Actual source code: ex16.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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;

     29:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

     37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     38:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     39:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

     85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     86:                 Create the eigensolver and set various options
     87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    101:   /*
    102:      Set solver parameters at runtime
    103:   */
    104:   PEPSetFromOptions(pep);

    106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107:                       Solve the eigensystem
    108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    110:   PEPSolve(pep);

    112:   /*
    113:      Optional: Get some information from the solver and display it
    114:   */
    115:   PEPGetDimensions(pep,&nev,NULL,NULL);
    116:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

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

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

    165: /*TEST

    167:    testset:
    168:       args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
    169:       requires: !complex
    170:       output_file: output/ex16_1.out
    171:       test:
    172:          suffix: 1
    173:          args: -pep_type {{toar qarnoldi}}
    174:       test:
    175:          suffix: 1_linear
    176:          args: -pep_type linear -pep_linear_explicitmatrix
    177:       test:
    178:          suffix: 1_linear_symm
    179:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite
    180:          requires: !single
    181:       test:
    182:          suffix: 1_stoar
    183:          args: -pep_type stoar
    184:          requires: !single

    186: TEST*/