Date: 2026-03-09T09:12:01+00:00

Actual source code: spring.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 spring problem is a QEP from the finite element model of a damped
     19:    mass-spring system. This implementation supports only scalar parameters,
     20:    that is all masses, dampers and springs have the same constants.
     21:    Furthermore, this implementation does not consider different constants
     22:    for dampers and springs connecting adjacent masses or masses to the ground.
     23: */

     25: static char help[] = "FEM model of a damped mass-spring system.\n\n"
     26:   "The command line options are:\n"
     27:   "  -n <n> ... dimension of the matrices.\n"
     28:   "  -mu <value> ... mass (default 1).\n"
     29:   "  -tau <value> ... damping constant of the dampers (default 10).\n"
     30:   "  -kappa <value> ... damping constant of the springs (default 5).\n\n";

     32: #include <slepcpep.h>

     34: int main(int argc,char **argv)
     35: {
     36:   Mat            M,C,K,A[3];      /* problem matrices */
     37:   PEP            pep;             /* polynomial eigenproblem solver context */
     38:   PetscInt       n=5,Istart,Iend,i;
     39:   PetscReal      mu=1.0,tau=10.0,kappa=5.0;
     40:   PetscBool      terse;

     42:   PetscFunctionBeginUser;
     43:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     46:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL));
     47:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
     48:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
     49:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nDamped mass-spring system, n=%" PetscInt_FMT " mu=%g tau=%g kappa=%g\n\n",n,(double)mu,(double)tau,(double)kappa));

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   /* K is a tridiagonal */
     56:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
     57:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
     58:   PetscCall(MatSetFromOptions(K));

     60:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     61:   for (i=Istart;i<Iend;i++) {
     62:     if (i>0) PetscCall(MatSetValue(K,i,i-1,-kappa,INSERT_VALUES));
     63:     PetscCall(MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES));
     64:     if (i<n-1) PetscCall(MatSetValue(K,i,i+1,-kappa,INSERT_VALUES));
     65:   }

     67:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
     68:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

     70:   /* C is a tridiagonal */
     71:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
     72:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
     73:   PetscCall(MatSetFromOptions(C));

     75:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
     76:   for (i=Istart;i<Iend;i++) {
     77:     if (i>0) PetscCall(MatSetValue(C,i,i-1,-tau,INSERT_VALUES));
     78:     PetscCall(MatSetValue(C,i,i,tau*3.0,INSERT_VALUES));
     79:     if (i<n-1) PetscCall(MatSetValue(C,i,i+1,-tau,INSERT_VALUES));
     80:   }

     82:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
     83:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

     85:   /* M is a diagonal matrix */
     86:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
     87:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
     88:   PetscCall(MatSetFromOptions(M));
     89:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
     90:   for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(M,i,i,mu,INSERT_VALUES));
     91:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
     92:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

     94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     95:                 Create the eigensolver and solve the problem
     96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     98:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
     99:   A[0] = K; A[1] = C; A[2] = M;
    100:   PetscCall(PEPSetOperators(pep,3,A));
    101:   PetscCall(PEPSetFromOptions(pep));
    102:   PetscCall(PEPSolve(pep));

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:                     Display solution and clean up
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    108:   /* show detailed info unless -terse option is given by user */
    109:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    110:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    111:   else {
    112:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    113:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    114:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    115:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    116:   }
    117:   PetscCall(PEPDestroy(&pep));
    118:   PetscCall(MatDestroy(&M));
    119:   PetscCall(MatDestroy(&C));
    120:   PetscCall(MatDestroy(&K));
    121:   PetscCall(SlepcFinalize());
    122:   return 0;
    123: }

    125: /*TEST

    127:    testset:
    128:       args: -pep_nev 4 -n 24 -pep_ncv 18 -pep_target -.5 -st_type sinvert -pep_scale diagonal -terse
    129:       output_file: output/spring_1.out
    130:       filter: sed -e "s/[+-]0\.0*i//g"
    131:       test:
    132:          suffix: 1
    133:          args: -pep_type {{toar linear}} -pep_conv_norm
    134:       test:
    135:          suffix: 1_stoar
    136:          args: -pep_type stoar -pep_hermitian -pep_conv_rel
    137:       test:
    138:          suffix: 1_qarnoldi
    139:          args: -pep_type qarnoldi -pep_conv_rel
    140:       test:
    141:          suffix: 1_cuda
    142:          args: -mat_type aijcusparse
    143:          requires: cuda
    144:       test:
    145:          suffix: 1_hip
    146:          args: -mat_type aijhipsparse
    147:          requires: hip

    149:    test:
    150:       suffix: 2
    151:       args: -pep_type jd -pep_jd_minimality_index 1 -pep_nev 4 -n 24 -pep_ncv 18 -pep_target -50 -terse
    152:       requires: !single
    153:       filter: sed -e "s/[+-]0\.0*i//g"

    155:    test:
    156:       suffix: 3
    157:       args: -n 300 -pep_hermitian -pep_interval -10.1,-9.5 -pep_type stoar -st_type sinvert -st_pc_type cholesky -terse
    158:       filter: sed -e "s/52565/52566/" | sed -e "s/90758/90759/"
    159:       requires: !single

    161:    test:
    162:       suffix: 4
    163:       args: -n 300 -pep_hyperbolic -pep_interval -9.6,-.527 -pep_type stoar -st_type sinvert -st_pc_type cholesky -terse
    164:       requires: !single
    165:       timeoutfactor: 2

    167:    test:
    168:       suffix: 5
    169:       args: -n 300 -pep_hyperbolic -pep_interval -.506,-.3 -pep_type stoar -st_type sinvert -st_pc_type cholesky -pep_stoar_nev 11 -terse
    170:       requires: !single

    172:    test:
    173:       suffix: 6
    174:       args: -n 24 -pep_ncv 18 -pep_target -.5 -terse -pep_type jd -pep_jd_restart .6 -pep_jd_fix .001
    175:       requires: !single

    177: TEST*/