Actual source code: test9.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[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid.\n\n"
     12:   "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n"
     13:   "This example illustrates how the user can set the initial vector.\n\n"
     14:   "The command line options are:\n"
     15:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

     17: #include <slepceps.h>

     19: /*
     20:    User-defined routines
     21: */
     22: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
     23: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);

     25: /*
     26:    Check if computed eigenvectors have unit norm
     27: */
     28: PetscErrorCode CheckNormalizedVectors(EPS eps)
     29: {
     30:   PetscInt       i,nconv;
     31:   Mat            A;
     32:   Vec            xr,xi;
     33:   PetscReal      error=0.0,normr;
     34: #if !defined(PETSC_USE_COMPLEX)
     35:   PetscReal      normi;
     36: #endif

     38:   PetscFunctionBeginUser;
     39:   PetscCall(EPSGetConverged(eps,&nconv));
     40:   if (nconv>0) {
     41:     PetscCall(EPSGetOperators(eps,&A,NULL));
     42:     PetscCall(MatCreateVecs(A,&xr,&xi));
     43:     for (i=0;i<nconv;i++) {
     44:       PetscCall(EPSGetEigenvector(eps,i,xr,xi));
     45: #if defined(PETSC_USE_COMPLEX)
     46:       PetscCall(VecNorm(xr,NORM_2,&normr));
     47:       error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
     48: #else
     49:       PetscCall(VecNormBegin(xr,NORM_2,&normr));
     50:       PetscCall(VecNormBegin(xi,NORM_2,&normi));
     51:       PetscCall(VecNormEnd(xr,NORM_2,&normr));
     52:       PetscCall(VecNormEnd(xi,NORM_2,&normi));
     53:       error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
     54: #endif
     55:     }
     56:     PetscCall(VecDestroy(&xr));
     57:     PetscCall(VecDestroy(&xi));
     58:     if (error>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error));
     59:   }
     60:   PetscFunctionReturn(PETSC_SUCCESS);
     61: }

     63: int main(int argc,char **argv)
     64: {
     65:   Vec            v0;              /* initial vector */
     66:   Mat            A;               /* operator matrix */
     67:   EPS            eps;             /* eigenproblem solver context */
     68:   PetscReal      tol=0.5*PETSC_SMALL;
     69:   PetscInt       N,m=15,nev;
     70:   PetscScalar    origin=0.0;
     71:   PetscBool      flg,delay,skipnorm=PETSC_FALSE;

     73:   PetscFunctionBeginUser;
     74:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     76:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     77:   N = m*(m+1)/2;
     78:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));
     79:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL));

     81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     82:      Compute the operator matrix that defines the eigensystem, Ax=kx
     83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     85:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     86:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     87:   PetscCall(MatSetFromOptions(A));
     88:   PetscCall(MatMarkovModel(m,A));

     90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     91:                 Create the eigensolver and set various options
     92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     94:   /*
     95:      Create eigensolver context
     96:   */
     97:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

     99:   /*
    100:      Set operators. In this case, it is a standard eigenvalue problem
    101:   */
    102:   PetscCall(EPSSetOperators(eps,A,NULL));
    103:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
    104:   PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT));

    106:   /*
    107:      Set the custom comparing routine in order to obtain the eigenvalues
    108:      closest to the target on the right only
    109:   */
    110:   PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&origin));

    112:   /*
    113:      Set solver parameters at runtime
    114:   */
    115:   PetscCall(EPSSetFromOptions(eps));
    116:   PetscCall(PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg));
    117:   if (flg) {
    118:     PetscCall(EPSArnoldiGetDelayed(eps,&delay));
    119:     if (delay) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n"));
    120:   }

    122:   /*
    123:      Set the initial vector. This is optional, if not done the initial
    124:      vector is set to random values
    125:   */
    126:   PetscCall(MatCreateVecs(A,&v0,NULL));
    127:   PetscCall(VecSetValue(v0,0,-1.5,INSERT_VALUES));
    128:   PetscCall(VecSetValue(v0,1,2.1,INSERT_VALUES));
    129:   PetscCall(VecAssemblyBegin(v0));
    130:   PetscCall(VecAssemblyEnd(v0));
    131:   PetscCall(EPSSetInitialSpace(eps,1,&v0));

    133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    134:                       Solve the eigensystem
    135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    137:   PetscCall(EPSSolve(eps));
    138:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    139:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:                     Display solution and clean up
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    145:   PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    146:   if (!skipnorm) PetscCall(CheckNormalizedVectors(eps));
    147:   PetscCall(EPSDestroy(&eps));
    148:   PetscCall(MatDestroy(&A));
    149:   PetscCall(VecDestroy(&v0));
    150:   PetscCall(SlepcFinalize());
    151:   return 0;
    152: }

