Actual source code: ex36.c

slepc-3.21.1 2024-04-26
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```  1: /*
2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

6:    This file is part of SLEPc.
8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */

11: static char help[] = "Use the matrix exponential to compute rightmost eigenvalues.\n\n"
12:   "Same problem as ex9.c but with explicitly created matrix. The command line options are:\n"
13:   "  -n <n>, where <n> = block dimension of the 2x2 block matrix.\n"
14:   "  -L <L>, where <L> = bifurcation parameter.\n"
15:   "  -alpha <alpha>, -beta <beta>, -delta1 <delta1>,  -delta2 <delta2>,\n"
16:   "       where <alpha> <beta> <delta1> <delta2> = model parameters.\n\n";

18: #include <slepceps.h>
19: #include <slepcmfn.h>

21: /*
22:    This example computes the eigenvalues with largest real part of the
23:    following matrix

25:         A = [ tau1*T+(beta-1)*I     alpha^2*I
26:                   -beta*I        tau2*T-alpha^2*I ],

28:    where

30:         T = tridiag{1,-2,1}
31:         h = 1/(n+1)
32:         tau1 = delta1/(h*L)^2
33:         tau2 = delta2/(h*L)^2

35:    but it builds A explicitly, as opposed to ex9.c
36: */

38: /* Routines for shell spectral transformation */
39: PetscErrorCode STApply_Exp(ST,Vec,Vec);
40: PetscErrorCode STBackTransform_Exp(ST,PetscInt,PetscScalar*,PetscScalar*);

42: int main(int argc,char **argv)
43: {
44:   Mat            A;               /* operator matrix */
45:   EPS            eps;             /* eigenproblem solver context */
46:   ST             st;              /* spectral transformation context */
47:   MFN            mfn;             /* matrix function solver object to compute exp(A)*v */
48:   FN             f;
49:   EPSType        type;
50:   PetscScalar    alpha,beta,tau1,tau2,delta1,delta2,L,h;
51:   PetscInt       n=30,i,Istart,Iend,nev;
52:   PetscBool      isShell,terse;

54:   PetscFunctionBeginUser;
55:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
56: #if defined(PETSC_HAVE_COMPLEX)
57:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
58:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model with matrix exponential, n=%" PetscInt_FMT "\n\n",n));

60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61:         Generate the matrix
62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

64:   alpha  = 2.0;
65:   beta   = 5.45;
66:   delta1 = 0.008;
67:   delta2 = 0.004;
68:   L      = 0.51302;

70:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL));
71:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-alpha",&alpha,NULL));
72:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-beta",&beta,NULL));
73:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL));
74:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-delta2",&delta2,NULL));

76:   h = 1.0 / (PetscReal)(n+1);
77:   tau1 = delta1 / ((h*L)*(h*L));
78:   tau2 = delta2 / ((h*L)*(h*L));

80:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
81:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2*n,2*n));
82:   PetscCall(MatSetFromOptions(A));

84:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
85:   for (i=Istart;i<Iend;i++) {
86:     if (i<n) {  /* upper blocks */
87:       if (i>0) PetscCall(MatSetValue(A,i,i-1,tau1,INSERT_VALUES));
88:       if (i<n-1) PetscCall(MatSetValue(A,i,i+1,tau1,INSERT_VALUES));
89:       PetscCall(MatSetValue(A,i,i,-2.0*tau1+beta-1.0,INSERT_VALUES));
90:       PetscCall(MatSetValue(A,i,i+n,alpha*alpha,INSERT_VALUES));
91:     } else {  /* lower blocks */
92:       if (i>n) PetscCall(MatSetValue(A,i,i-1,tau2,INSERT_VALUES));
93:       if (i<2*n-1) PetscCall(MatSetValue(A,i,i+1,tau2,INSERT_VALUES));
94:       PetscCall(MatSetValue(A,i,i,-2.0*tau2-alpha*alpha,INSERT_VALUES));
95:       PetscCall(MatSetValue(A,i,i-n,-beta,INSERT_VALUES));
96:     }
97:   }
98:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
99:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:                 Create the eigensolver and set various options
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

105:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
106:   PetscCall(EPSSetOperators(eps,A,NULL));
107:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
108:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
109:   PetscCall(EPSGetST(eps,&st));
110:   PetscCall(STSetType(st,STSHELL));
111:   PetscCall(EPSSetFromOptions(eps));

113:   /*
114:      Initialize shell spectral transformation
115:   */
116:   PetscCall(PetscObjectTypeCompare((PetscObject)st,STSHELL,&isShell));
117:   if (isShell) {

119:     /* Create the MFN object to be used by the spectral transform */
120:     PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
121:     PetscCall(MFNSetOperator(mfn,A));
122:     PetscCall(MFNGetFN(mfn,&f));
123:     PetscCall(FNSetType(f,FNEXP));
124:     PetscCall(FNSetScale(f,0.03,1.0));  /* this can be set with -fn_scale */
125:     PetscCall(MFNSetFromOptions(mfn));

