from __future__ import absolute_import, division, print_function
# from mmtbx.ncs.ncs_utils import convert_phil_format
import sys, os, string
from operator import itemgetter
from libtbx.utils import Sorry
from libtbx.utils import null_out
import scitbx.rigid_body
from six.moves import zip
from six.moves import range
from copy import deepcopy
 # hierarchy:  there can be any number of ncs groups.
 #   each group has a set of NCS operators and centers and may apply
 #      to a part of the structure.
 #  for group in ncs.ncs_groups(): returns list of groups
 #  id=group.chain_and_residue_id() returns id of where it applies
 #  for center in group.centers(): returns list of centers of ncs regions in group
 #  for rota_matr in group.rota_matrices(): returns rota matrices
 #  for trans_orth in group.translations_orth(): returns translation matrices

 # NOTE: symmetry operators map NCS position i on to NCS position 0 (they are
 #  inverses of the operators mapping position 0 on to i).

# Defaults for tolerances:
# Set 2017-12-23 to match values in find_ncs.py; these are very relaxed...
# previous values were tol_z=0.01, tol_r=.01,abs_tol_t=.10,rel_tol_t=0.001

default_tol_z=0.01
default_tol_r=0.02
default_abs_tol_t=2.0
default_rel_tol_t=0.05

def abs(aa):
  if aa>=0:return aa
  return -aa

def is_in_range(z,z_min,z_max):
    if z<z_min or z>z_max: return False
    return True

def remove_quotes_from_chain_id(chain_residue_id):
  # remove the quotes from the chain names in group:
  if chain_residue_id is None:
     return

  [group,list_of_resseq_list]=chain_residue_id
  new_group=[]
  for chain_id in group:
    new_group.append(remove_single_quotes(chain_id))
  return [new_group,list_of_resseq_list]

def remove_single_quotes(text):
  # Remove single quotes from ends of a string if they occur on both ends.
  if not text: return text
  if not type(text)==type("abc"): return text
  if text.startswith("'") and text.endswith("'"):
    text=text[1:-1]
  return text


def is_identity(r,t,tol=1.e-2):
  identity_r=[1,0,0,0,1,0,0,0,1]
  identity_t=[0,0,0]
  for i in range(9):
    if abs(r[i]-identity_r[i])>tol: return False
  for i in range(3):
    if abs(t[i]-identity_t[i])>tol: return False
  return True

def is_same_transform(r1,t1,r2,t2,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t):

    # require everything to be very similar
    for i in range(9):
      if abs(r1[i]-r2[i])>tol_r: return False
    for i in range(3):
      dd=abs(t1[i]-t2[i])
      dd2=0.5*(abs(t1[i])+abs(t2[i]))
      if dd>abs_tol_t and dd>rel_tol_t*dd2: # definitely does not match
        return False
    return True
def crystal_symmetry_to_ncs(crystal_symmetry=None):

  # convert r,t fractional to r_orth,t_orth  orthogonal
  #  r x + t = x'
  #   x_orth=Ax   A = orthogonalization_matrix
  #  r_orth  (Ax) + t_orth = Ax'
  #  A-1 r_orth A  x + A-1 t_orth = x'
  #  r= (A-1 r_orth A)     t=A-1 t_orth
  #  r_orth = A r A-1     t_orth = A t

  from scitbx import matrix
  a=matrix.sqr(crystal_symmetry.unit_cell().orthogonalization_matrix())
  a_inv=a.inverse()

  trans_orth=[]
  ncs_rota_matr=[]
  ncs_center_orth=[]
  center=matrix.col((0.41,0.43,0.39)) # just a point near center of cell
  center_orth=crystal_symmetry.unit_cell().orthogonalize(center)

  for rt_mx in crystal_symmetry.space_group().all_ops():
    r=matrix.sqr(rt_mx.r().as_rational().as_float())
    t=matrix.col(rt_mx.t().as_rational().as_float())

    # Try to put each center for this ncs operator inside the cell
    c=matrix.col(rt_mx * center) # Note: forward (not inverse)
    coordinate_offset=matrix.col(offset_inside_cell(c,
       unit_cell=crystal_symmetry.unit_cell(),orthogonalize=False))
    c_offset=c+coordinate_offset

    r_orth=matrix.sqr(a * r * a_inv)
    t_orth= matrix.col(a * (t + coordinate_offset))
    c_value=crystal_symmetry.unit_cell().orthogonalize(c_offset)

    r_orth_inv=r_orth.inverse()
    t_orth_inv=-r_orth_inv*t_orth

    ncs_rota_matr.append(r_orth_inv)
    trans_orth.append(t_orth_inv)
    ncs_center_orth.append(c_value)

