Line | Branch | Exec | Source |
---|---|---|---|
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[] = "A quadratic eigenproblem defined using shell matrices.\n\n" | ||
12 | "The command line options are:\n" | ||
13 | " -n <n>, where <n> = number of grid subdivisions in x and y dimensions.\n\n"; | ||
14 | |||
15 | #include <slepcpep.h> | ||
16 | |||
17 | /* | ||
18 | User-defined routines | ||
19 | */ | ||
20 | PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y); | ||
21 | PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag); | ||
22 | PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y); | ||
23 | PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag); | ||
24 | PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y); | ||
25 | PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag); | ||
26 | |||
27 | 30 | int main(int argc,char **argv) | |
28 | { | ||
29 | 30 | Mat M,C,K,A[3]; /* problem matrices */ | |
30 | 30 | PEP pep; /* polynomial eigenproblem solver context */ | |
31 | 30 | PEPType type; | |
32 | 30 | PetscInt N,n=10,nev; | |
33 | 30 | PetscMPIInt size; | |
34 | 30 | PetscBool terse; | |
35 | 30 | ST st; | |
36 | |||
37 |
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30 | PetscFunctionBeginUser; |
38 |
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30 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
39 |
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30 | PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); |
40 |
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30 | PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only"); |
41 | |||
42 |
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30 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
43 | 30 | N = n*n; | |
44 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem with shell matrices, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n)); |
45 | |||
46 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
47 | Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0 | ||
48 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
49 | |||
50 | /* K is the 2-D Laplacian */ | ||
51 |
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30 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&K)); |
52 |
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30 | PetscCall(MatShellSetOperation(K,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Laplacian2D)); |
53 |
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30 | PetscCall(MatShellSetOperation(K,MATOP_MULT_TRANSPOSE,(PetscErrorCodeFn*)MatMult_Laplacian2D)); |
54 |
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30 | PetscCall(MatShellSetOperation(K,MATOP_GET_DIAGONAL,(PetscErrorCodeFn*)MatGetDiagonal_Laplacian2D)); |
55 | |||
56 | /* C is the zero matrix */ | ||
57 |
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30 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&C)); |
58 |
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30 | PetscCall(MatShellSetOperation(C,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Zero)); |
59 |
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30 | PetscCall(MatShellSetOperation(C,MATOP_MULT_TRANSPOSE,(PetscErrorCodeFn*)MatMult_Zero)); |
60 |
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30 | PetscCall(MatShellSetOperation(C,MATOP_GET_DIAGONAL,(PetscErrorCodeFn*)MatGetDiagonal_Zero)); |
61 | |||
62 | /* M is the identity matrix */ | ||
63 |
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30 | PetscCall(MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,NULL,&M)); |
64 |
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30 | PetscCall(MatShellSetOperation(M,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Identity)); |
65 |
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30 | PetscCall(MatShellSetOperation(M,MATOP_MULT_TRANSPOSE,(PetscErrorCodeFn*)MatMult_Identity)); |
66 |
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30 | PetscCall(MatShellSetOperation(M,MATOP_GET_DIAGONAL,(PetscErrorCodeFn*)MatGetDiagonal_Identity)); |
67 | |||
68 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
69 | Create the eigensolver and set various options | ||
70 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
71 | |||
72 | /* | ||
73 | Create eigensolver context | ||
74 | */ | ||
75 |
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30 | PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep)); |
76 | |||
77 | /* | ||
78 | Set matrices and problem type | ||
79 | */ | ||
80 | 30 | A[0] = K; A[1] = C; A[2] = M; | |
81 |
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30 | PetscCall(PEPSetOperators(pep,3,A)); |
82 |
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30 | PetscCall(PEPGetST(pep,&st)); |
83 |
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30 | PetscCall(STSetMatMode(st,ST_MATMODE_SHELL)); |
84 | |||
85 | /* | ||
86 | Set solver parameters at runtime | ||
87 | */ | ||
88 |
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30 | PetscCall(PEPSetFromOptions(pep)); |
89 | |||
90 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
91 | Solve the eigensystem | ||
92 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
93 | |||
94 |
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30 | PetscCall(PEPSolve(pep)); |
95 | |||
96 | /* | ||
97 | Optional: Get some information from the solver and display it | ||
98 | */ | ||
99 |
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30 | PetscCall(PEPGetType(pep,&type)); |
100 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type)); |
101 |
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30 | PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL)); |
102 |
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30 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev)); |
103 | |||
104 | /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
105 | Display solution and clean up | ||
106 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ | ||
107 | |||
108 | /* show detailed info unless -terse option is given by user */ | ||
109 |
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30 | PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse)); |
110 |
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30 | if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,NULL)); |
111 | else { | ||