127:     /* Set callback functions */
128:     PetscCall(STShellSetApply(st,STApply_Exp));
129:     PetscCall(STShellSetBackTransform(st,STBackTransform_Exp));
130:     PetscCall(STShellSetContext(st,mfn));
131:     PetscCall(PetscObjectSetName((PetscObject)st,"STEXP"));
132:   }

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:                       Solve the eigensystem
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

138:   PetscCall(EPSSolve(eps));
139:   PetscCall(EPSGetType(eps,&type));
140:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
141:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
142:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145:                     Display solution and clean up
146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

148:   /* show detailed info unless -terse option is given by user */
149:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
150:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
151:   else {
152:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
153:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
154:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
155:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
156:   }
157:   PetscCall(EPSDestroy(&eps));
158:   PetscCall(MatDestroy(&A));
159:   if (isShell) PetscCall(MFNDestroy(&mfn));
160: #else
161:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires C99 complex numbers");
162: #endif
163:   PetscCall(SlepcFinalize());
164:   return 0;
165: }

167: /* ------------------------------------------------------------------- */
168: /*
169:    STBackTransform_Exp - Undoes the exp(A) transformation by taking logarithms.

171:    Input Parameters:
172: +  st - spectral transformation context
173: -  n  - number of eigenvalues to transform

175:    Input/Output Parameters:
176: +  eigr - pointer to real part of eigenvalues
177: -  eigi - pointer to imaginary part of eigenvalues
178: */
179: PetscErrorCode STBackTransform_Exp(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
180: {
181: #if defined(PETSC_HAVE_COMPLEX)
182:   PetscInt       j;
183:   MFN            mfn;
184:   FN             fn;
185:   PetscScalar    tau,eta;
186: #if !defined(PETSC_USE_COMPLEX)
187:   PetscComplex   theta,lambda;
188: #endif

190:   PetscFunctionBeginUser;
191:   PetscCall(STShellGetContext(st,&mfn));
192:   PetscCall(MFNGetFN(mfn,&fn));
193:   PetscCall(FNGetScale(fn,&tau,&eta));
194:   for (j=0;j<n;j++) {
195: #if defined(PETSC_USE_COMPLEX)
196:     eigr[j] = PetscLogComplex(eigr[j]/eta)/tau;
197: #else
198:     theta   = PetscCMPLX(eigr[j],eigi[j])/eta;
199:     lambda  = PetscLogComplex(theta)/tau;
200:     eigr[j] = PetscRealPartComplex(lambda);
201:     eigi[j] = PetscImaginaryPartComplex(lambda);
202: #endif
203:   }
204:   PetscFunctionReturn(PETSC_SUCCESS);
205: #else
206:   return 0;
207: #endif
208: }

210: /*
211:    STApply_Exp - Applies the operator exp(tau*A) to a given vector using an MFN object.

213:    Input Parameters:
214: +  st - spectral transformation context
215: -  x  - input vector

217:    Output Parameter:
218: .  y - output vector
219: */
220: PetscErrorCode STApply_Exp(ST st,Vec x,Vec y)
221: {
222:   MFN            mfn;

224:   PetscFunctionBeginUser;
225:   PetscCall(STShellGetContext(st,&mfn));
226:   PetscCall(MFNSolve(mfn,x,y));
227:   PetscFunctionReturn(PETSC_SUCCESS);
228: }

230: /*TEST

232:    testset:
233:       args: -eps_nev 4 -mfn_ncv 16 -terse
234:       requires: c99_complex !single
235:       filter: sed -e "s/-2/+2/g"
236:       output_file: output/ex36_1.out
237:       test:
238:          suffix: 1
239:          requires: !__float128
240:       test:
242:          args: -eps_tol 1e-14
243:          requires: __float128

245:    test:
246:       suffix: 2
247:       args: -n 56 -eps_nev 2 -st_type sinvert -eps_target -390 -eps_target_magnitude -eps_type power
248:       args: -eps_power_shift_type {{constant rayleigh}} -eps_two_sided {{0 1}} -eps_tol 1e-14 -terse
249:       requires: c99_complex !single
250:       filter: sed -e "s/[+-]0\.0*i//g"

252:    test:
253:       suffix: 3
254:       args: -n 100 -st_type sinvert -eps_type ciss -rg_type ellipse -rg_ellipse_center 0 -rg_ellipse_radius 6 -eps_all -eps_tol 1e-6 -terse
255:       requires: c99_complex !single
256:       filter: sed -e "s/-3.37036-3.55528i, -3.37036+3.55528i/-3.37036+3.55528i, -3.37036-3.55528i/" -e "s/-1.79853-3.03216i, -1.79853+3.03216i/-1.79853+3.03216i, -1.79853-3.03216i/" -e "s/-0.67471-2.52856i, -0.67471+2.52856i/-0.67471+2.52856i, -0.67471-2.52856i/" -e "s/0.00002-2.13950i, 0.00002+2.13950i/0.00002+2.13950i, 0.00002-2.13950i/"

258: TEST*/
```