Date: 2026-03-09T09:12:33+00:00

Actual source code: ex36.c

      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:   PetscFunctionBeginUser;
     55:   PetscCall(SlepcInitialize(&argc,&argv,NULL,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:
    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*/