHELL. Note that the Jacobi method
303: is already provided within PETSc.
304: */
305: PetscErrorCode SampleShellPCApply(void *ctx,Vec x,Vec y)
306: {
307: SampleShellPC *shell = (SampleShellPC*)ctx;
308: PetscErrorCode ierr;
310: VecPointwiseMult(y,x,shell->diag);
312: return 0;
313: }
314: /* ------------------------------------------------------------------- */
317: /*
318: SampleShellPCDestroy - This routine destroys a user-defined
319: preconditioner context.
321: Input Parameter:
322: . shell - user-defined preconditioner context
323: */
324: PetscErrorCode SampleShellPCDestroy(SampleShellPC *shell)
325: {
328: VecDestroy(shell->diag);
329: PetscFree(shell);
331: return 0;
332: }