Date: 2022-08-09T09:05:56+00:00

Actual source code: ex27.c
slepc-3.17.2 2022-08-09
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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:   SlepcInitialize(&argc,&argv,(char*)0,help);
     44:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     45:   PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL);
     46:   PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%" PetscInt_FMT "%s\n\n",n,split?" (in split form)":"");

     48:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     49:      Create nonlinear eigensolver context
     50:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     52:   NEPCreate(PETSC_COMM_WORLD,&nep);

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:      Select the NLEIGS solver and set required options for it
     56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     69:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     70:      Define the nonlinear problem
     71:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

    124:   /*
    125:      Set solver parameters at runtime
    126:   */
    127:   NEPSetFromOptions(nep);

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

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:                     Display solution and clean up
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

    198:   /*
    199:      Assemble matrix
    200:   */
    201:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    202:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    203:   if (fun != B) {
    204:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    205:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    206:   }
    207:   PetscFunctionReturn(0);
    208: }

    210: /* ------------------------------------------------------------------- */
    211: /*
    212:    FormJacobian - Computes Jacobian matrix  T'(lambda)
    213: */
    214: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    215: {
    216:   Vec            d;

    219:   MatCreateVecs(jac,&d,NULL);
    220:   VecSet(d,0.5/PetscSqrtScalar(lambda));
    221:   MatDiagonalSet(jac,d,INSERT_VALUES);
    222:   VecDestroy(&d);
    223:   PetscFunctionReturn(0);
    224: }

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

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

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

    245: /*TEST

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

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

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

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

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

    315: TEST*/