Actual source code: ex36.c

slepc-3.17.1 2022-04-11
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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.
  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;

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

 59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 60:         Generate the matrix
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

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

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

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

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

138:   EPSSolve(eps);
139:   EPSGetType(eps,&type);
140:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
141:   EPSGetDimensions(eps,&nev,NULL,NULL);
142:   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:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
150:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
151:   else {
152:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
153:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
154:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
155:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
156:   }
157:   EPSDestroy(&eps);
158:   MatDestroy(&A);
159:   if (isShell) MFNDestroy(&mfn);
160: #else
161:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires C99 complex numbers");
162: #endif
163:   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

191:   STShellGetContext(st,&mfn);
192:   MFNGetFN(mfn,&fn);
193:   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(0);
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;

225:   STShellGetContext(st,&mfn);
226:   MFNSolve(mfn,x,y);
227:   PetscFunctionReturn(0);
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:
241:          suffix: 1_quad
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*/