Date: 2023-09-05T10:18:23+00:00

Actual source code: ex27.c
slepc-3.19.2 2023-09-05
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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[] = "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,(char*)0,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(MatSetUp(A[0]));
     82:     PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
     83:     for (i=Istart;i<Iend;i++) {
     84:       if (i>0) PetscCall(MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES));
     85:       if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES));
     86:       PetscCall(MatSetValue(A[0],i,i,-2.0,INSERT_VALUES));
     87:     }
     88:     PetscCall(MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY));
     89:     PetscCall(MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY));

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

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

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

    116:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
    117:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
    118:     PetscCall(MatSetFromOptions(J));
    119:     PetscCall(MatSeqAIJSetPreallocation(J,1,NULL));
    120:     PetscCall(MatMPIAIJSetPreallocation(J,1,NULL,1,NULL));
    121:     PetscCall(MatSetUp(J));
    122:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,NULL));
    123:   }

    125:   /*
    126:      Set solver parameters at runtime
    127:   */
    128:   PetscCall(NEPSetFromOptions(nep));

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

    139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    140:                     Display solution and clean up
    141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    143:   /* show detailed info unless -terse option is given by user */
    144:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    145:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL));
    146:   else {
    147:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    148:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    149:     PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    150:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    151:   }
    152:   PetscCall(NEPDestroy(&nep));
    153:   if (split) {
    154:     PetscCall(MatDestroy(&A[0]));
    155:     PetscCall(MatDestroy(&A[1]));
    156:     PetscCall(FNDestroy(&f[0]));
    157:     PetscCall(FNDestroy(&f[1]));
    158:   } else {
    159:     PetscCall(MatDestroy(&F));
    160:     PetscCall(MatDestroy(&J));
    161:   }
    162:   PetscCall(SlepcFinalize());
    163:   return 0;
    164: }

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

    176:   PetscFunctionBeginUser;
    177:   /*
    178:      Compute Function entries and insert into matrix
    179:   */
    180:   t = PetscSqrtScalar(lambda);
    181:   PetscCall(MatGetSize(fun,&n,NULL));
    182:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
    183:   if (Istart==0) FirstBlock=PETSC_TRUE;
    184:   if (Iend==n) LastBlock=PETSC_TRUE;
    185:   value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
    186:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
    187:     col[0]=i-1; col[1]=i; col[2]=i+1;
    188:     PetscCall(MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES));
    189:   }
    190:   if (LastBlock) {
    191:     i=n-1; col[0]=n-2; col[1]=n-1;
    192:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
    193:   }
    194:   if (FirstBlock) {
    195:     i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
    196:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
    197:   }

    199:   /*
    200:      Assemble matrix
    201:   */
    202:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    203:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    204:   if (fun != B) {
    205:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    206:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    207:   }
    208:   PetscFunctionReturn(PETSC_SUCCESS);
    209: }

    211: /* ------------------------------------------------------------------- */
    212: /*
    213:    FormJacobian - Computes Jacobian matrix  T'(lambda)
    214: */
    215: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    216: {
    217:   Vec            d;

    219:   PetscFunctionBeginUser;
    220:   PetscCall(MatCreateVecs(jac,&d,NULL));
    221:   PetscCall(VecSet(d,0.5/PetscSqrtScalar(lambda)));
    222:   PetscCall(MatDiagonalSet(jac,d,INSERT_VALUES));
    223:   PetscCall(VecDestroy(&d));
    224:   PetscFunctionReturn(PETSC_SUCCESS);
    225: }

    227: /* ------------------------------------------------------------------- */
    228: /*
    229:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
    230:    the function T(.) is not analytic.

    232:    In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
    233: */
    234: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
    235: {
    236:   PetscReal h;
    237:   PetscInt  i;

    239:   PetscFunctionBeginUser;
    240:   h = 11.0/(*maxnp-1);
    241:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
    242:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
    243:   PetscFunctionReturn(PETSC_SUCCESS);
    244: }

    246: /*TEST

    248:    testset:
    249:       args: -nep_nev 3 -terse
    250:       output_file: output/ex27_1.out
    251:       requires: !single
    252:       filter: sed -e "s/[+-]0\.0*i//g"
    253:       test:
    254:          suffix: 1
    255:          args: -nep_nleigs_interpolation_degree 90
    256:       test:
    257:          suffix: 3
    258:          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
    259:       test:
    260:          suffix: 5
    261:          args: -mat_type aijcusparse
    262:          requires: cuda

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

    281:    testset:
    282:       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
    283:       requires: complex !single
    284:       output_file: output/ex27_7.out
    285:       timeoutfactor: 2
    286:       test:
    287:          suffix: 7
    288:       test:
    289:          suffix: 7_par
    290:          nsize: 2
    291:          args: -nep_ciss_partitions 2

    293:    testset:
    294:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 8 -rg_ellipse_radius .7 -rg_ellipse_vscale 0.1 -terse
    295:       requires: complex
    296:       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/"
    297:       output_file: output/ex27_7.out
    298:       timeoutfactor: 2
    299:       test:
    300:          suffix: 8
    301:       test:
    302:          suffix: 8_parallel
    303:          nsize: 4
    304:          args: -nep_ciss_partitions 4 -ds_parallel distributed
    305:       test:
    306:          suffix: 8_hpddm
    307:          args: -nep_ciss_ksp_type hpddm
    308:          requires: hpddm

    310:    test:
    311:       suffix: 9
    312:       args: -nep_nev 4 -n 20 -terse
    313:       requires: !single
    314:       filter: sed -e "s/[+-]0\.0*i//g"

    316: TEST*/