Date: 2021-02-01T14:42:00+00:00

Actual source code: test9.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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. "
     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: {
     31:   PetscInt       i,nconv;
     32:   Mat            A;
     33:   Vec            xr,xi;
     34:   PetscReal      error=0.0,normr;
     35: #if !defined(PETSC_USE_COMPLEX)
     36:   PetscReal      normi;
     37: #endif

     40:   EPSGetConverged(eps,&nconv);
     41:   if (nconv>0) {
     42:     EPSGetOperators(eps,&A,NULL);
     43:     MatCreateVecs(A,&xr,&xi);
     44:     for (i=0;i<nconv;i++) {
     45:       EPSGetEigenvector(eps,i,xr,xi);
     46: #if defined(PETSC_USE_COMPLEX)
     47:       VecNorm(xr,NORM_2,&normr);
     48:       error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
     49: #else
     50:       VecNormBegin(xr,NORM_2,&normr);
     51:       VecNormBegin(xi,NORM_2,&normi);
     52:       VecNormEnd(xr,NORM_2,&normr);
     53:       VecNormEnd(xi,NORM_2,&normi);
     54:       error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
     55: #endif
     56:     }
     57:     VecDestroy(&xr);
     58:     VecDestroy(&xi);
     59:     if (error>100*PETSC_MACHINE_EPSILON) {
     60:       PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
     61:     }
     62:   }
     63:   return(0);
     64: }

     66: int main(int argc,char **argv)
     67: {
     68:   Vec            v0;              /* initial vector */
     69:   Mat            A;               /* operator matrix */
     70:   EPS            eps;             /* eigenproblem solver context */
     71:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
     72:   PetscInt       N,m=15,nev;
     73:   PetscScalar    origin=0.0;
     74:   PetscBool      flg,delay,skipnorm=PETSC_FALSE;

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

     79:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     80:   N = m*(m+1)/2;
     81:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n\n",N,m);
     82:   PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:      Compute the operator matrix that defines the eigensystem, Ax=kx
     86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     88:   MatCreate(PETSC_COMM_WORLD,&A);
     89:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     90:   MatSetFromOptions(A);
     91:   MatSetUp(A);
     92:   MatMarkovModel(m,A);

     94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     95:                 Create the eigensolver and set various options
     96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     98:   /*
     99:      Create eigensolver context
    100:   */
    101:   EPSCreate(PETSC_COMM_WORLD,&eps);

    103:   /*
    104:      Set operators. In this case, it is a standard eigenvalue problem
    105:   */
    106:   EPSSetOperators(eps,A,NULL);
    107:   EPSSetProblemType(eps,EPS_NHEP);
    108:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

    110:   /*
    111:      Set the custom comparing routine in order to obtain the eigenvalues
    112:      closest to the target on the right only
    113:   */
    114:   EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);

    117:   /*
    118:      Set solver parameters at runtime
    119:   */
    120:   EPSSetFromOptions(eps);
    121:   PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg);
    122:   if (flg) {
    123:     EPSArnoldiGetDelayed(eps,&delay);
    124:     if (delay) {
    125:       PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n");
    126:     }
    127:   }

    129:   /*
    130:      Set the initial vector. This is optional, if not done the initial
    131:      vector is set to random values
    132:   */
    133:   MatCreateVecs(A,&v0,NULL);
    134:   VecSetValue(v0,0,-1.5,INSERT_VALUES);
    135:   VecSetValue(v0,1,2.1,INSERT_VALUES);
    136:   VecAssemblyBegin(v0);
    137:   VecAssemblyEnd(v0);
    138:   EPSSetInitialSpace(eps,1,&v0);

    140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:                       Solve the eigensystem
    142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    144:   EPSSolve(eps);
    145:   EPSGetDimensions(eps,&nev,NULL,NULL);
    146:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    149:                     Display solution and clean up
    150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    152:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    153:   if (!skipnorm) { CheckNormalizedVectors(eps); }
    154:   EPSDestroy(&eps);
    155:   MatDestroy(&A);
    156:   VecDestroy(&v0);
    157:   SlepcFinalize();
    158:   return ierr;
    159: }

