Date: 2022-08-09T09:05:50+00:00

Actual source code: test2.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: */
     10: /*
     11:    Example based on spring problem in NLEVP collection [1]. See the parameters
     12:    meaning at Example 2 in [2].

     14:    [1] T. Betcke, N. J. Higham, V. Mehrmann, C. Schroder, and F. Tisseur,
     15:        NLEVP: A Collection of Nonlinear Eigenvalue Problems, MIMS EPrint
     16:        2010.98, November 2010.
     17:    [2] F. Tisseur, Backward error and condition of polynomial eigenvalue
     18:        problems, Linear Algebra and its Applications, 309 (2000), pp. 339--361,
     19:        April 2000.
     20: */

     22: static char help[] = "Test the solution of a PEP from a finite element model of "
     23:   "damped mass-spring system (problem from NLEVP collection).\n\n"
     24:   "The command line options are:\n"
     25:   "  -n <n> ... number of grid subdivisions.\n"
     26:   "  -mu <value> ... mass (default 1).\n"
     27:   "  -tau <value> ... damping constant of the dampers (default 10).\n"
     28:   "  -kappa <value> ... damping constant of the springs (default 5).\n"
     29:   "  -initv ... set an initial vector.\n\n";

     31: #include <slepcpep.h>

     33: /*
     34:    Check if computed eigenvectors have unit norm
     35: */
     36: PetscErrorCode CheckNormalizedVectors(PEP pep)
     37: {
     38:   PetscInt       i,nconv;
     39:   Mat            A;
     40:   Vec            xr,xi;
     41:   PetscReal      error=0.0,normr;
     42: #if !defined(PETSC_USE_COMPLEX)
     43:   PetscReal      normi;
     44: #endif

     47:   PEPGetConverged(pep,&nconv);
     48:   if (nconv>0) {
     49:     PEPGetOperators(pep,0,&A);
     50:     MatCreateVecs(A,&xr,&xi);
     51:     for (i=0;i<nconv;i++) {
     52:       PEPGetEigenpair(pep,i,NULL,NULL,xr,xi);
     53: #if defined(PETSC_USE_COMPLEX)
     54:       VecNorm(xr,NORM_2,&normr);
     55:       error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
     56: #else
     57:       VecNormBegin(xr,NORM_2,&normr);
     58:       VecNormBegin(xi,NORM_2,&normi);
     59:       VecNormEnd(xr,NORM_2,&normr);
     60:       VecNormEnd(xi,NORM_2,&normi);
     61:       error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
     62: #endif
     63:     }
     64:     VecDestroy(&xr);
     65:     VecDestroy(&xi);
     66:     if (error>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
     67:   }
     68:   PetscFunctionReturn(0);
     69: }

     71: int main(int argc,char **argv)
     72: {
     73:   Mat            M,C,K,A[3];      /* problem matrices */
     74:   PEP            pep;             /* polynomial eigenproblem solver context */
     75:   PetscInt       n=30,Istart,Iend,i,nev;
     76:   PetscReal      mu=1.0,tau=10.0,kappa=5.0;
     77:   PetscBool      initv=PETSC_FALSE,skipnorm=PETSC_FALSE;
     78:   Vec            IV[2];

     80:   SlepcInitialize(&argc,&argv,(char*)0,help);

     82:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     83:   PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL);
     84:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     85:   PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL);
     86:   PetscOptionsGetBool(NULL,NULL,"-initv",&initv,NULL);
     87:   PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);

     89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     90:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     93:   /* K is a tridiagonal */
     94:   MatCreate(PETSC_COMM_WORLD,&K);
     95:   MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);
     96:   MatSetFromOptions(K);
     97:   MatSetUp(K);

     99:   MatGetOwnershipRange(K,&Istart,&Iend);
    100:   for (i=Istart;i<Iend;i++) {
    101:     if (i>0) MatSetValue(K,i,i-1,-kappa,INSERT_VALUES);
    102:     MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES);
    103:     if (i<n-1) MatSetValue(K,i,i+1,-kappa,INSERT_VALUES);
    104:   }

    106:   MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
    107:   MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);

    109:   /* C is a tridiagonal */
    110:   MatCreate(PETSC_COMM_WORLD,&C);
    111:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);
    112:   MatSetFromOptions(C);
    113:   MatSetUp(C);

    115:   MatGetOwnershipRange(C,&Istart,&Iend);
    116:   for (i=Istart;i<Iend;i++) {
    117:     if (i>0) MatSetValue(C,i,i-1,-tau,INSERT_VALUES);
    118:     MatSetValue(C,i,i,tau*3.0,INSERT_VALUES);
    119:     if (i<n-1) MatSetValue(C,i,i+1,-tau,INSERT_VALUES);
    120:   }

    122:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    123:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    125:   /* M is a diagonal matrix */
    126:   MatCreate(PETSC_COMM_WORLD,&M);
    127:   MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n);
    128:   MatSetFromOptions(M);
    129:   MatSetUp(M);
    130:   MatGetOwnershipRange(M,&Istart,&Iend);
    131:   for (i=Istart;i<Iend;i++) MatSetValue(M,i,i,mu,INSERT_VALUES);
    132:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
    133:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

