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[] = "Illustrates how to obtain invariant subspaces. "
12 : "Based on ex9.\n"
13 : "The command line options are:\n"
14 : " -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
15 : " -L <L>, where <L> = bifurcation parameter.\n"
16 : " -alpha <alpha>, -beta <beta>, -delta1 <delta1>, -delta2 <delta2>,\n"
17 : " where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";
18 :
19 : #include <slepceps.h>
20 :
21 : /*
22 : This example computes the eigenvalues with largest real part of the
23 : following matrix
24 :
25 : A = [ tau1*T+(beta-1)*I alpha^2*I
26 : -beta*I tau2*T-alpha^2*I ],
27 :
28 : where
29 :
30 : T = tridiag{1,-2,1}
31 : h = 1/(n+1)
32 : tau1 = delta1/(h*L)^2
33 : tau2 = delta2/(h*L)^2
34 : */
35 :
36 : /* Matrix operations */
37 : PetscErrorCode MatMult_Brussel(Mat,Vec,Vec);
38 : PetscErrorCode MatGetDiagonal_Brussel(Mat,Vec);
39 :
40 : typedef struct {
41 : Mat T;
42 : Vec x1,x2,y1,y2;
43 : PetscScalar alpha,beta,tau1,tau2,sigma;
44 : } CTX_BRUSSEL;
45 :
46 8 : int main(int argc,char **argv)
47 : {
48 8 : EPS eps;
49 8 : Mat A;
50 8 : Vec *Q,v;
51 8 : PetscScalar delta1,delta2,L,h,kr,ki;
52 8 : PetscReal errest,tol,re,im,lev;
53 8 : PetscInt N=30,n,i,j,Istart,Iend,nev,nconv;
54 8 : CTX_BRUSSEL *ctx;
55 8 : PetscBool errok,trueres;
56 :
57 8 : PetscFunctionBeginUser;
58 8 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
59 8 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL));
60 8 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model, n=%" PetscInt_FMT "\n\n",N));
61 :
62 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
63 : Generate the matrix
64 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
65 :
66 8 : PetscCall(PetscNew(&ctx));
67 8 : ctx->alpha = 2.0;
68 8 : ctx->beta = 5.45;
69 8 : delta1 = 0.008;
70 8 : delta2 = 0.004;
71 8 : L = 0.51302;
72 :
73 8 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
74 8 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&ctx->alpha,NULL));
75 8 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&ctx->beta,NULL));
76 8 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
77 8 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));
78 :
79 : /* Create matrix T */
80 8 : PetscCall(MatCreate(PETSC_COMM_WORLD,&ctx->T));
81 8 : PetscCall(MatSetSizes(ctx->T,PETSC_DECIDE,PETSC_DECIDE,N,N));
82 8 : PetscCall(MatSetFromOptions(ctx->T));
83 8 : PetscCall(MatGetOwnershipRange(ctx->T,&Istart,&Iend));
84 348 : for (i=Istart;i<Iend;i++) {
85 340 : if (i>0) PetscCall(MatSetValue(ctx->T,i,i-1,1.0,INSERT_VALUES));
86 340 : if (i<N-1) PetscCall(MatSetValue(ctx->T,i,i+1,1.0,INSERT_VALUES));
87 340 : PetscCall(MatSetValue(ctx->T,i,i,-2.0,INSERT_VALUES));
88 : }
89 8 : PetscCall(MatAssemblyBegin(ctx->T,MAT_FINAL_ASSEMBLY));
90 8 : PetscCall(MatAssemblyEnd(ctx->T,MAT_FINAL_ASSEMBLY));
91 8 : PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
92 :
93 : /* Fill the remaining information in the shell matrix context
94 : and create auxiliary vectors */
95 8 : h = 1.0 / (PetscReal)(N+1);
96 8 : ctx->tau1 = delta1 / ((h*L)*(h*L));
97 8 : ctx->tau2 = delta2 / ((h*L)*(h*L));
98 8 : ctx->sigma = 0.0;
99 8 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x1));
100 8 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->x2));
101 8 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y1));
102 8 : PetscCall(VecCreateMPIWithArray(PETSC_COMM_WORLD,1,n,PETSC_DECIDE,NULL,&ctx->y2));
103 :
104 : /* Create the shell matrix */
