Date: 2021-09-20T09:44:11+00:00

Actual source code: ex27.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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;
     39:   PetscBool      terse,split=PETSC_TRUE;
     40:   RG             rg;
     41:   FN             f[2];
     42:   PetscScalar    coeffs;

     44:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     46:   PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL);
     47:   PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%D%s\n\n",n,split?" (in split form)":"");

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

     53:   NEPCreate(PETSC_COMM_WORLD,&nep);

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

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

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

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

     91:     MatCreate(PETSC_COMM_WORLD,&A[1]);
     92:     MatSetSizes(A[1],PETSC_DECIDE,PETSC_DECIDE,n,n);
     93:     MatSetFromOptions(A[1]);
     94:     MatSetUp(A[1]);
     95:     MatAssemblyBegin(A[1],MAT_FINAL_ASSEMBLY);
     96:     MatAssemblyEnd(A[1],MAT_FINAL_ASSEMBLY);
     97:     MatShift(A[1],1.0);

     99:     /*
    100:        Define functions for the split form
    101:      */
    102:     FNCreate(PETSC_COMM_WORLD,&f[0]);
    103:     FNSetType(f[0],FNRATIONAL);
    104:     coeffs = 1.0;
    105:     FNRationalSetNumerator(f[0],1,&coeffs);
    106:     FNCreate(PETSC_COMM_WORLD,&f[1]);
    107:     FNSetType(f[1],FNSQRT);
    108:     NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN);

    110:   } else {
    111:     /*
    112:        Callback form: create matrix and set Function evaluation routine
    113:      */
    114:     MatCreate(PETSC_COMM_WORLD,&F);
    115:     MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
    116:     MatSetFromOptions(F);
    117:     MatSeqAIJSetPreallocation(F,3,NULL);
    118:     MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
    119:     MatSetUp(F);
    120:     NEPSetFunction(nep,F,F,FormFunction,NULL);

    122:     MatCreate(PETSC_COMM_WORLD,&J);
    123:     MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
    124:     MatSetFromOptions(J);
    125:     MatSeqAIJSetPreallocation(J,1,NULL);
    126:     MatMPIAIJSetPreallocation(J,1,NULL,1,NULL);
    127:     MatSetUp(J);
    128:     NEPSetJacobian(nep,J,FormJacobian,NULL);
    129:   }

    131:   /*
    132:      Set solver parameters at runtime
    133:   */
    134:   NEPSetFromOptions(nep);

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:                       Solve the eigensystem
    138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    139:   NEPSolve(nep);
    140:   NEPGetType(nep,&type);
    141:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
    142:   NEPGetDimensions(nep,&nev,NULL,NULL);
    143:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:                     Display solution and clean up
    147:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    149:   /* show detailed info unless -terse option is given by user */
    150:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    151:   if (terse) {
    152:     NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL);
    153:   } else {
    154:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    155:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    156:     NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    157:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    158:   }
    159:   NEPDestroy(&nep);
    160:   if (split) {
    161:     MatDestroy(&A[0]);
    162:     MatDestroy(&A[1]);
    163:     FNDestroy(&f[0]);
    164:     FNDestroy(&f[1]);
    165:   } else {
    166:     MatDestroy(&F);
    167:     MatDestroy(&J);
    168:   }
    169:   SlepcFinalize();
    170:   return ierr;
    171: }

    173: /* ------------------------------------------------------------------- */
    174: /*
    175:    FormFunction - Computes Function matrix  T(lambda)
    176: */
    177: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    178: {
    180:   PetscInt       i,n,col[3],Istart,Iend;
    181:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
    182:   PetscScalar    value[3],t;

    185:   /*
    186:      Compute Function entries and insert into matrix
    187:   */
    188:   t = PetscSqrtScalar(lambda);
    189:   MatGetSize(fun,&n,NULL);
    190:   MatGetOwnershipRange(fun,&Istart,&Iend);
    191:   if (Istart==0) FirstBlock=PETSC_TRUE;
    192:   if (Iend==n) LastBlock=PETSC_TRUE;
    193:   value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
    194:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
    195:     col[0]=i-1; col[1]=i; col[2]=i+1;
    196:     MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES);
    197:   }
    198:   if (LastBlock) {
    199:     i=n-1; col[0]=n-2; col[1]=n-1;
    200:     MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES);
    201:   }
    202:   if (FirstBlock) {
    203:     i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
    204:     MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES);
    205:   }

    207:   /*
    208:      Assemble matrix
    209:   */
    210:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    211:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    212:   if (fun != B) {
    213:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    214:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    215:   }
    216:   return(0);
    217: }

    219: /* ------------------------------------------------------------------- */
    220: /*
    221:    FormJacobian - Computes Jacobian matrix  T'(lambda)
    222: */
    223: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    224: {
    226:   Vec            d;

    229:   MatCreateVecs(jac,&d,NULL);
    230:   VecSet(d,0.5/PetscSqrtScalar(lambda));
    231:   MatDiagonalSet(jac,d,INSERT_VALUES);
    232:   VecDestroy(&d);
    233:   return(0);
    234: }

    236: /* ------------------------------------------------------------------- */
    237: /*
    238:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
    239:    the function T(.) is not analytic.

    241:    In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
    242: */
    243: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
    244: {
    245:   PetscReal h;
    246:   PetscInt  i;

    249:   h = 11.0/(*maxnp-1);
    250:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
    251:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
    252:   return(0);
    253: }

    255: /*TEST

    257:    testset:
    258:       args: -nep_nev 3 -terse
    259:       output_file: output/ex27_1.out
    260:       requires: !single
    261:       filter: sed -e "s/[+-]0\.0*i//g"
    262:       test:
    263:          suffix: 1
    264:          args: -nep_nleigs_interpolation_degree 90
    265:       test:
    266:          suffix: 3
    267:          args: -nep_tol 1e-8 -nep_nleigs_rk_shifts 1.06,1.1,1.12,1.15 -nep_conv_norm
    268:       test:
    269:          suffix: 5
    270:          args: -mat_type aijcusparse
    271:          requires: cuda

    273:    testset:
    274:       args: -split 0 -nep_nev 3 -terse
    275:       output_file: output/ex27_2.out
    276:       filter: sed -e "s/[+-]0\.0*i//g"
    277:       test:
    278:          suffix: 2
    279:          args: -nep_nleigs_interpolation_degree 90
    280:          requires: !single
    281:       test:
    282:          suffix: 4
    283:          args: -nep_nleigs_rk_shifts 1.06,1.1,1.12,1.15 -nep_nleigs_interpolation_degree 90
    284:          requires: double
    285:       test:
    286:          suffix: 6
    287:          args: -mat_type aijcusparse
    288:          requires: cuda !single

    290:    test:
    291:       suffix: 9
    292:       args: -nep_nev 4 -n 20 -terse
    293:       requires: !single
    294:       filter: sed -e "s/[+-]0\.0*i//g"

    296: TEST*/