Date: 2026-03-31T13:23:26+00:00

Actual source code: ex27.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[] = "Simple nonlinear eigenproblem using the NLEIGS solver.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = matrix dimension.\n"
     14:   "  -split <0/1>, to select the split form in the problem definition (enabled by default)\n";

     16: /*
     17:    Solve T(lambda)x=0 using NLEIGS solver
     18:       with T(lambda) = -D+sqrt(lambda)*I
     19:       where D is the Laplacian operator in 1 dimension
     20:       and with the interpolation interval [.01,16]
     21: */

     23: #include <slepcnep.h>

     25: /*
     26:    User-defined routines
     27: */
     28: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     29: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
     30: PetscErrorCode ComputeSingularities(NEP,PetscInt*,PetscScalar*,void*);

     32: int main(int argc,char **argv)
     33: {
     34:   NEP            nep;             /* nonlinear eigensolver context */
     35:   Mat            F,J,A[2];
     36:   NEPType        type;
     37:   PetscInt       n=100,nev,Istart,Iend,i;
     38:   PetscBool      terse,split=PETSC_TRUE;
     39:   RG             rg;
     40:   FN             f[2];
     41:   PetscScalar    coeffs;

     43:   PetscFunctionBeginUser;
     44:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     46:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL));
     47:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%" PetscInt_FMT "%s\n\n",n,split?" (in split form)":""));

     49:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     50:      Create nonlinear eigensolver context
     51:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     56:      Select the NLEIGS solver and set required options for it
     57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     59:   PetscCall(NEPSetType(nep,NEPNLEIGS));
     60:   PetscCall(NEPNLEIGSSetSingularitiesFunction(nep,ComputeSingularities,NULL));
     61:   PetscCall(NEPGetRG(nep,&rg));
     62:   PetscCall(RGSetType(rg,RGINTERVAL));
     63: #if defined(PETSC_USE_COMPLEX)
     64:   PetscCall(RGIntervalSetEndpoints(rg,0.01,16.0,-0.001,0.001));
     65: #else
     66:   PetscCall(RGIntervalSetEndpoints(rg,0.01,16.0,0,0));
     67: #endif
     68:   PetscCall(NEPSetTarget(nep,1.1));

     70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:      Define the nonlinear problem
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     74:   if (split) {
     75:     /*
     76:        Create matrices for the split form
     77:     */
     78:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[0]));
     79:     PetscCall(MatSetSizes(A[0],PETSC_DECIDE,PETSC_DECIDE,n,n));
     80:     PetscCall(MatSetFromOptions(A[0]));
     81:     PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
     82:     for (i=Istart;i<Iend;i++) {
     83:       if (i>0) PetscCall(MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES));
     84:       if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES));
     85:       PetscCall(MatSetValue(A[0],i,i,-2.0,INSERT_VALUES));
     86:     }
     87:     PetscCall(MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY));
     88:     PetscCall(MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY));

     90:     PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&A[1]));

     92:     /*
     93:        Define functions for the split form
     94:      */
     95:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
     96:     PetscCall(FNSetType(f[0],FNRATIONAL));
     97:     coeffs = 1.0;
     98:     PetscCall(FNRationalSetNumerator(f[0],1,&coeffs));
     99:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
    100:     PetscCall(FNSetType(f[1],FNSQRT));
    101:     PetscCall(NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN));

    103:   } else {
    104:     /*
    105:        Callback form: create matrix and set Function evaluation routine
    106:      */
    107:     PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
    108:     PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
    109:     PetscCall(MatSetFromOptions(F));
    110:     PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
    111:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
    112:     PetscCall(NEPSetFunction(nep,F,F,FormFunction,NULL));

    114:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
    115:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
    116:     PetscCall(MatSetFromOptions(J));
    117:     PetscCall(MatSeqAIJSetPreallocation(J,1,NULL));
    118:     PetscCall(MatMPIAIJSetPreallocation(J,1,NULL,1,NULL));
    119:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,NULL));
    120:   }

    122:   /*
    123:      Set solver parameters at runtime
    124:   */
    125:   PetscCall(NEPSetFromOptions(nep));

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:                       Solve the eigensystem
    129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    130:   PetscCall(NEPSolve(nep));
    131:   PetscCall(NEPGetType(nep,&type));
    132:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type));
    133:   PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
    134:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:                     Display solution and clean up
    138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    140:   /* show detailed info unless -terse option is given by user */
    141:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    142:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL));
    143:   else {
    144:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    145:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    146:     PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    147:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    148:   }
    149:   PetscCall(NEPDestroy(&nep));
    150:   if (split) {
    151:     PetscCall(MatDestroy(&A[0]));
    152:     PetscCall(MatDestroy(&A[1]));
    153:     PetscCall(FNDestroy(&f[0]));
    154:     PetscCall(FNDestroy(&f[1]));
    155:   } else {
    156:     PetscCall(MatDestroy(&F));
    157:     PetscCall(MatDestroy(&J));
    158:   }
    159:   PetscCall(SlepcFinalize());
    160:   return 0;
    161: }

    163: /* ------------------------------------------------------------------- */
    164: /*
    165:    FormFunction - Computes Function matrix  T(lambda)
    166: */
    167: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    168: {
    169:   PetscInt       i,n,col[3],Istart,Iend;
    170:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
    171:   PetscScalar    value[3],t;