    135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136:                 Create the eigensolver and set various options
    137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    139:   PEPCreate(PETSC_COMM_WORLD,&pep);
    140:   A[0] = K; A[1] = C; A[2] = M;
    141:   PEPSetOperators(pep,3,A);
    142:   PEPSetProblemType(pep,PEP_GENERAL);
    143:   PEPSetTolerances(pep,PETSC_SMALL,PETSC_DEFAULT);
    144:   if (initv) { /* initial vector */
    145:     MatCreateVecs(K,&IV[0],NULL);
    146:     VecSetValue(IV[0],0,-1.0,INSERT_VALUES);
    147:     VecSetValue(IV[0],1,0.5,INSERT_VALUES);
    148:     VecAssemblyBegin(IV[0]);
    149:     VecAssemblyEnd(IV[0]);
    150:     MatCreateVecs(K,&IV[1],NULL);
    151:     VecSetValue(IV[1],0,4.0,INSERT_VALUES);
    152:     VecSetValue(IV[1],2,1.5,INSERT_VALUES);
    153:     VecAssemblyBegin(IV[1]);
    154:     VecAssemblyEnd(IV[1]);
    155:     PEPSetInitialSpace(pep,2,IV);
    156:     VecDestroy(&IV[0]);
    157:     VecDestroy(&IV[1]);
    158:   }
    159:   PEPSetFromOptions(pep);

    161:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    162:                       Solve the eigensystem
    163:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    165:   PEPSolve(pep);
    166:   PEPGetDimensions(pep,&nev,NULL,NULL);
    167:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:                     Display solution and clean up
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    173:   PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    174:   if (!skipnorm) CheckNormalizedVectors(pep);
    175:   PEPDestroy(&pep);
    176:   MatDestroy(&M);
    177:   MatDestroy(&C);
    178:   MatDestroy(&K);
    179:   SlepcFinalize();
    180:   return 0;
    181: }

    183: /*TEST

    185:    testset:
    186:       args: -pep_nev 4 -initv
    187:       requires: !single
    188:       output_file: output/test2_1.out
    189:       test:
    190:          suffix: 1
    191:          args: -pep_type {{toar linear}}
    192:       test:
    193:          suffix: 1_toar_mgs
    194:          args: -pep_type toar -bv_orthog_type mgs
    195:       test:
    196:          suffix: 1_qarnoldi
    197:          args: -pep_type qarnoldi -bv_orthog_refine never
    198:       test:
    199:          suffix: 1_linear_gd
    200:          args: -pep_type linear -pep_linear_eps_type gd -pep_linear_explicitmatrix

    202:    testset:
    203:       args: -pep_target -0.43 -pep_nev 4 -pep_ncv 20 -st_type sinvert
    204:       output_file: output/test2_2.out
    205:       test:
    206:          suffix: 2
    207:          args: -pep_type {{toar linear}}
    208:       test:
    209:          suffix: 2_toar_scaleboth
    210:          args: -pep_type toar -pep_scale both
    211:       test:
    212:          suffix: 2_toar_transform
    213:          args: -pep_type toar -st_transform
    214:       test:
    215:          suffix: 2_qarnoldi
    216:          args: -pep_type qarnoldi -bv_orthog_refine always
    217:       test:
    218:          suffix: 2_linear_explicit
    219:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_linearization 0,1
    220:       test:
    221:          suffix: 2_linear_explicit_her
    222:          args: -pep_type linear -pep_linear_explicitmatrix -pep_hermitian -pep_linear_linearization 0,1
    223:       test:
    224:          suffix: 2_stoar
    225:          args: -pep_type stoar -pep_hermitian
    226:       test:
    227:          suffix: 2_jd
    228:          args: -pep_type jd -st_type precond -pep_max_it 200 -pep_ncv 24
    229:          requires: !single

    231:    test:
    232:       suffix: 3
    233:       args: -pep_nev 12 -pep_extract {{none norm residual structured}} -pep_monitor_cancel
    234:       requires: !single

    236:    testset:
    237:       args: -st_type sinvert -pep_target -0.43 -pep_nev 4
    238:       output_file: output/test2_2.out
    239:       test:
    240:          suffix: 4_schur
    241:          args: -pep_refine simple -pep_refine_scheme schur
    242:       test:
    243:          suffix: 4_mbe
    244:          args: -pep_refine simple -pep_refine_scheme mbe -pep_refine_ksp_type preonly -pep_refine_pc_type lu
    245:       test:
    246:          suffix: 4_explicit
    247:          args: -pep_refine simple -pep_refine_scheme explicit
    248:       test:
    249:          suffix: 4_multiple_schur
    250:          args: -pep_refine multiple -pep_refine_scheme schur
    251:          requires: !single
    252:       test:
    253:          suffix: 4_multiple_mbe
    254:          args: -pep_refine multiple -pep_refine_scheme mbe -pep_refine_ksp_type preonly -pep_refine_pc_type lu -pep_refine_pc_factor_shift_type nonzero
    255:       test:
    256:          suffix: 4_multiple_explicit
    257:          args: -pep_refine multiple -pep_refine_scheme explicit
    258:          requires: !single