    154: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    155: {
    156:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    157:   PetscReal       pd,pu;
    158:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

    160:   PetscFunctionBeginUser;
    161:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
    162:   for (i=1;i<=m;i++) {
    163:     jmax = m-i+1;
    164:     for (j=1;j<=jmax;j++) {
    165:       ix = ix + 1;
    166:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    167:       if (j!=jmax) {
    168:         pd = cst*(PetscReal)(i+j-1);
    169:         /* north */
    170:         if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
    171:         else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
    172:         /* east */
    173:         if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
    174:         else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
    175:       }
    176:       /* south */
    177:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    178:       if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
    179:       /* west */
    180:       if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
    181:     }
    182:   }
    183:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    184:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    185:   PetscFunctionReturn(PETSC_SUCCESS);
    186: }

    188: /*
    189:     Function for user-defined eigenvalue ordering criterion.

    191:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    192:     one of them as the preferred one according to the criterion.
    193:     In this example, the preferred value is the one furthest away from the origin.
    194: */
    195: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    196: {
    197:   PetscScalar origin = *(PetscScalar*)ctx;
    198:   PetscReal   d;

    200:   PetscFunctionBeginUser;
    201:   d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
    202:   *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
    203:   PetscFunctionReturn(PETSC_SUCCESS);
    204: }

    206: /*TEST

    208:    testset:
    209:       args: -eps_nev 4
    210:       output_file: output/test9_1.out
    211:       filter: sed -e "s/97136/97137/g"
    212:       test:
    213:          suffix: 1
    214:          args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 8 -eps_max_it 300
    215:       test:
    216:          suffix: 1_gd
    217:          args: -eps_type gd -st_pc_type none
    218:       test:
    219:          suffix: 1_gd2
    220:          args: -eps_type gd -eps_gd_double_expansion -st_pc_type none

    222:    test:
    223:       suffix: 2
    224:       args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_max_it 1500
    225:       requires: double
    226:       output_file: output/test9_1.out

    228:    test:
    229:       suffix: 3
    230:       nsize: 2
    231:       args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm
    232:       requires: !single
    233:       output_file: output/test9_3.out

    235:    test:
    236:       suffix: 4
    237:       args: -eps_nev 4 -eps_true_residual
    238:       requires: !single
    239:       output_file: output/test9_1.out

    241:    test:
    242:       suffix: 5
    243:       args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2
    244:       filter: sed -e "s/[+-]0\.0*i//g"
    245:       requires: !single

    247:    test:
    248:       suffix: 5_arpack
    249:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10
    250:       requires: arpack !single
    251:       output_file: output/test9_5.out

    253:    testset:
    254:       args: -eps_type ciss -eps_tol 1e-9 -rg_type ellipse -rg_ellipse_center 0.55 -rg_ellipse_radius 0.05 -rg_ellipse_vscale 0.1 -eps_ciss_usest 0 -eps_all
    255:       requires: !single
    256:       output_file: output/test9_6.out
    257:       test:
    258:          suffix: 6
    259:       test:
    260:          suffix: 6_hankel
    261:          args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 64
    262:       test:
    263:          suffix: 6_cheby
    264:          args: -eps_ciss_quadrule chebyshev
    265:       test:
    266:          suffix: 6_hankel_cheby
    267:          args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 64
    268:       test:
    269:          suffix: 6_refine
    270:          args: -eps_ciss_moments 4 -eps_ciss_blocksize 5 -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 2
    271:       test:
    272:          suffix: 6_bcgs
    273:          args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type ilu -eps_ciss_integration_points 8

    275:    test:
    276:       suffix: 6_cheby_interval
    277:       args: -eps_type ciss -eps_tol 1e-9 -rg_type interval -rg_interval_endpoints 0.5,0.6 -eps_ciss_quadrule chebyshev -eps_ciss_usest 0 -eps_all
    278:       requires: !single
    279:       output_file: output/test9_6.out

    281:    testset:
    282:       args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values
    283:       filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"
    284:       test:
    285:          suffix: 7_real
    286:          requires: !single !complex
    287:       test:
    288:          suffix: 7
    289:          requires: !single complex

    291:    test:
    292:       suffix: 8
    293:       args: -eps_nev 4 -eps_ncv 7 -eps_view_values draw -eps_monitor draw::draw_lg
    294:       requires: x
    295:       output_file: output/test9_1.out

    297:    test:
    298:       suffix: 5_ksphpddm
    299:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10
    300:       requires: hpddm
    301:       output_file: output/test9_5.out

    303:    test:
    304:       suffix: 5_pchpddm
    305:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10
    306:       requires: hpddm
    307:       output_file: output/test9_5.out

    309: TEST*/