Actual source code: ex2.c
2: static char help[] = "Solves a linear system in parallel with KSP.\n\
3: Input parameters include:\n\
4: -view_exact_sol : write exact solution vector to stdout\n\
5: -m <mesh_x> : number of mesh points in x-direction\n\
6: -n <mesh_y> : number of mesh points in y-direction\n\n";
8: /*
9: Include "petscksp.h" so that we can use KSP solvers.
10: */
11: #include <petscksp.h>
13: int main(int argc,char **args)
14: {
15: Vec x,b,u; /* approx solution, RHS, exact solution */
16: Mat A; /* linear system matrix */
17: KSP ksp; /* linear solver context */
18: PetscReal norm; /* norm of solution error */
19: PetscInt i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
20: PetscBool flg;
21: PetscScalar v;
23: PetscInitialize(&argc,&args,(char*)0,help);
24: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
25: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
26: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
27: Compute the matrix and right-hand-side vector that define
28: the linear system, Ax = b.
29: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
30: /*
31: Create parallel matrix, specifying only its global dimensions.
32: When using MatCreate(), the matrix format can be specified at
33: runtime. Also, the parallel partitioning of the matrix is
34: determined by PETSc at runtime.
36: Performance tuning note: For problems of substantial size,
37: preallocation of matrix memory is crucial for attaining good
38: performance. See the matrix chapter of the users manual for details.
39: */
40: MatCreate(PETSC_COMM_WORLD,&A);
41: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
42: MatSetFromOptions(A);
43: MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
44: MatSeqAIJSetPreallocation(A,5,NULL);
45: MatSeqSBAIJSetPreallocation(A,1,5,NULL);
46: MatMPISBAIJSetPreallocation(A,1,5,NULL,5,NULL);
47: MatMPISELLSetPreallocation(A,5,NULL,5,NULL);
48: MatSeqSELLSetPreallocation(A,5,NULL);
50: /*
51: Currently, all PETSc parallel matrix formats are partitioned by
52: contiguous chunks of rows across the processors. Determine which
53: rows of the matrix are locally owned.
54: */
55: MatGetOwnershipRange(A,&Istart,&Iend);
57: /*
58: Set matrix elements for the 2-D, five-point stencil in parallel.
59: - Each processor needs to insert only elements that it owns
60: locally (but any non-local elements will be sent to the
61: appropriate processor during matrix assembly).
62: - Always specify global rows and columns of matrix entries.
64: Note: this uses the less common natural ordering that orders first
65: all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
66: instead of J = I +- m as you might expect. The more standard ordering
67: would first do all variables for y = h, then y = 2h etc.
69: */
70: for (Ii=Istart; Ii<Iend; Ii++) {
71: v = -1.0; i = Ii/n; j = Ii - i*n;
72: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
73: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
74: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
75: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
76: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
77: }
79: /*
80: Assemble matrix, using the 2-step process:
81: MatAssemblyBegin(), MatAssemblyEnd()
82: Computations can be done while messages are in transition
83: by placing code between these two statements.
84: */
85: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
88: /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
89: MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
91: /*
92: Create parallel vectors.
93: - We form 1 vector from scratch and then duplicate as needed.
94: - When using VecCreate(), VecSetSizes and VecSetFromOptions()
95: in this example, we specify only the
96: vector's global dimension; the parallel partitioning is determined
97: at runtime.
98: - When solving a linear system, the vectors and matrices MUST
99: be partitioned accordingly. PETSc automatically generates
100: appropriately partitioned matrices and vectors when MatCreate()
101: and VecCreate() are used with the same communicator.
102: - The user can alternatively specify the local vector and matrix
103: dimensions when more sophisticated partitioning is needed
104: (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
105: below).
106: */
107: VecCreate(PETSC_COMM_WORLD,&u);
108: VecSetSizes(u,PETSC_DECIDE,m*n);
109: VecSetFromOptions(u);
110: VecDuplicate(u,&b);
111: VecDuplicate(b,&x);
113: /*
114: Set exact solution; then compute right-hand-side vector.