    161: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    162: {
    163:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    164:   PetscReal       pd,pu;
    165:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    166:   PetscErrorCode  ierr;

    169:   MatGetOwnershipRange(A,&Istart,&Iend);
    170:   for (i=1;i<=m;i++) {
    171:     jmax = m-i+1;
    172:     for (j=1;j<=jmax;j++) {
    173:       ix = ix + 1;
    174:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    175:       if (j!=jmax) {
    176:         pd = cst*(PetscReal)(i+j-1);
    177:         /* north */
    178:         if (i==1) {
    179:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    180:         } else {
    181:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    182:         }
    183:         /* east */
    184:         if (j==1) {
    185:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    186:         } else {
    187:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    188:         }
    189:       }
    190:       /* south */
    191:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    192:       if (j>1) {
    193:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    194:       }
    195:       /* west */
    196:       if (i>1) {
    197:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    198:       }
    199:     }
    200:   }
    201:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    202:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    203:   return(0);
    204: }

    206: /*
    207:     Function for user-defined eigenvalue ordering criterion.

    209:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    210:     one of them as the preferred one according to the criterion.
    211:     In this example, the preferred value is the one furthest away from the origin.
    212: */
    213: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    214: {
    215:   PetscScalar origin = *(PetscScalar*)ctx;
    216:   PetscReal   d;

    219:   d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
    220:   *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
    221:   return(0);
    222: }

    224: /*TEST

    226:    testset:
    227:       args: -eps_nev 4
    228:       requires: !single
    229:       output_file: output/test9_1.out
    230:       test:
    231:          suffix: 1
    232:          args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 7 -eps_max_it 300
    233:       test:
    234:          suffix: 1_gd
    235:          args: -eps_type gd -st_pc_type none
    236:       test:
    237:          suffix: 1_gd2
    238:          args: -eps_type gd -eps_gd_double_expansion -st_pc_type none

    240:    test:
    241:       suffix: 2
    242:       args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_ncv 7 -eps_max_it 1500
    243:       requires: double
    244:       output_file: output/test9_1.out

    246:    test:
    247:       suffix: 3
    248:       nsize: 2
    249:       args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm
    250:       requires: !single
    251:       output_file: output/test9_3.out

    253:    test:
    254:       suffix: 4
    255:       args: -eps_nev 4 -eps_true_residual
    256:       output_file: output/test9_1.out

    258:    test:
    259:       suffix: 5
    260:       args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2
    261:       requires: !single

    263:    test:
    264:       suffix: 5_arpack
    265:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10
    266:       requires: arpack
    267:       output_file: output/test9_5.out

    269:    testset:
    270:       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
    271:       requires: double
    272:       output_file: output/test9_6.out
    273:       test:
    274:          suffix: 6
    275:       test:
    276:          suffix: 6_hankel
    277:          args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 64
    278:       test:
    279:          suffix: 6_cheby
    280:          args: -eps_ciss_quadrule chebyshev
    281:       test:
    282:          suffix: 6_hankel_cheby
    283:          args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 64
    284:       test:
    285:          suffix: 6_refine
    286:          args: -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 1
    287:       test:
    288:          suffix: 6_bcgs
    289:          args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type sor -eps_ciss_integration_points 12

    291:    test:
    292:       suffix: 7
    293:       args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values
    294:       requires: !single
    295:       filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"

    297:    test:
    298:       suffix: 8
    299:       args: -eps_nev 4 -eps_view_values draw -eps_monitor_lg
    300:       requires: x
    301:       output_file: output/test9_1.out

    303:    test:
    304:       suffix: 5_ksphpddm
    305:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10
    306:       requires: hpddm
    307:       output_file: output/test9_5.out

    309:    test:
    310:       suffix: 5_pchpddm
    311:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10
    312:       requires: hpddm
    313:       output_file: output/test9_5.out

    315: TEST*/