Date: 2021-02-01T14:42:17+00:00

Actual source code: test10.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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[] = "Tests multiple calls to NEPSolve(). Based on ex22.c.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
     14:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

     16: /*
     17:    Solve parabolic partial differential equation with time delay tau

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

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

     24:    Discretization leads to a DDE of dimension n

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

     28:    which results in the nonlinear eigenproblem

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

     33: #include <slepcnep.h>

     35: /*
     36:    Check if computed eigenvectors have unit norm
     37: */
     38: PetscErrorCode CheckNormalizedVectors(NEP nep)
     39: {
     41:   PetscInt       i,nconv;
     42:   Mat            A;
     43:   Vec            xr,xi;
     44:   PetscReal      error=0.0,normr;
     45: #if !defined(PETSC_USE_COMPLEX)
     46:   PetscReal      normi;
     47: #endif

     50:   NEPGetConverged(nep,&nconv);
     51:   if (nconv>0) {
     52:     NEPGetSplitOperatorTerm(nep,0,&A,NULL);
     53:     MatCreateVecs(A,&xr,&xi);
     54:     for (i=0;i<nconv;i++) {
     55:       NEPGetEigenpair(nep,i,NULL,NULL,xr,xi);
     56: #if defined(PETSC_USE_COMPLEX)
     57:       VecNorm(xr,NORM_2,&normr);
     58:       error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
     59: #else
     60:       VecNormBegin(xr,NORM_2,&normr);
     61:       VecNormBegin(xi,NORM_2,&normi);
     62:       VecNormEnd(xr,NORM_2,&normr);
     63:       VecNormEnd(xi,NORM_2,&normi);
     64:       error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
     65: #endif
     66:     }
     67:     VecDestroy(&xr);
     68:     VecDestroy(&xi);
     69:     if (error>100*PETSC_MACHINE_EPSILON) {
     70:       PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
     71:     }
     72:   }
     73:   return(0);
     74: }

     76: int main(int argc,char **argv)
     77: {
     78:   NEP            nep;             /* nonlinear eigensolver context */
     79:   Mat            Id,A,B;          /* problem matrices */
     80:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
     81:   Mat            mats[3];
     82:   FN             funs[3];
     83:   PetscScalar    coeffs[2],b;
     84:   PetscInt       n=128,Istart,Iend,i;
     85:   PetscReal      tau=0.001,h,a=20,xi;
     86:   PetscBool      skipnorm=PETSC_FALSE;

     89:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     90:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     91:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     92:   PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);
     93:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
     94:   h = PETSC_PI/(PetscReal)(n+1);

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:              Create functions that define the split operator
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    100:   /* f1=-lambda */
    101:   FNCreate(PETSC_COMM_WORLD,&f1);
    102:   FNSetType(f1,FNRATIONAL);
    103:   coeffs[0] = -1.0; coeffs[1] = 0.0;
    104:   FNRationalSetNumerator(f1,2,coeffs);

    106:   /* f2=1.0 */
    107:   FNCreate(PETSC_COMM_WORLD,&f2);
    108:   FNSetType(f2,FNRATIONAL);
    109:   coeffs[0] = 1.0;
    110:   FNRationalSetNumerator(f2,1,coeffs);

    112:   /* f3=exp(-tau*lambda) */
    113:   FNCreate(PETSC_COMM_WORLD,&f3);
    114:   FNSetType(f3,FNEXP);
    115:   FNSetScale(f3,-tau,1.0);

    117:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118:                          Create problem matrices
    119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    121:   /* Identity matrix */
    122:   MatCreate(PETSC_COMM_WORLD,&Id);
    123:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
    124:   MatSetFromOptions(Id);
    125:   MatSetUp(Id);
    126:   MatGetOwnershipRange(Id,&Istart,&Iend);
    127:   for (i=Istart;i<Iend;i++) {
    128:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
    129:   }
    130:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
    131:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
    132:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

    134:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
    135:   MatCreate(PETSC_COMM_WORLD,&A);
    136:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
    137:   MatSetFromOptions(A);
    138:   MatSetUp(A);
    139:   MatGetOwnershipRange(A,&Istart,&Iend);
    140:   for (i=Istart;i<Iend;i++) {
    141:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
    142:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
    143:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
    144:   }
    145:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    146:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    147:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

    149:   /* B = diag(b(xi)) */
    150:   MatCreate(PETSC_COMM_WORLD,&B);
    151:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
    152:   MatSetFromOptions(B);
    153:   MatSetUp(B);
    154:   MatGetOwnershipRange(B,&Istart,&Iend);
    155:   for (i=Istart;i<Iend;i++) {
    156:     xi = (i+1)*h;
    157:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    158:     MatSetValue(B,i,i,b,INSERT_VALUES);
    159:   }
    160:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    161:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    162:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

