Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 :
11 : static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
12 : "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
13 : "The command line options are:\n"
14 : " -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";
15 :
16 : #include <slepceps.h>
17 : #include <petscblaslapack.h>
18 :
19 : /*
20 : User-defined routines
21 : */
22 : PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
23 : PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);
24 :
25 18 : int main(int argc,char **argv)
26 : {
27 18 : Mat A; /* operator matrix */
28 18 : EPS eps; /* eigenproblem solver context */
29 18 : PetscReal tol=1000*PETSC_MACHINE_EPSILON;
30 18 : PetscMPIInt size;
31 18 : PetscInt N,n=10,nev;
32 :
33 18 : PetscFunctionBeginUser;
34 18 : PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
35 18 : PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
36 18 : PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only");
37 :
38 18 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
39 18 : N = n*n;
40 18 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n));
41 :
42 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43 : Compute the operator matrix that defines the eigensystem, Ax=kx
44 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45 :
46 18 : PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A));
47 18 : PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D));
48 18 : PetscCall(MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D));
49 18 : PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D));
50 :
51 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
52 : Create the eigensolver and set various options
53 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54 :
55 : /*
56 : Create eigensolver context
57 : */
58 18 : PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
59 :
60 : /*
61 : Set operators. In this case, it is a standard eigenvalue problem
62 : */
63 18 : PetscCall(EPSSetOperators(eps,A,NULL));
64 18 : PetscCall(EPSSetProblemType(eps,EPS_HEP));
65 18 : PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT));
66 :
67 : /*
68 : Set solver parameters at runtime
69 : */
70 18 : PetscCall(EPSSetFromOptions(eps));
71 :
72 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
73 : Solve the eigensystem
74 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
75 :
76 18 : PetscCall(EPSSolve(eps));
77 18 : PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
78 18 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
79 :
80 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81 : Display solution and clean up
82 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83 :
84 18 : PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
85 18 : PetscCall(EPSDestroy(&eps));
86 18 : PetscCall(MatDestroy(&A));
87 18 : PetscCall(SlepcFinalize());
88 : return 0;
89 : }
90 :
91 : /*
92 : Compute the matrix vector multiplication y<---T*x where T is a nx by nx
93 : tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
94 : DU on the superdiagonal.
95 : */
96 1001960 : static void tv(int nx,const PetscScalar *x,PetscScalar *y)
97 : {
98 1001960 : PetscScalar dd,dl,du;
99 1001960 : int j;
100 :
101 1001960 : dd = 4.0;
102 1001960 : dl = -1.0;
103 1001960 : du = -1.0;
104 :
105 1001960 : y[0] = dd*x[0] + du*x[1];
106 16701040 : for (j=1;j<nx-1;j++)
107 15699080 : y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
108 1001960 : y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
109 1001960 : }
110 :
111 : /*
112 : Matrix-vector product subroutine for the 2D Laplacian.
113 :
114 : The matrix used is the 2 dimensional discrete Laplacian on unit square with
115 : zero Dirichlet boundary condition.
116 :
117 : Computes y <-- A*x, where A is the block tridiagonal matrix
118 :
119 : | T -I |
120 : |-I T -I |
121 : A = | -I T |
122 : | ... -I|
123 : | -I T|
124 :
125 : The subroutine TV is called to compute y<--T*x.