112 | ✗ | PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL)); | |
113 | ✗ | PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD)); | |
114 | ✗ | PetscCall(PEPErrorView(pep,PEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD)); | |
115 | ✗ | PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD)); | |
116 | } | ||
117 |
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30 | PetscCall(PEPDestroy(&pep)); |
118 |
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30 | PetscCall(MatDestroy(&M)); |
119 |
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30 | PetscCall(MatDestroy(&C)); |
120 |
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30 | PetscCall(MatDestroy(&K)); |
121 |
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30 | PetscCall(SlepcFinalize()); |
122 | return 0; | ||
123 | } | ||
124 | |||
125 | /* | ||
126 | Compute the matrix vector multiplication y<---T*x where T is a nx by nx | ||
127 | tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and | ||
128 | DU on the superdiagonal. | ||
129 | */ | ||
130 | 48630 | static void tv(int nx,const PetscScalar *x,PetscScalar *y) | |
131 | { | ||
132 | 48630 | PetscScalar dd,dl,du; | |
133 | 48630 | int j; | |
134 | |||
135 | 48630 | dd = 4.0; | |
136 | 48630 | dl = -1.0; | |
137 | 48630 | du = -1.0; | |
138 | |||
139 | 48630 | y[0] = dd*x[0] + du*x[1]; | |
140 |
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437670 | for (j=1;j<nx-1;j++) |
141 | 389040 | y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1]; | |
142 | 48630 | y[nx-1] = dl*x[nx-2] + dd*x[nx-1]; | |
143 | 48630 | } | |
144 | |||
145 | /* | ||
146 | Matrix-vector product subroutine for the 2D Laplacian. | ||
147 | |||
148 | The matrix used is the 2 dimensional discrete Laplacian on unit square with | ||
149 | zero Dirichlet boundary condition. | ||
150 | |||
151 | Computes y <-- A*x, where A is the block tridiagonal matrix | ||
152 | |||
153 | | T -I | | ||
154 | |-I T -I | | ||
155 | A = | -I T | | ||
156 | | ... -I| | ||
157 | | -I T| | ||
158 | |||
159 | The subroutine TV is called to compute y<--T*x. | ||
160 | */ | ||
161 | 4863 | PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y) | |
162 | { | ||
163 | 4863 | void *ctx; | |
164 | 4863 | int nx,lo,i,j; | |
165 | 4863 | const PetscScalar *px; | |
166 | 4863 | PetscScalar *py; | |
167 | |||
168 |
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4863 | PetscFunctionBeginUser; |
169 |
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4863 | PetscCall(MatShellGetContext(A,&ctx)); |
170 | 4863 | nx = *(int*)ctx; | |
171 |
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4863 | PetscCall(VecGetArrayRead(x,&px)); |
172 |
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4863 | PetscCall(VecGetArray(y,&py)); |
173 | |||
174 | 4863 | tv(nx,&px[0],&py[0]); | |
175 |
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58356 | for (i=0;i<nx;i++) py[i] -= px[nx+i]; |
176 | |||
177 |
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43767 | for (j=2;j<nx;j++) { |
178 | 38904 | lo = (j-1)*nx; | |
179 | 38904 | tv(nx,&px[lo],&py[lo]); | |
180 |
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466848 | for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i]; |
181 | } | ||
182 | |||
183 | 4863 | lo = (nx-1)*nx; | |
184 | 4863 | tv(nx,&px[lo],&py[lo]); | |
185 |
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58356 | for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i]; |
186 | |||
187 |
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4863 | PetscCall(VecRestoreArrayRead(x,&px)); |
188 |
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4863 | PetscCall(VecRestoreArray(y,&py)); |
189 |
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973 | PetscFunctionReturn(PETSC_SUCCESS); |
190 | } | ||
191 | |||
192 | 20 | PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag) | |
193 | { | ||
194 |
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20 | PetscFunctionBeginUser; |
195 |
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20 | PetscCall(VecSet(diag,4.0)); |
196 |
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4 | PetscFunctionReturn(PETSC_SUCCESS); |
197 | } | ||
198 | |||
199 | /* | ||
200 | Matrix-vector product subroutine for the Null matrix. | ||
201 | */ | ||
202 | 4863 | PetscErrorCode MatMult_Zero(Mat A,Vec x,Vec y) | |
203 | { | ||
204 |
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4863 | PetscFunctionBeginUser; |
205 |
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4863 | PetscCall(VecSet(y,0.0)); |
206 |
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973 | PetscFunctionReturn(PETSC_SUCCESS); |
207 | } | ||
208 | |||
209 | 20 | PetscErrorCode MatGetDiagonal_Zero(Mat A,Vec diag) | |
210 | { | ||
211 |
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20 | PetscFunctionBeginUser; |
212 |
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20 | PetscCall(VecSet(diag,0.0)); |
213 |
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4 | PetscFunctionReturn(PETSC_SUCCESS); |
214 | } | ||
215 | |||
216 | /* | ||
217 | Matrix-vector product subroutine for the Identity matrix. | ||
218 | */ | ||
219 | 2990 | PetscErrorCode MatMult_Identity(Mat A,Vec x,Vec y) | |
220 | { | ||
221 |
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2990 | PetscFunctionBeginUser; |
222 |
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2990 | PetscCall(VecCopy(x,y)); |
223 |
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598 | PetscFunctionReturn(PETSC_SUCCESS); |
224 | } | ||
225 | |||
226 | 30 | PetscErrorCode MatGetDiagonal_Identity(Mat A,Vec diag) | |
227 | { | ||
228 |
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30 | PetscFunctionBeginUser; |
229 |
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30 | PetscCall(VecSet(diag,1.0)); |
230 |
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6 | PetscFunctionReturn(PETSC_SUCCESS); |
231 | } | ||
232 | |||
233 | /*TEST | ||
234 | |||
235 | test: | ||
236 | suffix: 1 | ||
237 | args: -pep_type {{toar qarnoldi linear}} -pep_nev 4 -terse | ||
238 | filter: grep -v Solution | sed -e "s/2.7996[1-8]i/2.79964i/g" | sed -e "s/2.7570[5-9]i/2.75708i/g" | sed -e "s/0.00000-2.79964i, 0.00000+2.79964i/0.00000+2.79964i, 0.00000-2.79964i/" | sed -e "s/0.00000-2.75708i, 0.00000+2.75708i/0.00000+2.75708i, 0.00000-2.75708i/" | ||
239 | |||
240 | TEST*/ | ||
241 |