115: By default we use an exact solution of a vector with all
116: elements of 1.0;
117: */
118: VecSet(u,1.0);
119: MatMult(A,u,b);
121: /*
122: View the exact solution vector if desired
123: */
124: flg = PETSC_FALSE;
125: PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
126: if (flg) VecView(u,PETSC_VIEWER_STDOUT_WORLD);
128: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129: Create the linear solver and set various options
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: KSPCreate(PETSC_COMM_WORLD,&ksp);
133: /*
134: Set operators. Here the matrix that defines the linear system
135: also serves as the preconditioning matrix.
136: */
137: KSPSetOperators(ksp,A,A);
139: /*
140: Set linear solver defaults for this problem (optional).
141: - By extracting the KSP and PC contexts from the KSP context,
142: we can then directly call any KSP and PC routines to set
143: various options.
144: - The following two statements are optional; all of these
145: parameters could alternatively be specified at runtime via
146: KSPSetFromOptions(). All of these defaults can be
147: overridden at runtime, as indicated below.
148: */
149: KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,PETSC_DEFAULT);
151: /*
152: Set runtime options, e.g.,
153: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
154: These options will override those specified above as long as
155: KSPSetFromOptions() is called _after_ any other customization
156: routines.
157: */
158: KSPSetFromOptions(ksp);
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Solve the linear system
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
164: KSPSolve(ksp,b,x);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Check the solution and clean up
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: VecAXPY(x,-1.0,u);
170: VecNorm(x,NORM_2,&norm);
171: KSPGetIterationNumber(ksp,&its);
173: /*
174: Print convergence information. PetscPrintf() produces a single
175: print statement from all processes that share a communicator.
176: An alternative is PetscFPrintf(), which prints to a file.
177: */
178: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
180: /*
181: Free work space. All PETSc objects should be destroyed when they
182: are no longer needed.
183: */
184: KSPDestroy(&ksp);
185: VecDestroy(&u)); PetscCall(VecDestroy(&x);
186: VecDestroy(&b)); PetscCall(MatDestroy(&A);
188: /*
189: Always call PetscFinalize() before exiting a program. This routine
190: - finalizes the PETSc libraries as well as MPI
191: - provides summary and diagnostic information if certain runtime
192: options are chosen (e.g., -log_view).
193: */
194: PetscFinalize();
195: return 0;
196: }
198: /*TEST
200: build:
201: requires: !single
203: test:
204: suffix: chebyest_1
205: args: -m 80 -n 80 -ksp_pc_side right -pc_type ksp -ksp_ksp_type chebyshev -ksp_ksp_max_it 5 -ksp_ksp_chebyshev_esteig 0.9,0,0,1.1 -ksp_monitor_short
207: test:
208: suffix: chebyest_2
209: args: -m 80 -n 80 -ksp_pc_side right -pc_type ksp -ksp_ksp_type chebyshev -ksp_ksp_max_it 5 -ksp_ksp_chebyshev_esteig 0.9,0,0,1.1 -ksp_esteig_ksp_type cg -ksp_monitor_short
211: test:
212: args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always
214: test:
215: suffix: 2
216: nsize: 2
217: args: -ksp_monitor_short -m 5 -n 5 -ksp_gmres_cgs_refinement_type refine_always
219: test:
220: suffix: 3
221: args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
223: test:
224: suffix: 4
225: args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always
227: test:
228: suffix: 5
229: nsize: 2
