I quickly created a WIEN2k 17.1 test case (as shown below) and believe I have reproduced the issue.

The 7_SrPtAs.bands.agr that was generated shows 6 lines between the M and K labels with data toler /1.d-07/.  The 5_SrPtAs.bands.agr that was generated using data toler /1.d-05/ does not have those lines.  [ https://github.com/gsabo/WIEN2k-Patches/blob/master/17.1/SrPtAs_bandstructure_vlines.pdf ]

However, the agr files are missing the SIGMA label specified in SRC_templates/hcp.klist and no vertical line appears at SIGMA.  The SIGMA label does seem to appear okay in the PostScript (ps) file created by "plot bandstructure" in w2web.

It may be that the vertical lines are because I just used an improper k-path for this structure, didn't include other special point labels, or perhaps, the algorithm used by the code to generate the vertical lines is limited or not yet designed to properly handle hexagonal lattice.  So I feel the issue might not be due to the data toler /1.d-07/, but something to do with eps1, eps2, and eps3 formulas used on lines 67-69 in bz_lin.f.

Currently, another way I can think of to remove the vertical lines as a workaround, would be to plot the bandstructure (using a less automated method; plotting more by hand) in another program, such as Origin [ https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg15255.html ], using case.spaghetti_ene or use the Grace GUI (xmgrace) to edit by hand the agr file by selecting Plot->Axis properties followed by editing the "Tick location - Label" fields under the Special tab.

username@computername:~/wiendata/SrPtAs$ ls SrPtAs.struct
SrPtAs.struct
username@computername:~/wiendata/SrPtAs$ init_lapw -b
...
  init_lapw finished ok
username@computername:~/wiendata/SrPtAs$ run_lapw
...
in cycle 9    ETEST: .0001754200000000   CTEST: .008216
hup: Command not found.
 LAPW0 END
 LAPW1 END
 LAPW2 END
 CORE  END
 MIXER END
ec cc and fc_conv 1 1 1

>   stop
username@computername:~/wiendata/SrPtAs$ cp $WIENROOT/SRC_templates/hcp.klist SrPtAs.klist_band
username@computername:~/wiendata/SrPtAs$ x lapw1 -band
 LAPW1 END
114.3u 2.9s 1:57.54 99.7% 0+0k 0+79704io 0pf+0w
username@computername:~/wiendata/SrPtAs$ x lapw2 -band -qtl
 LAPW2 END
16.5u 0.4s 0:17.00 99.7% 0+0k 8+51528io 1pf+0w
username@computername:~/wiendata/SrPtAs$ grepline_lapw :FER *.scf 1
in  1 files:
SrPtAs.scf::FER  : F E R M I - ENERGY(TETRAH.M.)=   0.5715462774
username@computername:~/wiendata/SrPtAs$ sed -n 9p SrPtAs.insp
1      0.xxxx                      # Fermi switch,  Fermi-level (in Ry units)
username@computername:~/wiendata/SrPtAs$ gedit SrPtAs.insp
username@computername:~/wiendata/SrPtAs$ sed -n 9p SrPtAs.insp
1      0.5715462774                      # Fermi switch, Fermi-level (in Ry units)
username@computername:~/wiendata/SrPtAs$ x spaghetti
 SPAGH: Read band energy from case.output1
 number of k-points read in case.vector=          61
SPAGH END
0.1u 0.0s 0:00.22 86.3% 0+0k 8+2000io 0pf+0w
username@computername:~/wiendata/SrPtAs$ cp SrPtAs.bands.agr 7_SrPtAs.bands.agr
username@computername:~/wiendata/SrPtAs$ xmgrace 7_SrPtAs.bands.agr

*Change data toler  /1.d-07/ to /1.d-05/*

username@computername:~/WIEN2k/SRC_spaghetti$ wget https://raw.githubusercontent.com/gsabo/WIEN2k-Patches/master/17.1/bz_lin.patch
...
username@computername:~/WIEN2k/SRC_spaghetti$ patch -b bz_lin.f bz_lin.patch
patching file bz_lin.f
username@computername:~/WIEN2k/SRC_spaghetti$ make
username@computername:~/WIEN2k/SRC_spaghetti$ cp spaghetti ..
username@computername:~/WIEN2k/SRC_spaghetti$ cd ~/wiendata/SrPtAs/
username@computername:~/wiendata/SrPtAs$ x spaghetti
 SPAGH: Read band energy from case.output1
 number of k-points read in case.vector=          61
SPAGH END
0.1u 0.0s 0:00.19 100.0% 0+0k 0+2000io 0pf+0w
username@computername:~/wiendata/SrPtAs$ cp SrPtAs.bands.agr 5_SrPtAs.bands.agr username@computername:~/wiendata/SrPtAs$ xmgrace 5_SrPtAs.bands.agr