105 8 : PetscCall(MatCreateShell(PETSC_COMM_WORLD,2*n,2*n,2*N,2*N,(void*)ctx,&A));
106 8 : PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Brussel));
107 8 : PetscCall(MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Brussel));
108 :
109 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110 : Create the eigensolver and solve the problem
111 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112 :
113 8 : PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
114 8 : PetscCall(EPSSetOperators(eps,A,NULL));
115 8 : PetscCall(EPSSetProblemType(eps,EPS_NHEP));
116 8 : PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
117 8 : PetscCall(EPSSetTrueResidual(eps,PETSC_FALSE));
118 8 : PetscCall(EPSSetFromOptions(eps));
119 8 : PetscCall(EPSSolve(eps));
120 :
121 8 : PetscCall(EPSGetTrueResidual(eps,&trueres));
122 : /*if (trueres) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computing true residuals explicitly\n\n"));*/
123 :
124 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125 : Display solution and clean up
126 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127 :
128 8 : PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
129 8 : PetscCall(EPSGetTolerances(eps,&tol,NULL));
130 8 : PetscCall(EPSGetConverged(eps,&nconv));
131 8 : if (nconv<nev) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Problem: less than %" PetscInt_FMT " eigenvalues converged\n\n",nev));
132 : else {
133 : /* Check that all converged eigenpairs satisfy the requested tolerance
134 : (in this example we use the solver's error estimate instead of computing
135 : the residual norm explicitly) */
136 : errok = PETSC_TRUE;
137 40 : for (i=0;i<nev;i++) {
138 32 : PetscCall(EPSGetErrorEstimate(eps,i,&errest));
139 32 : PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL));
140 32 : errok = (errok && errest<5.0*SlepcAbsEigenvalue(kr,ki)*tol)? PETSC_TRUE: PETSC_FALSE;
141 : }
142 8 : if (!errok) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Problem: some of the first %" PetscInt_FMT " relative errors are higher than the tolerance\n\n",nev));
143 : else {
144 8 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," All requested eigenvalues computed up to the required tolerance:"));
145 16 : for (i=0;i<=(nev-1)/8;i++) {
146 8 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n "));
147 40 : for (j=0;j<PetscMin(8,nev-8*i);j++) {
148 32 : PetscCall(EPSGetEigenpair(eps,8*i+j,&kr,&ki,NULL,NULL));
149 : #if defined(PETSC_USE_COMPLEX)
150 32 : re = PetscRealPart(kr);
151 32 : im = PetscImaginaryPart(kr);
152 : #else
153 : re = kr;
154 : im = ki;
155 : #endif
156 32 : if (PetscAbs(re)/PetscAbs(im)<PETSC_SMALL) re = 0.0;
157 32 : if (PetscAbs(im)/PetscAbs(re)<PETSC_SMALL) im = 0.0;
158 32 : if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%.5f%+.5fi",(double)re,(double)im));
159 20 : else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%.5f",(double)re));
160 32 : if (8*i+j+1<nev) PetscCall(PetscPrintf(PETSC_COMM_WORLD,", "));
161 : }
162 : }
163 8 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n\n"));
164 : }
165 : }
166 :
167 : /* Get an orthogonal basis of the invariant subspace and check it is indeed
168 : orthogonal (note that eigenvectors are not orthogonal in this case) */
169 8 : if (nconv>1) {
170 8 : PetscCall(MatCreateVecs(A,&v,NULL));
171 8 : PetscCall(VecDuplicateVecs(v,nconv,&Q));
172 8 : PetscCall(EPSGetInvariantSubspace(eps,Q));
173 8 : PetscCall(VecCheckOrthonormality(Q,nconv,NULL,nconv,NULL,NULL,&lev));