126 : */
127 61779 : PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
128 : {
129 61779 : void *ctx;
130 61779 : int nx,lo,i,j;
131 61779 : const PetscScalar *px;
132 61779 : PetscScalar *py;
133 :
134 61779 : PetscFunctionBeginUser;
135 61779 : PetscCall(MatShellGetContext(A,&ctx));
136 61779 : nx = *(int*)ctx;
137 61779 : PetscCall(VecGetArrayRead(x,&px));
138 61779 : PetscCall(VecGetArray(y,&py));
139 :
140 61779 : tv(nx,&px[0],&py[0]);
141 1125518 : for (i=0;i<nx;i++) py[i] -= px[nx+i];
142 :
143 940181 : for (j=2;j<nx;j++) {
144 878402 : lo = (j-1)*nx;
145 878402 : tv(nx,&px[lo],&py[lo]);
146 17455884 : for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
147 : }
148 :
149 61779 : lo = (nx-1)*nx;
150 61779 : tv(nx,&px[lo],&py[lo]);
151 1125518 : for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];
152 :
153 61779 : PetscCall(VecRestoreArrayRead(x,&px));
154 61779 : PetscCall(VecRestoreArray(y,&py));
155 61779 : PetscFunctionReturn(PETSC_SUCCESS);
156 : }
157 :
158 1 : PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
159 : {
160 1 : PetscFunctionBeginUser;
161 1 : PetscCall(VecSet(diag,4.0));
162 1 : PetscFunctionReturn(PETSC_SUCCESS);
163 : }
164 :
165 : /*TEST
166 :
167 : testset:
168 : args: -n 20 -eps_nev 4 -eps_ncv 11 -eps_max_it 40000
169 : requires: !single
170 : output_file: output/test8_1.out
171 : test:
172 : suffix: 1
173 : args: -eps_type {{power subspace arnoldi}}
174 : test:
175 : suffix: 1_lanczos
176 : args: -eps_type lanczos -eps_lanczos_reorthog local
177 : test:
178 : suffix: 1_lapack
179 : args: -eps_type lapack
180 : timeoutfactor: 2
181 : test:
182 : suffix: 1_elemental
183 : args: -eps_type elemental
184 : requires: elemental
185 : test:
186 : suffix: 1_krylovschur_vecs
187 : args: -bv_type vecs -bv_orthog_refine always -eps_ncv 10 -vec_mdot_use_gemv 0
188 : test:
189 : suffix: 1_jd
190 : args: -eps_type jd -eps_jd_blocksize 3
191 : test:
192 : suffix: 1_gd
193 : args: -eps_type gd -eps_gd_blocksize 3 -eps_tol 1e-8
194 : test:
195 : suffix: 1_gd2
196 : args: -eps_type gd -eps_gd_double_expansion
197 : test:
198 : suffix: 1_primme
199 : args: -eps_type primme -eps_conv_abs -eps_largest_magnitude
200 : requires: primme
201 :
202 : testset:
203 : args: -eps_nev 4 -eps_smallest_real -eps_max_it 600
204 : output_file: output/test8_2.out
205 : test:
206 : suffix: 2
207 : args: -eps_type {{rqcg lobpcg}}
208 : test:
209 : suffix: 2_lanczos
210 : args: -eps_type lanczos -eps_lanczos_reorthog local
211 : test:
212 : suffix: 2_arpack
213 : args: -eps_type arpack -eps_ncv 6
214 : requires: arpack !single
215 : test:
216 : suffix: 2_primme
217 : args: -eps_type primme -eps_conv_abs -eps_primme_method lobpcg_orthobasisw -eps_ncv 24
218 : requires: primme
219 :
220 : testset:
221 : args: -eps_nev 12 -eps_mpd 9 -eps_smallest_real -eps_max_it 1000
222 : output_file: output/test8_3.out
223 : test:
224 : suffix: 3_rqcg
225 : args: -eps_type rqcg
226 : test:
227 : suffix: 3_lanczos
228 : args: -eps_type lanczos -eps_lanczos_reorthog local
229 : test:
230 : suffix: 3_lobpcg
231 : args: -eps_type lobpcg -eps_lobpcg_blocksize 3 -eps_lobpcg_locking 0 -st_ksp_type preonly -st_pc_type jacobi
232 : requires: !__float128
233 : test:
234 : suffix: 3_lobpcg_quad
235 : args: -eps_type lobpcg -eps_lobpcg_blocksize 3 -eps_lobpcg_locking 0 -st_ksp_type preonly -st_pc_type jacobi -eps_tol 1e-25
236 : requires: __float128
237 : TEST*/
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