Date: 2022-08-09T09:05:51+00:00

Actual source code: ex16.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 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:   SlepcInitialize(&argc,&argv,(char*)0,help);

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

     38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     39:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:                 Create the eigensolver and set various options
     86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     88:   /*
     89:      Create eigensolver context
     90:   */
     91:   PEPCreate(PETSC_COMM_WORLD,&pep);

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

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

    109:   /*
    110:      Set solver parameters at runtime
    111:   */
    112:   PEPSetFromOptions(pep);

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:                       Solve the eigensystem
    116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    118:   PEPSolve(pep);

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

    126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    127:                     Display solution and clean up
    128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    130:   /* show detailed info unless -terse option is given by user */
    131:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    132:   if (terse) PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    133:   else {
    134:     PEPGetConverged(pep,&nconv);
    135:     if (nconv>0) {
    136:       MatCreateVecs(M,&xr,&xi);
    137:       /* display eigenvalues and relative errors */
    138:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,
    139:            "\n           k          ||P(k)x||/||kx||\n"
    140:            "   ----------------- ------------------\n"));
    141:       for (i=0;i<nconv;i++) {
    142:         /* get converged eigenpairs */
    143:         PEPGetEigenpair(pep,i,&kr,&ki,xr,xi);
    144:         /* compute the relative error associated to each eigenpair */
    145:         PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error);
    146: #if defined(PETSC_USE_COMPLEX)
    147:         re = PetscRealPart(kr);
    148:         im = PetscImaginaryPart(kr);
    149: #else
    150:         re = kr;
    151:         im = ki;
    152: #endif
    153:         if (im!=0.0) PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi   %12g\n",(double)re,(double)im,(double)error);
    154:         else PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);
    155:       }
    156:       PetscPrintf(PETSC_COMM_WORLD,"\n");
    157:       VecDestroy(&xr);
    158:       VecDestroy(&xi);
    159:     }
    160:   }
    161:   PEPDestroy(&pep);
    162:   MatDestroy(&M);
    163:   MatDestroy(&C);
    164:   MatDestroy(&K);
    165:   SlepcFinalize();
    166:   return 0;
    167: }

    169: /*TEST

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

    194: TEST*/