    164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    165:               Create nonlinear eigensolver and set options
    166:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    168:   NEPCreate(PETSC_COMM_WORLD,&nep);
    169:   mats[0] = A;  funs[0] = f2;
    170:   mats[1] = Id; funs[1] = f1;
    171:   mats[2] = B;  funs[2] = f3;
    172:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
    173:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
    174:   NEPSetFromOptions(nep);

    176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    177:                       Solve the eigensystem
    178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    180:   NEPSolve(nep);
    181:   NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    182:   if (!skipnorm) { CheckNormalizedVectors(nep); }

    184:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    185:                    Create problem matrices of size 2*n
    186:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    188:   MatDestroy(&Id);
    189:   MatDestroy(&A);
    190:   MatDestroy(&B);
    191:   n *= 2;
    192:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
    193:   h = PETSC_PI/(PetscReal)(n+1);

    195:   /* Identity matrix */
    196:   MatCreate(PETSC_COMM_WORLD,&Id);
    197:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
    198:   MatSetFromOptions(Id);
    199:   MatSetUp(Id);
    200:   MatGetOwnershipRange(Id,&Istart,&Iend);
    201:   for (i=Istart;i<Iend;i++) {
    202:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
    203:   }
    204:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
    205:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
    206:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

    208:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
    209:   MatCreate(PETSC_COMM_WORLD,&A);
    210:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
    211:   MatSetFromOptions(A);
    212:   MatSetUp(A);
    213:   MatGetOwnershipRange(A,&Istart,&Iend);
    214:   for (i=Istart;i<Iend;i++) {
    215:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
    216:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
    217:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
    218:   }
    219:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    220:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    221:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

    223:   /* B = diag(b(xi)) */
    224:   MatCreate(PETSC_COMM_WORLD,&B);
    225:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
    226:   MatSetFromOptions(B);
    227:   MatSetUp(B);
    228:   MatGetOwnershipRange(B,&Istart,&Iend);
    229:   for (i=Istart;i<Iend;i++) {
    230:     xi = (i+1)*h;
    231:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    232:     MatSetValue(B,i,i,b,INSERT_VALUES);
    233:   }
    234:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    235:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    236:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

    238:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    239:        Solve again, calling NEPReset() since matrix size has changed
    240:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    242:   NEPReset(nep);  /* if this is omitted, it will be called in NEPSetSplitOperators() */
    243:   mats[0] = A;  funs[0] = f2;
    244:   mats[1] = Id; funs[1] = f1;
    245:   mats[2] = B;  funs[2] = f3;
    246:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
    247:   NEPSolve(nep);
    248:   NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    249:   if (!skipnorm) { CheckNormalizedVectors(nep); }

    251:   NEPDestroy(&nep);
    252:   MatDestroy(&Id);
    253:   MatDestroy(&A);
    254:   MatDestroy(&B);
    255:   FNDestroy(&f1);
    256:   FNDestroy(&f2);
    257:   FNDestroy(&f3);
    258:   SlepcFinalize();
    259:   return ierr;
    260: }

    262: /*TEST

    264:    testset:
    265:       nsize: 2
    266:       requires: !single
    267:       output_file: output/test10_1.out
    268:       test:
    269:          suffix: 1
    270:          args: -nep_type narnoldi -nep_target 0.55
    271:       test:
    272:          suffix: 1_rii
    273:          args: -nep_type rii -nep_target 0.55 -nep_rii_hermitian
    274:       test:
    275:          suffix: 1_narnoldi
    276:          args: -nep_type narnoldi -nep_target 0.55 -nep_narnoldi_lag_preconditioner 2
    277:       test:
    278:          suffix: 1_slp
    279:          args: -nep_type slp -nep_slp_st_pc_type redundant
    280:       test:
    281:          suffix: 1_interpol
    282:          args: -nep_type interpol -rg_type interval -rg_interval_endpoints .5,1,-.1,.1 -nep_target .7 -nep_interpol_st_pc_type redundant
    283:       test:
    284:          suffix: 1_narnoldi_sync
    285:          args: -nep_type narnoldi -ds_parallel synchronized

    287:    testset:
    288:       args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
    289:       requires: !single
    290:       output_file: output/test10_2.out
    291:       test:
    292:          suffix: 2_interpol
    293:          args: -nep_type interpol -nep_interpol_pep_type jd -nep_interpol_st_pc_type sor
    294:       test:
    295:          suffix: 2_nleigs
    296:          args: -nep_type nleigs
    297:          requires: complex
    298:       test:
    299:          suffix: 2_nleigs_real
    300:          args: -nep_type nleigs -rg_interval_endpoints .5,15
    301:          requires: !complex

    303: TEST*/