230: args: -ksp_monitor_short -m 5 -n 5 -mat_view draw -ksp_gmres_cgs_refinement_type refine_always -nox
231: output_file: output/ex2_2.out
233: test:
234: suffix: bjacobi
235: nsize: 4
236: args: -pc_type bjacobi -pc_bjacobi_blocks 1 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres
238: test:
239: suffix: bjacobi_2
240: nsize: 4
241: args: -pc_type bjacobi -pc_bjacobi_blocks 2 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres -ksp_view
243: test:
244: suffix: bjacobi_3
245: nsize: 4
246: args: -pc_type bjacobi -pc_bjacobi_blocks 4 -ksp_monitor_short -sub_pc_type jacobi -sub_ksp_type gmres
248: test:
249: suffix: qmrcgs
250: args: -ksp_type qmrcgs -pc_type ilu
251: output_file: output/ex2_fbcgs.out
253: test:
254: suffix: qmrcgs_2
255: nsize: 3
256: args: -ksp_type qmrcgs -pc_type bjacobi
257: output_file: output/ex2_fbcgs_2.out
259: test:
260: suffix: fbcgs
261: args: -ksp_type fbcgs -pc_type ilu
263: test:
264: suffix: fbcgs_2
265: nsize: 3
266: args: -ksp_type fbcgsr -pc_type bjacobi
268: test:
269: suffix: groppcg
270: args: -ksp_monitor_short -ksp_type groppcg -m 9 -n 9
272: test:
273: suffix: mkl_pardiso_cholesky
274: requires: mkl_pardiso
275: args: -ksp_type preonly -pc_type cholesky -mat_type sbaij -pc_factor_mat_solver_type mkl_pardiso
277: test:
278: suffix: mkl_pardiso_lu
279: requires: mkl_pardiso
280: args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type mkl_pardiso
282: test:
283: suffix: pipebcgs
284: args: -ksp_monitor_short -ksp_type pipebcgs -m 9 -n 9
286: test:
287: suffix: pipecg
288: args: -ksp_monitor_short -ksp_type pipecg -m 9 -n 9
290: test:
291: suffix: pipecgrr
292: args: -ksp_monitor_short -ksp_type pipecgrr -m 9 -n 9
294: test:
295: suffix: pipecr
296: args: -ksp_monitor_short -ksp_type pipecr -m 9 -n 9
298: test:
299: suffix: pipelcg
300: args: -ksp_monitor_short -ksp_type pipelcg -m 9 -n 9 -pc_type none -ksp_pipelcg_pipel 2 -ksp_pipelcg_lmax 2
301: filter: grep -v "sqrt breakdown in iteration"
303: test:
304: suffix: sell
305: args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -m 9 -n 9 -mat_type sell
307: test:
308: requires: mumps
309: suffix: sell_mumps
310: args: -ksp_type preonly -m 9 -n 12 -mat_type sell -pc_type lu -pc_factor_mat_solver_type mumps -pc_factor_mat_ordering_type natural
312: test:
313: suffix: telescope
314: nsize: 4
315: args: -m 100 -n 100 -ksp_converged_reason -pc_type telescope -pc_telescope_reduction_factor 4 -telescope_pc_type bjacobi
317: test:
318: suffix: umfpack
319: requires: suitesparse
320: args: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_type umfpack
322: test:
323: suffix: spqr
324: requires: suitesparse
325: args: -ksp_type preonly -pc_type qr -pc_factor_mat_solver_type spqr
327: test:
328: suffix: pc_symmetric
329: args: -m 10 -n 9 -ksp_converged_reason -ksp_type gmres -ksp_pc_side symmetric -pc_type cholesky
331: test:
332: suffix: pipeprcg
333: args: -ksp_monitor_short -ksp_type pipeprcg -m 9 -n 9
335: test:
336: suffix: pipeprcg_rcw
337: args: -ksp_monitor_short -ksp_type pipeprcg -recompute_w false -m 9 -n 9
339: test:
340: suffix: pipecg2
341: args: -ksp_monitor_short -ksp_type pipecg2 -m 9 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}
343: test:
344: suffix: pipecg2_2
345: nsize: 4
346: args: -ksp_monitor_short -ksp_type pipecg2 -m 15 -n 9 -ksp_norm_type {{preconditioned unpreconditioned natural}}
348: test:
349: suffix: hpddm
350: nsize: 4
351: requires: hpddm
352: filter: sed -e "s/ iterations 9/ iterations 8/g"
353: args: -ksp_converged_reason -ksp_type hpddm -ksp_hpddm_precision {{single double}shared output} -ksp_pc_side {{left right}shared output}
355: TEST*/