Actual source code: test15.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[] = "Illustrates the use of a user-defined stopping test.\n\n"
     12:   "This is based on ex22.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     15:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

     17: /*
     18:    Solve parabolic partial differential equation with time delay tau

     20:             u_t = u_xx + a*u(t) + b*u(t-tau)
     21:             u(0,t) = u(pi,t) = 0

     23:    with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).

     25:    Discretization leads to a DDE of dimension n

     27:             -u' = A*u(t) + B*u(t-tau)

     29:    which results in the nonlinear eigenproblem

     31:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
     32: */

     34: #include <slepcnep.h>

     36: /*
     37:    User-defined routines
     38: */
     39: PetscErrorCode MyStoppingTest(NEP,PetscInt,PetscInt,PetscInt,PetscInt,NEPConvergedReason*,void*);

     41: typedef struct {
     42:   PetscInt    lastnconv;      /* last value of nconv; used in stopping test */
     43:   PetscInt    nreps;          /* number of repetitions of nconv; used in stopping test */
     44: } CTX_DELAY;

     46: int main(int argc,char **argv)
     47: {
     48:   NEP            nep;
     49:   Mat            Id,A,B;
     50:   FN             f1,f2,f3;
     51:   RG             rg;
     52:   CTX_DELAY      *ctx;
     53:   Mat            mats[3];
     54:   FN             funs[3];
     55:   PetscScalar    coeffs[2],b;
     56:   PetscInt       n=128,Istart,Iend,i,mpd;
     57:   PetscReal      tau=0.001,h,a=20,xi;
     58:   PetscBool      terse;
     59:   PetscViewer    viewer;

     61:   PetscFunctionBeginUser;
     62:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     63:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     64:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
     65:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
     66:   h = PETSC_PI/(PetscReal)(n+1);

     68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69:      Create nonlinear eigensolver context
     70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     72:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));

     74:   /* Identity matrix */
     75:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
     76:   PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));

     78:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     79:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     80:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
     81:   PetscCall(MatSetFromOptions(A));
     82:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
     83:   for (i=Istart;i<Iend;i++) {
     84:     if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
     85:     if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
     86:     PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     87:   }
     88:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
     89:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
     90:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));

     92:   /* B = diag(b(xi)) */
     93:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
     94:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
     95:   PetscCall(MatSetFromOptions(B));
     96:   PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
     97:   for (i=Istart;i<Iend;i++) {
     98:     xi = (i+1)*h;
     99:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    100:     PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES));
    101:   }
    102:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    103:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    104:   PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));

    106:   /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
    107:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
    108:   PetscCall(FNSetType(f1,FNRATIONAL));
    109:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    110:   PetscCall(FNRationalSetNumerator(f1,2,coeffs));

    112:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
    113:   PetscCall(FNSetType(f2,FNRATIONAL));
    114:   coeffs[0] = 1.0;
    115:   PetscCall(FNRationalSetNumerator(f2,1,coeffs));

    117:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
    118:   PetscCall(FNSetType(f3,FNEXP));
    119:   PetscCall(FNSetScale(f3,-tau,1.0));

    121:   /* Set the split operator */
    122:   mats[0] = A;  funs[0] = f2;
    123:   mats[1] = Id; funs[1] = f1;
    124:   mats[2] = B;  funs[2] = f3;
    125:   PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:                 Customize nonlinear solver; set runtime options
    129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    131:   PetscCall(NEPSetType(nep,NEPNLEIGS));
    132:   PetscCall(NEPGetRG(nep,&rg));
    133:   PetscCall(RGSetType(rg,RGINTERVAL));
    134: #if defined(PETSC_USE_COMPLEX)
    135:   PetscCall(RGIntervalSetEndpoints(rg,5,20,-0.001,0.001));
    136: #else
    137:   PetscCall(RGIntervalSetEndpoints(rg,5,20,-0.0,0.0));
    138: #endif
    139:   PetscCall(NEPSetTarget(nep,15.0));
    140:   PetscCall(NEPSetWhichEigenpairs(nep,NEP_TARGET_MAGNITUDE));

    142:   /*
    143:      Set solver options. In particular, we must allocate sufficient
    144:      storage for all eigenpairs that may converge (ncv). This is
    145:      application-dependent.
    146:   */
    147:   mpd = 40;
    148:   PetscCall(NEPSetDimensions(nep,2*mpd,3*mpd,mpd));
    149:   PetscCall(NEPSetTolerances(nep,PETSC_CURRENT,2000));
    150:   PetscCall(PetscNew(&ctx));
    151:   ctx->lastnconv = 0;
    152:   ctx->nreps     = 0;
    153:   PetscCall(NEPSetStoppingTestFunction(nep,MyStoppingTest,(void*)ctx,NULL));

    155:   PetscCall(NEPSetFromOptions(nep));

    157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158:                       Solve the eigensystem
    159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    161:   PetscCall(NEPSolve(nep));

    163:   /* show detailed info unless -terse option is given by user */
    164:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
    165:   PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
    166:   PetscCall(NEPConvergedReasonView(nep,viewer));
    167:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    168:   if (!terse) PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,viewer));
    169:   PetscCall(PetscViewerPopFormat(viewer));

    171:   PetscCall(NEPDestroy(&nep));
    172:   PetscCall(MatDestroy(&Id));
    173:   PetscCall(MatDestroy(&A));
    174:   PetscCall(MatDestroy(&B));
    175:   PetscCall(FNDestroy(&f1));
    176:   PetscCall(FNDestroy(&f2));
    177:   PetscCall(FNDestroy(&f3));
    178:   PetscCall(PetscFree(ctx));
    179:   PetscCall(SlepcFinalize());
    180:   return 0;
    181: }

    183: /*
    184:     Function for user-defined stopping test.

    186:     Ignores the value of nev. It only takes into account the number of
    187:     eigenpairs that have converged in recent outer iterations (restarts);
    188:     if no new eigenvalues have converged in the last few restarts,
    189:     we stop the iteration, assuming that no more eigenvalues are present
    190:     inside the region.
    191: */
    192: PetscErrorCode MyStoppingTest(NEP nep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,NEPConvergedReason *reason,void *ptr)
    193: {
    194:   CTX_DELAY      *ctx = (CTX_DELAY*)ptr;

    196:   PetscFunctionBeginUser;
    197:   /* check usual termination conditions, but ignoring the case nconv>=nev */
    198:   PetscCall(NEPStoppingBasic(nep,its,max_it,nconv,PETSC_INT_MAX,reason,NULL));
    199:   if (*reason==NEP_CONVERGED_ITERATING) {
    200:     /* check if nconv is the same as before */
    201:     if (nconv==ctx->lastnconv) ctx->nreps++;
    202:     else {
    203:       ctx->lastnconv = nconv;
    204:       ctx->nreps     = 0;
    205:     }
    206:     /* check if no eigenvalues converged in last 10 restarts */
    207:     if (nconv && ctx->nreps>10) *reason = NEP_CONVERGED_USER;
    208:   }
    209:   PetscFunctionReturn(PETSC_SUCCESS);
    210: }

    212: /*TEST

    214:    test:
    215:       suffix: 1
    216:       args: -terse

    218: TEST*/