Actual source code: ex36.c
slepc-3.16.1 2021-11-17
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
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;
55: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
56: #if defined(PETSC_HAVE_COMPLEX)
57: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
58: PetscPrintf(PETSC_COMM_WORLD,"\nBrusselator wave model with matrix exponential, n=%D\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: PetscOptionsGetScalar(NULL,NULL,"-L",&L,NULL);
71: PetscOptionsGetScalar(NULL,NULL,"-alpha",&alpha,NULL);
72: PetscOptionsGetScalar(NULL,NULL,"-beta",&beta,NULL);
73: PetscOptionsGetScalar(NULL,NULL,"-delta1",&delta1,NULL);
74: 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: MatCreate(PETSC_COMM_WORLD,&A);
81: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2*n,2*n);
82: MatSetFromOptions(A);
83: MatSetUp(A);
85: MatGetOwnershipRange(A,&Istart,&Iend);
86: for (i=Istart;i<Iend;i++) {
87: if (i<n) { /* upper blocks */
88: if (i>0) { MatSetValue(A,i,i-1,tau1,INSERT_VALUES); }
89: if (i<n-1) { MatSetValue(A,i,i+1,tau1,INSERT_VALUES); }
90: MatSetValue(A,i,i,-2.0*tau1+beta-1.0,INSERT_VALUES);
91: MatSetValue(A,i,i+n,alpha*alpha,INSERT_VALUES);
92: } else { /* lower blocks */
93: if (i>n) { MatSetValue(A,i,i-1,tau2,INSERT_VALUES); }
94: if (i<2*n-1) { MatSetValue(A,i,i+1,tau2,INSERT_VALUES); }
95: MatSetValue(A,i,i,-2.0*tau2-alpha*alpha,INSERT_VALUES);
96: MatSetValue(A,i,i-n,-beta,INSERT_VALUES);
97: }
98: }
99: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
100: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Create the eigensolver and set various options
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106: EPSCreate(PETSC_COMM_WORLD,&eps);
107: EPSSetOperators(eps,A,NULL);
108: EPSSetProblemType(eps,EPS_NHEP);
109: EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL);
110: EPSGetST(eps,&st);
111: STSetType(st,STSHELL);
112: EPSSetFromOptions(eps);
114: /*
115: Initialize shell spectral transformation
116: */
117: PetscObjectTypeCompare((PetscObject)st,STSHELL,&isShell);
118: if (isShell) {
120: /* Create the MFN object to be used by the spectral transform */
121: MFNCreate(PETSC_COMM_WORLD,&mfn);
122: MFNSetOperator(mfn,A);
123: MFNGetFN(mfn,&f);
124: FNSetType(f,FNEXP);
125: FNSetScale(f,0.03,1.0); /* this can be set with -fn_scale */
126: MFNSetFromOptions(mfn);
128: /* Set callback functions */
129: STShellSetApply(st,STApply_Exp);
130: STShellSetBackTransform(st,STBackTransform_Exp);
131: STShellSetContext(st,mfn);
132: PetscObjectSetName((PetscObject)st,"STEXP");
133: }
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Solve the eigensystem
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: EPSSolve(eps);
140: EPSGetType(eps,&type);
141: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
142: EPSGetDimensions(eps,&nev,NULL,NULL);
143: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
145: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146: Display solution and clean up
147: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: /* show detailed info unless -terse option is given by user */
150: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
151: if (terse) {
152: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
153: } else {
154: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
155: EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
156: EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
157: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
158: }
159: EPSDestroy(&eps);
160: MatDestroy(&A);
161: if (isShell) { MFNDestroy(&mfn); }
162: #else
163: SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires C99 complex numbers");
164: #endif
165: SlepcFinalize();
166: return ierr;
167: }
169: /* ------------------------------------------------------------------- */
170: /*
171: STBackTransform_Exp - Undoes the exp(A) transformation by taking logarithms.
173: Input Parameters:
174: + st - spectral transformation context
175: - n - number of eigenvalues to transform
177: Input/Output Parameters:
178: + eigr - pointer to real part of eigenvalues
179: - eigi - pointer to imaginary part of eigenvalues
180: */
181: PetscErrorCode STBackTransform_Exp(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
182: {
183: #if defined(PETSC_HAVE_COMPLEX)
185: PetscInt j;
186: MFN mfn;
187: FN fn;
188: PetscScalar tau,eta;
189: #if !defined(PETSC_USE_COMPLEX)
190: PetscComplex theta,lambda;
191: #endif
194: STShellGetContext(st,&mfn);
195: MFNGetFN(mfn,&fn);
196: FNGetScale(fn,&tau,&eta);
197: for (j=0;j<n;j++) {
198: #if defined(PETSC_USE_COMPLEX)
199: eigr[j] = PetscLogComplex(eigr[j]/eta)/tau;
200: #else
201: theta = PetscCMPLX(eigr[j],eigi[j])/eta;
202: lambda = PetscLogComplex(theta)/tau;
203: eigr[j] = PetscRealPartComplex(lambda);
204: eigi[j] = PetscImaginaryPartComplex(lambda);
205: #endif
206: }
207: return(0);
208: #else
209: return 0;
210: #endif
211: }
213: /*
214: STApply_Exp - Applies the operator exp(tau*A) to a given vector using an MFN object.
216: Input Parameters:
217: + st - spectral transformation context
218: - x - input vector
220: Output Parameter:
221: . y - output vector
222: */
223: PetscErrorCode STApply_Exp(ST st,Vec x,Vec y)
224: {
225: MFN mfn;
229: STShellGetContext(st,&mfn);
230: MFNSolve(mfn,x,y);
231: return(0);
232: }
234: /*TEST
236: testset:
237: args: -eps_nev 4 -mfn_ncv 16 -terse
238: requires: c99_complex !single
239: filter: sed -e "s/-2/+2/g"
240: output_file: output/ex36_1.out
241: test:
242: suffix: 1
243: requires: !__float128
244: test:
245: suffix: 1_quad
246: args: -eps_tol 1e-14
247: requires: __float128
249: test:
250: suffix: 2
251: args: -n 56 -eps_nev 2 -st_type sinvert -eps_target -390 -eps_target_magnitude -eps_type power
252: args: -eps_power_shift_type {{constant rayleigh}} -eps_two_sided {{0 1}} -eps_tol 1e-14 -terse
253: requires: c99_complex !single
254: filter: sed -e "s/[+-]0\.0*i//g"
256: test:
257: suffix: 3
258: 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
259: requires: c99_complex !single
260: 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/"
262: TEST*/