Date: 2023-11-27T17:18:57+00:00

Actual source code: test17.c
slepc-3.20.1 2023-11-27
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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[] = "Tests a user-provided preconditioner.\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"
     15:   "  -a <a>, where <a> is the coefficient that multiplies u in the equation.\n"
     16:   "  -split <0/1>, to select the split form in the problem definition (enabled by default).\n";

     18: /* Based on ex22.c (delay) */

     20: #include <slepcnep.h>

     22: /*
     23:    User-defined application context
     24: */
     25: typedef struct {
     26:   PetscScalar tau;
     27:   PetscReal   a;
     28: } ApplicationCtx;

     30: /*
     31:    Create problem matrices in split form
     32: */
     33: PetscErrorCode BuildSplitMatrices(PetscInt n,PetscReal a,Mat *Id,Mat *A,Mat *B)
     34: {
     35:   PetscInt       i,Istart,Iend;
     36:   PetscReal      h,xi;
     37:   PetscScalar    b;

     39:   PetscFunctionBeginUser;
     40:   h = PETSC_PI/(PetscReal)(n+1);

     42:   /* Identity matrix */
     43:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,Id));
     44:   PetscCall(MatSetOption(*Id,MAT_HERMITIAN,PETSC_TRUE));

     46:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
     47:   PetscCall(MatCreate(PETSC_COMM_WORLD,A));
     48:   PetscCall(MatSetSizes(*A,PETSC_DECIDE,PETSC_DECIDE,n,n));
     49:   PetscCall(MatSetFromOptions(*A));
     50:   PetscCall(MatSetUp(*A));
     51:   PetscCall(MatGetOwnershipRange(*A,&Istart,&Iend));
     52:   for (i=Istart;i<Iend;i++) {
     53:     if (i>0) PetscCall(MatSetValue(*A,i,i-1,1.0/(h*h),INSERT_VALUES));
     54:     if (i<n-1) PetscCall(MatSetValue(*A,i,i+1,1.0/(h*h),INSERT_VALUES));
     55:     PetscCall(MatSetValue(*A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     56:   }
     57:   PetscCall(MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY));
     58:   PetscCall(MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY));
     59:   PetscCall(MatSetOption(*A,MAT_HERMITIAN,PETSC_TRUE));

     61:   /* B = diag(b(xi)) */
     62:   PetscCall(MatCreate(PETSC_COMM_WORLD,B));
     63:   PetscCall(MatSetSizes(*B,PETSC_DECIDE,PETSC_DECIDE,n,n));
     64:   PetscCall(MatSetFromOptions(*B));
     65:   PetscCall(MatSetUp(*B));
     66:   PetscCall(MatGetOwnershipRange(*B,&Istart,&Iend));
     67:   for (i=Istart;i<Iend;i++) {
     68:     xi = (i+1)*h;
     69:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
     70:     PetscCall(MatSetValue(*B,i,i,b,INSERT_VALUES));
     71:   }
     72:   PetscCall(MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY));
     73:   PetscCall(MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY));
     74:   PetscCall(MatSetOption(*B,MAT_HERMITIAN,PETSC_TRUE));
     75:   PetscFunctionReturn(PETSC_SUCCESS);
     76: }

     78: /*
     79:    Create preconditioner matrices (only Ap=diag(A))
     80: */
     81: PetscErrorCode BuildSplitPreconditioner(PetscInt n,PetscReal a,Mat *Ap)
     82: {
     83:   PetscInt       i,Istart,Iend;
     84:   PetscReal      h;

     86:   PetscFunctionBeginUser;
     87:   h = PETSC_PI/(PetscReal)(n+1);