    260:    test:
    261:       suffix: 5
    262:       nsize: 2
    263:       args: -pep_type linear -pep_linear_explicitmatrix -pep_general -pep_target -0.43 -pep_nev 4 -pep_ncv 20 -st_type sinvert -pep_linear_st_ksp_type bcgs -pep_linear_st_pc_type bjacobi
    264:       output_file: output/test2_2.out

    266:    test:
    267:       suffix: 6
    268:       args: -pep_type linear -pep_nev 12 -pep_extract {{none norm residual}}
    269:       requires: !single
    270:       output_file: output/test2_3.out

    272:    test:
    273:       suffix: 7
    274:       args: -pep_nev 12 -pep_extract {{none norm residual structured}} -pep_refine multiple
    275:       requires: !single
    276:       output_file: output/test2_3.out

    278:    testset:
    279:       args: -st_type sinvert -pep_target -0.43 -pep_nev 4 -st_transform
    280:       output_file: output/test2_2.out
    281:       test:
    282:          suffix: 8_schur
    283:          args: -pep_refine simple -pep_refine_scheme schur
    284:       test:
    285:          suffix: 8_mbe
    286:          args: -pep_refine simple -pep_refine_scheme mbe -pep_refine_ksp_type preonly -pep_refine_pc_type lu
    287:       test:
    288:          suffix: 8_explicit
    289:          args: -pep_refine simple -pep_refine_scheme explicit
    290:       test:
    291:          suffix: 8_multiple_schur
    292:          args: -pep_refine multiple -pep_refine_scheme schur
    293:       test:
    294:          suffix: 8_multiple_mbe
    295:          args: -pep_refine multiple -pep_refine_scheme mbe -pep_refine_ksp_type preonly -pep_refine_pc_type lu
    296:       test:
    297:          suffix: 8_multiple_explicit
    298:          args: -pep_refine multiple -pep_refine_scheme explicit

    300:    testset:
    301:       nsize: 2
    302:       args: -st_type sinvert -pep_target -0.49 -pep_nev 4 -pep_refine_partitions 2 -st_ksp_type bcgs -st_pc_type bjacobi -pep_scale diagonal -pep_scale_its 4
    303:       output_file: output/test2_2.out
    304:       test:
    305:          suffix: 9_mbe
    306:          args: -pep_refine simple -pep_refine_scheme mbe -pep_refine_ksp_type preonly -pep_refine_pc_type lu
    307:       test:
    308:          suffix: 9_explicit
    309:          args: -pep_refine simple -pep_refine_scheme explicit
    310:       test:
    311:          suffix: 9_multiple_mbe
    312:          args: -pep_refine multiple -pep_refine_scheme mbe -pep_refine_ksp_type preonly -pep_refine_pc_type lu
    313:          requires: !single
    314:       test:
    315:          suffix: 9_multiple_explicit
    316:          args: -pep_refine multiple -pep_refine_scheme explicit
    317:          requires: !single

    319:    test:
    320:       suffix: 10
    321:       nsize: 4
    322:       args: -st_type sinvert -pep_target -0.43 -pep_nev 4 -pep_refine simple -pep_refine_scheme explicit -pep_refine_partitions 2 -st_ksp_type bcgs -st_pc_type bjacobi -pep_scale diagonal -pep_scale_its 4
    323:       output_file: output/test2_2.out

    325:    testset:
    326:       args: -pep_nev 4 -initv -mat_type aijcusparse
    327:       output_file: output/test2_1.out
    328:       requires: cuda !single
    329:       test:
    330:          suffix: 11_cuda
    331:          args: -pep_type {{toar linear}}
    332:       test:
    333:          suffix: 11_cuda_qarnoldi
    334:          args: -pep_type qarnoldi -bv_orthog_refine never
    335:       test:
    336:          suffix: 11_cuda_linear_gd
    337:          args: -pep_type linear -pep_linear_eps_type gd -pep_linear_explicitmatrix

    339:    test:
    340:       suffix: 12
    341:       nsize: 2
    342:       args: -pep_type jd -ds_parallel synchronized -pep_target -0.43 -pep_nev 4 -pep_ncv 20
    343:       requires: !single

    345:    test:
    346:       suffix: 13
    347:       args: -pep_nev 12 -pep_view_values draw -pep_monitor draw::draw_lg
    348:       requires: x !single
    349:       output_file: output/test2_3.out

    351:    test:
    352:       suffix: 14
    353:       requires: complex double
    354:       args: -pep_type ciss -rg_type ellipse -rg_ellipse_center -48.5 -rg_ellipse_radius 1.5 -pep_ciss_delta 1e-10

    356: TEST*/