*Restore data toler back to /1.d-07/*

username@computername:~/WIEN2k/SRC_spaghetti$ mv bz_lin.f.orig bz_lin.f
username@computername:~/WIEN2k/SRC_spaghetti$ make clean
...
username@computername:~/WIEN2k/SRC_spaghetti$ make
...
username@computername:~/WIEN2k/SRC_spaghetti$ cp spaghetti ..
SrPtAs                                                                         
H   LATTICE,NONEQUIV.ATOMS:  3 194_P63/mmc                                     
MODE OF CALC=RELA unit=ang                                                     
  8.121290  8.121290 17.174594 90.000000 90.000000120.000000                   
ATOM  -1: X=0.00000000 Y=0.00000000 Z=0.00000000
          MULT= 2          ISPLIT= 4
      -1: X=0.00000000 Y=0.00000000 Z=0.50000000
Sr         NPT=  781  R0=0.00001000 RMT=    2.0000   Z: 38.000                 
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -2: X=0.33333333 Y=0.66666667 Z=0.25000000
          MULT= 2          ISPLIT= 4
      -2: X=0.66666667 Y=0.33333333 Z=0.75000000
Pt         NPT=  781  R0=0.00000500 RMT=    2.0000   Z: 78.000                 
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -3: X=0.66666667 Y=0.33333333 Z=0.25000000
          MULT= 2          ISPLIT= 4
      -3: X=0.33333333 Y=0.66666667 Z=0.75000000
As         NPT=  781  R0=0.00005000 RMT=    2.0000   Z: 33.000                 
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
  24      NUMBER OF SYMMETRY OPERATIONS
-1 0 0 0.00000000
-1 1 0 0.00000000
 0 0-1 0.00000000
       1
-1 1 0 0.00000000
-1 0 0 0.00000000
 0 0 1 0.00000000
       2
-1 0 0 0.00000000
 0-1 0 0.00000000
 0 0-1 0.00000000
       3
-1 1 0 0.00000000
 0 1 0 0.00000000
 0 0 1 0.00000000
       4
 0-1 0 0.00000000
-1 0 0 0.00000000
 0 0 1 0.00000000
       5
 0 1 0 0.00000000
-1 1 0 0.00000000
 0 0-1 0.00000000
       6
 0-1 0 0.00000000
 1-1 0 0.00000000
 0 0 1 0.00000000
       7
 0 1 0 0.00000000
 1 0 0 0.00000000
 0 0-1 0.00000000
       8
 1-1 0 0.00000000
 0-1 0 0.00000000
 0 0-1 0.00000000
       9
 1 0 0 0.00000000
 0 1 0 0.00000000
 0 0 1 0.00000000
      10
 1-1 0 0.00000000
 1 0 0 0.00000000
 0 0-1 0.00000000
      11
 1 0 0 0.00000000
 1-1 0 0.00000000
 0 0 1 0.00000000
      12
 0 1 0 0.00000000
-1 1 0 0.00000000
 0 0 1 0.50000000
      13
 0-1 0 0.00000000
 1-1 0 0.00000000
 0 0-1 0.50000000
      14
-1 1 0 0.00000000
 0 1 0 0.00000000
 0 0-1 0.50000000
      15
-1 0 0 0.00000000
-1 1 0 0.00000000
 0 0 1 0.50000000
      16
 0 1 0 0.00000000
 1 0 0 0.00000000
 0 0 1 0.50000000
      17
 0-1 0 0.00000000
-1 0 0 0.00000000
 0 0-1 0.50000000
      18
 1-1 0 0.00000000
 0-1 0 0.00000000
 0 0 1 0.50000000
      19
 1 0 0 0.00000000
 0 1 0 0.00000000
 0 0-1 0.50000000
      20
-1 1 0 0.00000000
-1 0 0 0.00000000
 0 0-1 0.50000000
      21
-1 0 0 0.00000000
 0-1 0 0.00000000
 0 0 1 0.50000000
      22
 1-1 0 0.00000000
 1 0 0 0.00000000
 0 0 1 0.50000000
      23
 1 0 0 0.00000000
 1-1 0 0.00000000
 0 0-1 0.50000000
      24
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