     89:   /* Ap = diag(A) */
     90:   PetscCall(MatCreate(PETSC_COMM_WORLD,Ap));
     91:   PetscCall(MatSetSizes(*Ap,PETSC_DECIDE,PETSC_DECIDE,n,n));
     92:   PetscCall(MatSetFromOptions(*Ap));
     93:   PetscCall(MatSetUp(*Ap));
     94:   PetscCall(MatGetOwnershipRange(*Ap,&Istart,&Iend));
     95:   for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(*Ap,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     96:   PetscCall(MatAssemblyBegin(*Ap,MAT_FINAL_ASSEMBLY));
     97:   PetscCall(MatAssemblyEnd(*Ap,MAT_FINAL_ASSEMBLY));
     98:   PetscCall(MatSetOption(*Ap,MAT_HERMITIAN,PETSC_TRUE));
     99:   PetscFunctionReturn(PETSC_SUCCESS);
    100: }

    102: /*
    103:    Compute Function matrix  T(lambda)
    104: */
    105: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    106: {
    107:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    108:   PetscInt       i,n,Istart,Iend;
    109:   PetscReal      h,xi;
    110:   PetscScalar    b;

    112:   PetscFunctionBeginUser;
    113:   PetscCall(MatGetSize(fun,&n,NULL));
    114:   h = PETSC_PI/(PetscReal)(n+1);
    115:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
    116:   for (i=Istart;i<Iend;i++) {
    117:     if (i>0) PetscCall(MatSetValue(fun,i,i-1,1.0/(h*h),INSERT_VALUES));
    118:     if (i<n-1) PetscCall(MatSetValue(fun,i,i+1,1.0/(h*h),INSERT_VALUES));
    119:     xi = (i+1)*h;
    120:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    121:     PetscCall(MatSetValue(fun,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
    122:     if (B!=fun) PetscCall(MatSetValue(B,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
    123:   }
    124:   PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    125:   PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    126:   if (fun != B) {
    127:     PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    128:     PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    129:   }
    130:   PetscFunctionReturn(PETSC_SUCCESS);
    131: }

    133: /*
    134:    Compute Jacobian matrix  T'(lambda)
    135: */
    136: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    137: {
    138:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    139:   PetscInt       i,n,Istart,Iend;
    140:   PetscReal      h,xi;
    141:   PetscScalar    b;

    143:   PetscFunctionBeginUser;
    144:   PetscCall(MatGetSize(jac,&n,NULL));
    145:   h = PETSC_PI/(PetscReal)(n+1);
    146:   PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
    147:   for (i=Istart;i<Iend;i++) {
    148:     xi = (i+1)*h;
    149:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    150:     PetscCall(MatSetValue(jac,i,i,-1.0-user->tau*PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
    151:   }
    152:   PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
    153:   PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
    154:   PetscFunctionReturn(PETSC_SUCCESS);
    155: }

    157: int main(int argc,char **argv)
    158: {
    159:   NEP            nep;             /* nonlinear eigensolver context */
    160:   Mat            Id,A,B,Ap,J,F,P; /* problem matrices */
    161:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
    162:   ApplicationCtx ctx;             /* user-defined context */
    163:   Mat            mats[3];
    164:   FN             funs[3];
    165:   PetscScalar    coeffs[2];
    166:   PetscInt       n=128;
    167:   PetscReal      tau=0.001,a=20;
    168:   PetscBool      split=PETSC_TRUE;

    170:   PetscFunctionBeginUser;
    171:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
    172:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
    173:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
    174:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-a",&a,NULL));
    175:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL));
    176:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g, a=%g\n\n",n,(double)tau,(double)a));

