Date: 2026-05-01T10:02:06+00:00

Actual source code: sleeper.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: */
     10: /*
     11:    This example implements one of the problems found at
     12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     13:        The University of Manchester.
     14:    The details of the collection can be found at:
     15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     18:    The sleeper problem is a proportionally damped QEP describing the
     19:    oscillations of a rail track resting on sleepers.
     20: */

     22: static char help[] = "Oscillations of a rail track resting on sleepers.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, where <n> = dimension of the matrices.\n\n";

     26: #include <slepcpep.h>

     28: int main(int argc,char **argv)
     29: {
     30:   Mat            M,C,K,A[3];      /* problem matrices */
     31:   PEP            pep;             /* polynomial eigenproblem solver context */
     32:   PetscInt       n=10,Istart,Iend,i;
     33:   PetscBool      terse;

     35:   PetscFunctionBeginUser;
     36:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     38:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     39:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nRailtrack resting on sleepers, n=%" PetscInt_FMT "\n\n",n));

     41:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     42:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     43:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     45:   /* K is a pentadiagonal */
     46:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
     47:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
     48:   PetscCall(MatSetFromOptions(K));

     50:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     51:   for (i=Istart;i<Iend;i++) {
     52:     if (i==0) {
     53:       PetscCall(MatSetValue(K,i,n-1,-3.0,INSERT_VALUES));
     54:       PetscCall(MatSetValue(K,i,n-2,1.0,INSERT_VALUES));
     55:     }
     56:     if (i==1) PetscCall(MatSetValue(K,i,n-1,1.0,INSERT_VALUES));
     57:     if (i>0) PetscCall(MatSetValue(K,i,i-1,-3.0,INSERT_VALUES));
     58:     if (i>1) PetscCall(MatSetValue(K,i,i-2,1.0,INSERT_VALUES));
     59:     PetscCall(MatSetValue(K,i,i,5.0,INSERT_VALUES));
     60:     if (i==n-1) {
     61:       PetscCall(MatSetValue(K,i,0,-3.0,INSERT_VALUES));
     62:       PetscCall(MatSetValue(K,i,1,1.0,INSERT_VALUES));
     63:     }
     64:     if (i==n-2) PetscCall(MatSetValue(K,i,0,1.0,INSERT_VALUES));
     65:     if (i<n-1) PetscCall(MatSetValue(K,i,i+1,-3.0,INSERT_VALUES));
     66:     if (i<n-2) PetscCall(MatSetValue(K,i,i+2,1.0,INSERT_VALUES));
     67:   }

     69:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
     70:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

     72:   /* C is a circulant matrix */
     73:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
     74:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
     75:   PetscCall(MatSetFromOptions(C));

     77:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
     78:   for (i=Istart;i<Iend;i++) {
     79:     if (i==0) {
     80:       PetscCall(MatSetValue(C,i,n-1,-4.0,INSERT_VALUES));
     81:       PetscCall(MatSetValue(C,i,n-2,1.0,INSERT_VALUES));
     82:     }
     83:     if (i==1) PetscCall(MatSetValue(C,i,n-1,1.0,INSERT_VALUES));
     84:     if (i>0) PetscCall(MatSetValue(C,i,i-1,-4.0,INSERT_VALUES));
     85:     if (i>1) PetscCall(MatSetValue(C,i,i-2,1.0,INSERT_VALUES));
     86:     PetscCall(MatSetValue(C,i,i,7.0,INSERT_VALUES));
     87:     if (i==n-1) {
     88:       PetscCall(MatSetValue(C,i,0,-4.0,INSERT_VALUES));
     89:       PetscCall(MatSetValue(C,i,1,1.0,INSERT_VALUES));
     90:     }
     91:     if (i==n-2) PetscCall(MatSetValue(C,i,0,1.0,INSERT_VALUES));
     92:     if (i<n-1) PetscCall(MatSetValue(C,i,i+1,-4.0,INSERT_VALUES));
     93:     if (i<n-2) PetscCall(MatSetValue(C,i,i+2,1.0,INSERT_VALUES));
     94:   }

     96:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
     97:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

     99:   /* M is the identity matrix */
    100:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
    101:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
    102:   PetscCall(MatSetFromOptions(M));
    103:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
    104:   for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(M,i,i,1.0,INSERT_VALUES));
    105:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
    106:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

    108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    109:                 Create the eigensolver and solve the problem
    110:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    112:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    113:   A[0] = K; A[1] = C; A[2] = M;
    114:   PetscCall(PEPSetOperators(pep,3,A));
    115:   PetscCall(PEPSetFromOptions(pep));
    116:   PetscCall(PEPSolve(pep));

    118:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    119:                     Display solution and clean up
    120:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    122:   /* show detailed info unless -terse option is given by user */
    123:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    124:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    125:   else {
    126:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    127:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    128:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    129:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    130:   }
    131:   PetscCall(PEPDestroy(&pep));
    132:   PetscCall(MatDestroy(&M));
    133:   PetscCall(MatDestroy(&C));
    134:   PetscCall(MatDestroy(&K));
    135:   PetscCall(SlepcFinalize());
    136:   return 0;
    137: }

    139: /*TEST

    141:    testset:
    142:       args: -n 100 -pep_nev 4 -pep_ncv 24 -st_type sinvert -terse
    143:       output_file: output/sleeper_1.out
    144:       requires: !single
    145:       filter: sed -e "s/[+-]0\.0*i//g"
    146:       test:
    147:          suffix: 1
    148:          args: -pep_type {{toar linear}} -pep_ncv 20
    149:       test:
    150:          suffix: 1_qarnoldi
    151:          args: -pep_type qarnoldi -pep_qarnoldi_restart 0.4

    153:    testset:
    154:       args: -n 24 -pep_nev 4 -pep_ncv 9 -pep_target -.62 -terse
    155:       output_file: output/sleeper_2.out
    156:       test:
    157:          suffix: 2_toar
    158:          args: -pep_type toar -pep_toar_restart .3 -st_type sinvert
    159:       test:
    160:          suffix: 2_jd
    161:          args: -pep_type jd -pep_jd_restart .3 -pep_jd_projection orthogonal

    163:    test:
    164:       suffix: 3
    165:       args: -n 275 -pep_type stoar -pep_hermitian -st_type sinvert -pep_nev 2 -pep_target -.89 -terse
    166:       requires: !single

    168:    test:
    169:       suffix: 4
    170:       args: -n 270 -pep_type stoar -pep_hermitian -pep_interval -3,-2.51 -st_type sinvert -st_pc_type cholesky -terse
    171:       requires: !single

    173: TEST*/