Date: 2026-01-20T11:35:34+00:00

Actual source code: test17.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[] = "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(MatGetOwnershipRange(*A,&Istart,&Iend));
     51:   for (i=Istart;i<Iend;i++) {
     52:     if (i>0) PetscCall(MatSetValue(*A,i,i-1,1.0/(h*h),INSERT_VALUES));
     53:     if (i<n-1) PetscCall(MatSetValue(*A,i,i+1,1.0/(h*h),INSERT_VALUES));
     54:     PetscCall(MatSetValue(*A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
     55:   }
     56:   PetscCall(MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY));
     57:   PetscCall(MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY));
     58:   PetscCall(MatSetOption(*A,MAT_HERMITIAN,PETSC_TRUE));

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

     76: /*
     77:    Create preconditioner matrices (only Ap=diag(A))
     78: */
     79: PetscErrorCode BuildSplitPreconditioner(PetscInt n,PetscReal a,Mat *Ap)
     80: {
     81:   PetscInt       i,Istart,Iend;
     82:   PetscReal      h;

     84:   PetscFunctionBeginUser;
     85:   h = PETSC_PI/(PetscReal)(n+1);

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

     99: /*
    100:    Compute Function matrix  T(lambda)
    101: */
    102: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    103: {
    104:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    105:   PetscInt       i,n,Istart,Iend;
    106:   PetscReal      h,xi;
    107:   PetscScalar    b;

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

    130: /*
    131:    Compute Jacobian matrix  T'(lambda)
    132: */
    133: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    134: {
    135:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    136:   PetscInt       i,n,Istart,Iend;
    137:   PetscReal      h,xi;
    138:   PetscScalar    b;

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

    154: int main(int argc,char **argv)
    155: {
    156:   NEP            nep;             /* nonlinear eigensolver context */
    157:   Mat            Id,A,B,Ap,J,F,P; /* problem matrices */
    158:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
    159:   ApplicationCtx ctx;             /* user-defined context */
    160:   Mat            mats[3],M;
    161:   FN             funs[3];
    162:   PetscScalar    coeffs[2];
    163:   PetscInt       n=128,nterm;
    164:   PetscReal      tau=0.001,a=20;
    165:   PetscBool      split=PETSC_TRUE;
    166:   MatStructure   mstr;

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

    176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    177:               Create nonlinear eigensolver and solve the problem
    178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    225:   /* Set solver parameters at runtime */
    226:   PetscCall(NEPSetFromOptions(nep));

    228:   if (split) {
    229:     PetscCall(NEPGetSplitPreconditionerInfo(nep,&nterm,&mstr));
    230:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Nonlinear preconditioner with %" PetscInt_FMT " terms, with %s nonzero pattern\n",nterm,MatStructures[mstr]));
    231:     PetscCall(NEPGetSplitPreconditionerTerm(nep,0,&M));
    232:   }

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

    238:   PetscCall(NEPDestroy(&nep));
    239:   if (split) {
    240:     PetscCall(MatDestroy(&Id));
    241:     PetscCall(MatDestroy(&A));
    242:     PetscCall(MatDestroy(&B));
    243:     PetscCall(MatDestroy(&Ap));
    244:     PetscCall(FNDestroy(&f1));
    245:     PetscCall(FNDestroy(&f2));
    246:     PetscCall(FNDestroy(&f3));
    247:   } else {
    248:     PetscCall(MatDestroy(&F));
    249:     PetscCall(MatDestroy(&P));
    250:     PetscCall(MatDestroy(&J));
    251:   }
    252:   PetscCall(SlepcFinalize());
    253:   return 0;
    254: }

    256: /*TEST

    258:    testset:
    259:       args: -a 90000 -nep_nev 2
    260:       requires: double !defined(PETSCTEST_VALGRIND)
    261:       output_file: output/test17_1.out
    262:       timeoutfactor: 2
    263:       filter: grep -v "with 3 terms, with SAME"
    264:       test:
    265:          suffix: 1
    266:          args: -nep_type slp -nep_two_sided {{0 1}} -split {{0 1}}

    268:    testset:
    269:       args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .71
    270:       requires: !single
    271:       output_file: output/test17_2.out
    272:       filter: sed -e "s/[+-]0\.0*i//g" | grep -v "with 3 terms, with SAME"
    273:       test:
    274:          suffix: 2_interpol
    275:          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-8
    276:       test:
    277:          suffix: 2_nleigs
    278:          args: -nep_type nleigs -split {{0 1}}
    279:          requires: complex
    280:       test:
    281:          suffix: 2_nleigs_real
    282:          args: -nep_type nleigs -rg_interval_endpoints .5,11 -split {{0 1}} -nep_nleigs_ksp_type tfqmr -nep_nleigs_ksp_rtol 1e-10 -nep_tol 1e-7
    283:          requires: !complex !__float128

    285:    testset:
    286:       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
    287:       output_file: output/test17_3.out
    288:       requires: complex !single !defined(PETSCTEST_VALGRIND)
    289:       filter: grep -v "with 3 terms, with SAME"
    290:       test:
    291:          suffix: 3
    292:          args: -split {{0 1}}
    293:       test:
    294:          suffix: 3_par
    295:          nsize: 2
    296:          args: -nep_ciss_partitions 2

    298: TEST*/