    173:   PetscFunctionBeginUser;
    174:   /*
    175:      Compute Function entries and insert into matrix
    176:   */
    177:   t = PetscSqrtScalar(lambda);
    178:   PetscCall(MatGetSize(fun,&n,NULL));
    179:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
    180:   if (Istart==0) FirstBlock=PETSC_TRUE;
    181:   if (Iend==n) LastBlock=PETSC_TRUE;
    182:   value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
    183:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
    184:     col[0]=i-1; col[1]=i; col[2]=i+1;
    185:     PetscCall(MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES));
    186:   }
    187:   if (LastBlock) {
    188:     i=n-1; col[0]=n-2; col[1]=n-1;
    189:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
    190:   }
    191:   if (FirstBlock) {
    192:     i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
    193:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
    194:   }

    196:   /*
    197:      Assemble matrix
    198:   */
    199:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    200:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    201:   if (fun != B) {
    202:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    203:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    204:   }
    205:   PetscFunctionReturn(PETSC_SUCCESS);
    206: }

    208: /* ------------------------------------------------------------------- */
    209: /*
    210:    FormJacobian - Computes Jacobian matrix  T'(lambda)
    211: */
    212: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    213: {
    214:   Vec            d;

    216:   PetscFunctionBeginUser;
    217:   PetscCall(MatCreateVecs(jac,&d,NULL));
    218:   PetscCall(VecSet(d,0.5/PetscSqrtScalar(lambda)));
    219:   PetscCall(MatDiagonalSet(jac,d,INSERT_VALUES));
    220:   PetscCall(VecDestroy(&d));
    221:   PetscFunctionReturn(PETSC_SUCCESS);
    222: }

    224: /* ------------------------------------------------------------------- */
    225: /*
    226:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
    227:    the function T(.) is not analytic.

    229:    In this case, we discretize the singularity region (-inf,0)~(-1e+6,-1e-5)
    230: */
    231: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
    232: {
    233:   PetscReal h;
    234:   PetscInt  i;

    236:   PetscFunctionBeginUser;
    237:   h = 11.0/(*maxnp-1);
    238:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
    239:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
    240:   PetscFunctionReturn(PETSC_SUCCESS);
    241: }

    243: /*TEST

    245:    testset:
    246:       args: -nep_nev 3 -terse
    247:       output_file: output/ex27_1.out
    248:       requires: !single
    249:       filter: sed -e "s/[+-]0\.0*i//g"
    250:       test:
    251:          suffix: 1
    252:          args: -nep_nleigs_interpolation_degree 90
    253:       test:
    254:          suffix: 3
    255:          args: -nep_tol 1e-8 -nep_nleigs_rk_shifts 1.06,1.1,1.12,1.15 -nep_conv_norm -nep_nleigs_interpolation_degree 20
    256:       test:
    257:          suffix: 5_cuda
    258:          args: -mat_type aijcusparse
    259:          requires: cuda
    260:       test:
    261:          suffix: 5_hip
    262:          args: -mat_type aijhipsparse
    263:          requires: hip

    265:    testset:
    266:       args: -split 0 -nep_nev 3 -terse
    267:       output_file: output/ex27_2.out
    268:       filter: sed -e "s/[+-]0\.0*i//g"
    269:       test:
    270:          suffix: 2
    271:          args: -nep_nleigs_interpolation_degree 90
    272:          requires: !single
    273:       test:
    274:          suffix: 4
    275:          args: -nep_nleigs_rk_shifts 1.06,1.1,1.12,1.15 -nep_nleigs_interpolation_degree 20
    276:          requires: double
    277:       test:
    278:          suffix: 6_cuda
    279:          args: -mat_type aijcusparse
    280:          requires: cuda !single
    281:       test:
    282:          suffix: 6_hip
    283:          args: -mat_type aijhipsparse
    284:          requires: hip !single

    286:    testset:
    287:       args: -split 0 -nep_type ciss -nep_ciss_extraction {{ritz hankel caa}} -rg_type ellipse -rg_ellipse_center 8 -rg_ellipse_radius .7 -nep_ciss_moments 4 -rg_ellipse_vscale 0.1 -terse
    288:       requires: complex !single
    289:       output_file: output/ex27_7.out
    290:       timeoutfactor: 2
    291:       test:
    292:          suffix: 7
    293:       test:
    294:          suffix: 7_par
    295:          nsize: 2
    296:          args: -nep_ciss_partitions 2

    298:    testset:
    299:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 8 -rg_ellipse_radius .7 -rg_ellipse_vscale 0.1 -terse
    300:       requires: complex
    301:       filter: sed -e "s/ (in split form)//" | sed -e "s/56925/56924/" | sed -e "s/60753/60754/" | sed -e "s/92630/92629/" | sed -e "s/24705/24706/"
    302:       output_file: output/ex27_7.out
    303:       timeoutfactor: 2
    304:       test:
    305:          suffix: 8
    306:       test:
    307:          suffix: 8_parallel
    308:          nsize: 4
    309:          args: -nep_ciss_partitions 4 -ds_parallel distributed
    310:       test:
    311:          suffix: 8_hpddm
    312:          args: -nep_ciss_ksp_type hpddm
    313:          requires: hpddm

    315:    test:
    316:       suffix: 9
    317:       args: -nep_nev 4 -n 20 -terse
    318:       requires: !single
    319:       filter: sed -e "s/[+-]0\.0*i//g"

    321: TEST*/