Date: 2026-03-09T09:12:27+00:00

Actual source code: test11.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[] = "Solves the same problem as in ex5, but with a user-defined sorting criterion.\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 a custom spectrum selection.\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: */

     23: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);
     24: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     26: int main(int argc,char **argv)
     27: {
     28:   Vec            v0;              /* initial vector */
     29:   Mat            A;               /* operator matrix */
     30:   EPS            eps;             /* eigenproblem solver context */
     31:   ST             st;              /* spectral transformation associated */
     32:   PetscReal      tol=PETSC_SMALL;
     33:   PetscScalar    target=0.5;
     34:   PetscInt       N,m=15,nev;
     35:   char           str[50];

     37:   PetscFunctionBeginUser;
     38:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     40:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     41:   N = m*(m+1)/2;
     42:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m));
     43:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL));
     44:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE));
     45:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str));

     47:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     48:      Compute the operator matrix that defines the eigensystem, Ax=kx
     49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     51:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     52:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     53:   PetscCall(MatSetFromOptions(A));
     54:   PetscCall(MatMarkovModel(m,A));

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:                 Create the eigensolver and set various options
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     60:   /*
     61:      Create eigensolver context
     62:   */
     63:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

     65:   /*
     66:      Set operators. In this case, it is a standard eigenvalue problem
     67:   */
     68:   PetscCall(EPSSetOperators(eps,A,NULL));
     69:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
     70:   PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT));

     72:   /*
     73:      Set the custom comparing routine in order to obtain the eigenvalues
     74:      closest to the target on the right only
     75:   */
     76:   PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&target));

     78:   /*
     79:      Set solver parameters at runtime
     80:   */
     81:   PetscCall(EPSSetFromOptions(eps));

     83:   /*
     84:      Set the preconditioner based on A - target * I
     85:   */
     86:   PetscCall(EPSGetST(eps,&st));
     87:   PetscCall(STSetShift(st,target));

     89:   /*
     90:      Set the initial vector. This is optional, if not done the initial
     91:      vector is set to random values
     92:   */
     93:   PetscCall(MatCreateVecs(A,&v0,NULL));
     94:   PetscCall(VecSet(v0,1.0));
     95:   PetscCall(EPSSetInitialSpace(eps,1,&v0));

     97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     98:                       Solve the eigensystem
     99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    101:   PetscCall(EPSSolve(eps));
    102:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    103:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:                     Display solution and clean up
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
    110:   PetscCall(EPSDestroy(&eps));
    111:   PetscCall(MatDestroy(&A));
    112:   PetscCall(VecDestroy(&v0));
    113:   PetscCall(SlepcFinalize());
    114:   return 0;
    115: }

    117: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    118: {
    119:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    120:   PetscReal       pd,pu;
    121:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

    123:   PetscFunctionBeginUser;
    124:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
    125:   for (i=1;i<=m;i++) {
    126:     jmax = m-i+1;
    127:     for (j=1;j<=jmax;j++) {
    128:       ix = ix + 1;
    129:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    130:       if (j!=jmax) {
    131:         pd = cst*(PetscReal)(i+j-1);
    132:         /* north */
    133:         if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
    134:         else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
    135:         /* east */
    136:         if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
    137:         else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
    138:       }
    139:       /* south */
    140:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    141:       if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
    142:       /* west */
    143:       if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
    144:     }
    145:   }
    146:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    147:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    148:   PetscFunctionReturn(PETSC_SUCCESS);
    149: }

    151: /*
    152:     Function for user-defined eigenvalue ordering criterion.

    154:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    155:     one of them as the preferred one according to the criterion.
    156:     In this example, the preferred value is the one closest to the target,
    157:     but on the right side.
    158: */
    159: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    160: {
    161:   PetscScalar target = *(PetscScalar*)ctx;
    162:   PetscReal   da,db;
    163:   PetscBool   aisright,bisright;

    165:   PetscFunctionBeginUser;
    166:   if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
    167:   else aisright = PETSC_FALSE;
    168:   if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
    169:   else bisright = PETSC_FALSE;
    170:   if (aisright == bisright) {
    171:     /* both are on the same side of the target */
    172:     da = SlepcAbsEigenvalue(ar-target,ai);
    173:     db = SlepcAbsEigenvalue(br-target,bi);
    174:     if (da < db) *r = -1;
    175:     else if (da > db) *r = 1;
    176:     else *r = 0;
    177:   } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
    178:   else *r = 1;  /* 'b' is on the right */
    179:   PetscFunctionReturn(PETSC_SUCCESS);
    180: }

    182: /*TEST

    184:    testset:
    185:       args: -eps_nev 4
    186:       requires: !single
    187:       output_file: output/test11_1.out
    188:       test:
    189:          suffix: 1
    190:          args: -eps_type {{krylovschur arnoldi lapack}} -st_type sinvert
    191:       test:
    192:          suffix: 1_ks_cayley
    193:          args: -st_type cayley -st_cayley_antishift 1

    195:    test:
    196:       suffix: 2
    197:       args: -target 0.77 -eps_type gd -eps_nev 4 -eps_tol 1e-7 -eps_gd_krylov_start -eps_gd_blocksize 3
    198:       requires: double
    199:       filter: sed -e "s/[+-]0\.0*i//g"

    201: TEST*/