174 8 : if (lev<10*tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n"));
175 0 : else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)lev));
176 8 : PetscCall(VecDestroyVecs(nconv,&Q));
177 8 : PetscCall(VecDestroy(&v));
178 : }
179 :
180 8 : PetscCall(EPSDestroy(&eps));
181 8 : PetscCall(MatDestroy(&A));
182 8 : PetscCall(MatDestroy(&ctx->T));
183 8 : PetscCall(VecDestroy(&ctx->x1));
184 8 : PetscCall(VecDestroy(&ctx->x2));
185 8 : PetscCall(VecDestroy(&ctx->y1));
186 8 : PetscCall(VecDestroy(&ctx->y2));
187 8 : PetscCall(PetscFree(ctx));
188 8 : PetscCall(SlepcFinalize());
189 : return 0;
190 : }
191 :
192 6309 : PetscErrorCode MatMult_Brussel(Mat A,Vec x,Vec y)
193 : {
194 6309 : PetscInt n;
195 6309 : const PetscScalar *px;
196 6309 : PetscScalar *py;
197 6309 : CTX_BRUSSEL *ctx;
198 :
199 6309 : PetscFunctionBeginUser;
200 6309 : PetscCall(MatShellGetContext(A,&ctx));
201 6309 : PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
202 6309 : PetscCall(VecGetArrayRead(x,&px));
203 6309 : PetscCall(VecGetArray(y,&py));
204 6309 : PetscCall(VecPlaceArray(ctx->x1,px));
205 6309 : PetscCall(VecPlaceArray(ctx->x2,px+n));
206 6309 : PetscCall(VecPlaceArray(ctx->y1,py));
207 6309 : PetscCall(VecPlaceArray(ctx->y2,py+n));
208 :
209 6309 : PetscCall(MatMult(ctx->T,ctx->x1,ctx->y1));
210 6309 : PetscCall(VecScale(ctx->y1,ctx->tau1));
211 6309 : PetscCall(VecAXPY(ctx->y1,ctx->beta - 1.0 + ctx->sigma,ctx->x1));
212 6309 : PetscCall(VecAXPY(ctx->y1,ctx->alpha * ctx->alpha,ctx->x2));
213 :
214 6309 : PetscCall(MatMult(ctx->T,ctx->x2,ctx->y2));
215 6309 : PetscCall(VecScale(ctx->y2,ctx->tau2));
216 6309 : PetscCall(VecAXPY(ctx->y2,-ctx->beta,ctx->x1));
217 6309 : PetscCall(VecAXPY(ctx->y2,-ctx->alpha * ctx->alpha + ctx->sigma,ctx->x2));
218 :
219 6309 : PetscCall(VecRestoreArrayRead(x,&px));
220 6309 : PetscCall(VecRestoreArray(y,&py));
221 6309 : PetscCall(VecResetArray(ctx->x1));
222 6309 : PetscCall(VecResetArray(ctx->x2));
223 6309 : PetscCall(VecResetArray(ctx->y1));
224 6309 : PetscCall(VecResetArray(ctx->y2));
225 6309 : PetscFunctionReturn(PETSC_SUCCESS);
226 : }
227 :
228 0 : PetscErrorCode MatGetDiagonal_Brussel(Mat A,Vec diag)
229 : {
230 0 : Vec d1,d2;
231 0 : PetscInt n;
232 0 : PetscScalar *pd;
233 0 : MPI_Comm comm;
234 0 : CTX_BRUSSEL *ctx;
235 :
236 0 : PetscFunctionBeginUser;
237 0 : PetscCall(MatShellGetContext(A,&ctx));
238 0 : PetscCall(PetscObjectGetComm((PetscObject)A,&comm));
239 0 : PetscCall(MatGetLocalSize(ctx->T,&n,NULL));
240 0 : PetscCall(VecGetArray(diag,&pd));
241 0 : PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd,&d1));
242 0 : PetscCall(VecCreateMPIWithArray(comm,1,n,PETSC_DECIDE,pd+n,&d2));
243 :
244 0 : PetscCall(VecSet(d1,-2.0*ctx->tau1 + ctx->beta - 1.0 + ctx->sigma));
245 0 : PetscCall(VecSet(d2,-2.0*ctx->tau2 - ctx->alpha*ctx->alpha + ctx->sigma));
246 :
247 0 : PetscCall(VecDestroy(&d1));
248 0 : PetscCall(VecDestroy(&d2));
249 0 : PetscCall(VecRestoreArray(diag,&pd));
250 0 : PetscFunctionReturn(PETSC_SUCCESS);
251 : }
252 :
253 : /*TEST
254 :
255 : test:
256 : suffix: 1
257 : args: -eps_nev 4 -eps_true_residual {{0 1}}
258 : requires: !single
259 :
260 : test:
261 : suffix: 2
262 : args: -eps_nev 4 -eps_true_residual -eps_balance oneside -eps_tol 1e-7
263 : requires: !single
264 :
265 : test:
266 : suffix: 3
267 : args: -n 50 -eps_nev 4 -eps_ncv 16 -eps_type subspace -eps_largest_magnitude -bv_orthog_block {{gs tsqr chol tsqrchol svqb}}
268 : requires: !single
269 :
270 : TEST*/
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