Date: 2026-03-31T13:23:03+00:00

Actual source code: ex16.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: */

     11: static char help[] = "Simple quadratic eigenvalue problem.\n\n"
     12:   "The command line options are:\n"
     13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
     14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

     16: #include <slepcpep.h>

     18: int main(int argc,char **argv)
     19: {
     20:   Mat            M,C,K,A[3];      /* problem matrices */
     21:   PEP            pep;             /* polynomial eigenproblem solver context */
     22:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nconv;
     23:   PetscBool      flag,terse;
     24:   PetscReal      error,re,im;
     25:   PetscScalar    kr,ki;
     26:   Vec            xr,xi;
     27:   BV             V;
     28:   PetscRandom    rand;

     30:   PetscFunctionBeginUser;
     31:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     34:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
     35:   if (!flag) m=n;
     36:   N = n*m;
     37:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

     39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     40:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     43:   /* K is the 2-D Laplacian */
     44:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
     45:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N));
     46:   PetscCall(MatSetFromOptions(K));
     47:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     48:   for (II=Istart;II<Iend;II++) {
     49:     i = II/n; j = II-i*n;
     50:     if (i>0) PetscCall(MatSetValue(K,II,II-n,-1.0,INSERT_VALUES));
     51:     if (i<m-1) PetscCall(MatSetValue(K,II,II+n,-1.0,INSERT_VALUES));
     52:     if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
     53:     if (j<n-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
     54:     PetscCall(MatSetValue(K,II,II,4.0,INSERT_VALUES));
     55:   }
     56:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
     57:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

     59:   /* C is the 1-D Laplacian on horizontal lines */
     60:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
     61:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N));
     62:   PetscCall(MatSetFromOptions(C));
     63:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
     64:   for (II=Istart;II<Iend;II++) {
     65:     i = II/n; j = II-i*n;
     66:     if (j>0) PetscCall(MatSetValue(C,II,II-1,-1.0,INSERT_VALUES));
     67:     if (j<n-1) PetscCall(MatSetValue(C,II,II+1,-1.0,INSERT_VALUES));
     68:     PetscCall(MatSetValue(C,II,II,2.0,INSERT_VALUES));
     69:   }
     70:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
     71:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

     73:   /* M is a diagonal matrix */
     74:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
     75:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N));
     76:   PetscCall(MatSetFromOptions(M));
     77:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
     78:   for (II=Istart;II<Iend;II++) PetscCall(MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES));
     79:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
     80:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

     82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     83:                 Create the eigensolver and set various options
     84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     86:   /*
     87:      Create eigensolver context
     88:   */
     89:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));

     91:   /*
     92:      Set matrices and problem type
     93:   */
     94:   A[0] = K; A[1] = C; A[2] = M;
     95:   PetscCall(PEPSetOperators(pep,3,A));
     96:   PetscCall(PEPSetProblemType(pep,PEP_HERMITIAN));

     98:   /*
     99:      In complex scalars, use a real initial vector since in this example
    100:      the matrices are all real, then all vectors generated by the solver
    101:      will have a zero imaginary part. This is not really necessary.
    102:   */
    103:   PetscCall(PEPGetBV(pep,&V));
    104:   PetscCall(BVGetRandomContext(V,&rand));
    105:   PetscCall(PetscRandomSetInterval(rand,-1,1));

    107:   /*
    108:      Set solver parameters at runtime
    109:   */
    110:   PetscCall(PEPSetFromOptions(pep));

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                       Solve the eigensystem
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    116:   PetscCall(PEPSolve(pep));

    118:   /*
    119:      Optional: Get some information from the solver and display it
    120:   */
    121:   PetscCall(PEPGetDimensions(pep,&nev,NULL,NULL));
    122:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:                     Display solution and clean up
    126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    128:   /* show detailed info unless -terse option is given by user */
    129:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    130:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    131:   else {
    132:     PetscCall(PEPGetConverged(pep,&nconv));
    133:     if (nconv>0) {
    134:       PetscCall(MatCreateVecs(M,&xr,&xi));
    135:       /* display eigenvalues and relative errors */
    136:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,
    137:            "\n           k          ||P(k)x||/||kx||\n"
    138:            "   ----------------- ------------------\n"));
    139:       for (i=0;i<nconv;i++) {
    140:         /* get converged eigenpairs */
    141:         PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi));
    142:         /* compute the relative error associated to each eigenpair */
    143:         PetscCall(PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error));
    144: #if defined(PETSC_USE_COMPLEX)
    145:         re = PetscRealPart(kr);
    146:         im = PetscImaginaryPart(kr);
    147: #else
    148:         re = kr;
    149:         im = ki;
    150: #endif
    151:         if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi   %12g\n",(double)re,(double)im,(double)error));
    152:         else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error));
    153:       }
    154:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
    155:       PetscCall(VecDestroy(&xr));
    156:       PetscCall(VecDestroy(&xi));
    157:     }
    158:   }
    159:   PetscCall(PEPDestroy(&pep));
    160:   PetscCall(MatDestroy(&M));
    161:   PetscCall(MatDestroy(&C));
    162:   PetscCall(MatDestroy(&K));
    163:   PetscCall(SlepcFinalize());
    164:   return 0;
    165: }

    167: /*TEST

    169:    testset:
    170:       args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
    171:       output_file: output/ex16_1.out
    172:       test:
    173:          suffix: 1
    174:          args: -pep_type {{toar qarnoldi}}
    175:       test:
    176:          suffix: 1_linear
    177:          args: -pep_type linear -pep_linear_explicitmatrix
    178:          requires: !single
    179:       test:
    180:          suffix: 1_linear_symm
    181:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite -pep_scale scalar -pep_linear_bv_definite_tol 1e-12
    182:          requires: !single
    183:       test:
    184:          suffix: 1_stoar
    185:          args: -pep_type stoar -pep_scale scalar
    186:          requires: double
    187:       test:
    188:          suffix: 1_stoar_t
    189:          args: -pep_type stoar -pep_scale scalar -st_transform
    190:          requires: double

    192:    test:
    193:       suffix: 2
    194:       args: -pep_nev 2 -pep_smallest_magnitude -pep_ncv 48 -pep_max_it 500
    195:       filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
    196:       requires: !single

    198: TEST*/