    178:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    179:               Create nonlinear eigensolver and solve the problem
    180:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    182:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
    183:   if (split) {
    184:     PetscCall(BuildSplitMatrices(n,a,&Id,&A,&B));
    185:     /* f1=-lambda */
    186:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
    187:     PetscCall(FNSetType(f1,FNRATIONAL));
    188:     coeffs[0] = -1.0; coeffs[1] = 0.0;
    189:     PetscCall(FNRationalSetNumerator(f1,2,coeffs));
    190:     /* f2=1.0 */
    191:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
    192:     PetscCall(FNSetType(f2,FNRATIONAL));
    193:     coeffs[0] = 1.0;
    194:     PetscCall(FNRationalSetNumerator(f2,1,coeffs));
    195:     /* f3=exp(-tau*lambda) */
    196:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
    197:     PetscCall(FNSetType(f3,FNEXP));
    198:     PetscCall(FNSetScale(f3,-tau,1.0));
    199:     mats[0] = A;  funs[0] = f2;
    200:     mats[1] = Id; funs[1] = f1;
    201:     mats[2] = B;  funs[2] = f3;
    202:     PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
    203:     PetscCall(BuildSplitPreconditioner(n,a,&Ap));
    204:     mats[0] = Ap;
    205:     mats[1] = Id;
    206:     mats[2] = B;
    207:     PetscCall(NEPSetSplitPreconditioner(nep,3,mats,SAME_NONZERO_PATTERN));
    208:   } else {
    209:     /* callback form  */
    210:     ctx.tau = tau;
    211:     ctx.a   = a;
    212:     PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
    213:     PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
    214:     PetscCall(MatSetFromOptions(F));
    215:     PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
    216:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    217:     PetscCall(MatSetUp(F));
    218:     PetscCall(MatDuplicate(F,MAT_DO_NOT_COPY_VALUES,&P));
    219:     PetscCall(NEPSetFunction(nep,F,P,FormFunction,&ctx));
    220:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
    221:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
    222:     PetscCall(MatSetFromOptions(J));
    223:     PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
    224:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    225:     PetscCall(MatSetUp(J));
    226:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));
    227:   }

    229:   /* Set solver parameters at runtime */
    230:   PetscCall(NEPSetFromOptions(nep));

    232:   /* Solve the eigensystem */
    233:   PetscCall(NEPSolve(nep));
    234:   PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));

    236:   PetscCall(NEPDestroy(&nep));
    237:   if (split) {
    238:     PetscCall(MatDestroy(&Id));
    239:     PetscCall(MatDestroy(&A));
    240:     PetscCall(MatDestroy(&B));
    241:     PetscCall(MatDestroy(&Ap));
    242:     PetscCall(FNDestroy(&f1));
    243:     PetscCall(FNDestroy(&f2));
    244:     PetscCall(FNDestroy(&f3));
    245:   } else {
    246:     PetscCall(MatDestroy(&F));
    247:     PetscCall(MatDestroy(&P));
    248:     PetscCall(MatDestroy(&J));
    249:   }
    250:   PetscCall(SlepcFinalize());
    251:   return 0;
    252: }

    254: /*TEST

    256:    testset:
    257:       args: -a 90000 -nep_nev 2
    258:       requires: double !defined(PETSCTEST_VALGRIND)
    259:       output_file: output/test17_1.out
    260:       timeoutfactor: 2
    261:       test:
    262:          suffix: 1
    263:          args: -nep_type slp -nep_two_sided {{0 1}} -split {{0 1}}

    265:    testset:
    266:       args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
    267:       requires: !single
    268:       output_file: output/test17_2.out
    269:       filter: sed -e "s/[+-]0\.0*i//g"
    270:       test:
    271:          suffix: 2_interpol
    272:          args: -nep_type interpol -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type sor -nep_tol 1e-6 -nep_interpol_st_ksp_rtol 1e-7
    273:       test:
    274:          suffix: 2_nleigs
    275:          args: -nep_type nleigs -split {{0 1}}
    276:          requires: complex
    277:       test:
    278:          suffix: 2_nleigs_real
    279:          args: -nep_type nleigs -rg_interval_endpoints .5,15 -split {{0 1}} -nep_nleigs_ksp_type tfqmr
    280:          requires: !complex

    282:    testset:
    283:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -rg_ellipse_vscale 0.1 -nep_ciss_ksp_type bcgs -nep_ciss_pc_type sor
    284:       output_file: output/test17_3.out
    285:       requires: complex !single !defined(PETSCTEST_VALGRIND)
    286:       test:
    287:          suffix: 3
    288:          args: -split {{0 1}}
    289:       test:
    290:          suffix: 3_par
    291:          nsize: 2
    292:          args: -nep_ciss_partitions 2

    294: TEST*/