    chain_residue_id= [
        len(r_orth)*[None],
        len(r_orth)*[[]]
        ]

  ncs_obj=ncs()
  ncs_obj.import_ncs_group(
       ncs_rota_matr=ncs_rota_matr,
       center_orth=ncs_center_orth,
       trans_orth=trans_orth,
       chain_residue_id=chain_residue_id)

  return ncs_obj

def offset_inside_zero_one(x):
    if x >=0.0:
      return -1.0*int(x)  # 2.1 gives -2 to place inside (0,1)
    else:
      return 1.0-int(x)   # -2.1 gives + 3 to place inside (0,1)

def offset_inside_cell(center,unit_cell,orthogonalize=True):
    # put the center inside (0,1)
    from scitbx.math import  matrix
    c=matrix.col(center)
    if orthogonalize:
      c_frac=unit_cell.fractionalize(c)
    else:
      c_frac=c
    offset_frac=[]
    for x in c_frac:
     offset_frac.append(offset_inside_zero_one(x))
    if orthogonalize:
      return unit_cell.orthogonalize(matrix.col(offset_frac))
    else:
      return matrix.col(offset_frac)

def get_ncs_from_text(text=None,text_is_ncs_spec=None,rotate_about_z=None,
    rotate_about_y=None,rotate_about_new_y=None,ncs_name=None,out=sys.stdout):
  from mmtbx.ncs.ncs import ncs
  import iotbx.pdb
  ncs_object=ncs()
  if text_is_ncs_spec:
    ncs_object.read_ncs(lines=text.splitlines())
  else: # read BIOMTR
    from cctbx.array_family import flex
    pdb_inp=iotbx.pdb.input(lines=flex.split_lines(text),source_info='string')
    ncs_object.ncs_from_pdb_input_BIOMT(pdb_inp=pdb_inp,log=out)

  if rotate_about_new_y:
    ncs_object.rotate_about_y(rot_deg=rotate_about_new_y,invert_matrices=True)
  if rotate_about_z:
    ncs_object.rotate_about_z(rot_deg=rotate_about_z,invert_matrices=True)
  if rotate_about_y:
    ncs_object.rotate_about_y(rot_deg=rotate_about_y,invert_matrices=True)
  if ncs_name:
    ncs_object.set_ncs_name(ncs_name)
  return ncs_object


def get_helical_symmetry(helical_rot_deg=None,
     helical_trans_z_angstrom=None,max_ops=None):

  from scitbx import matrix
  rot=get_rot_z(rot_deg=helical_rot_deg)
  rot_inv=rot.inverse()
  trans_along_z=matrix.col((0,0,helical_trans_z_angstrom))

  n=max(2,int(360/helical_rot_deg))
  if max_ops and n> max(1,max_ops//2): n= max(1,max_ops//2)
  rots=[]
  trans=[]
  rots.append(matrix.sqr((1,0,0,0,1,0,0,0,1),))
  trans.append(matrix.col((0,0,0,)))

  for i in range(n):
    rots=[rot*rots[0]]+rots[:]
    trans=[trans[0]-trans_along_z]+trans[:]

  for i in range(n):
    rots.append(rot_inv*rots[-1])
    trans.append(trans[-1]+trans_along_z)

  from mmtbx.ncs.ncs import ncs
  ncs_object=ncs()
  ncs_name="Helical %5.2f deg  %6.2f Z-trans " %(
        helical_rot_deg,helical_trans_z_angstrom)
  ncs_object.ncs_from_import(rot_list=rots,trans_list=trans)
  ncs_object.set_ncs_name(ncs_name)


  return ncs_object

def get_d_symmetry(n=None,two_fold_along_x=True,ncs_name=None):
  return get_c_symmetry(n=n,is_d=True,two_fold_along_x=two_fold_along_x,
     ncs_name=ncs_name)

def get_rot_z(rot_deg=None):
  import math
  theta=rot_deg*3.14159/180.
  cc=math.cos(theta)
  ss=math.sin(theta)
  from scitbx import matrix
  return matrix.sqr((cc,ss,0,-ss,cc,0,0,0,1,))

def get_rot_y(rot_deg=None):
  import math
  theta=rot_deg*3.14159/180.
  cc=math.cos(theta)
  ss=math.sin(theta)
  from scitbx import matrix
  return matrix.sqr((cc,0,ss,
                     0,1,0,
                    -ss,0,cc,
                     ))

def get_c_symmetry(n=None,is_d=False,two_fold_along_x=None,ncs_name=None):
  # generate n-fold C symmetry
  oper=get_rot_z(rot_deg=360./n)
  oper_inv=oper.inverse()
  rots=[]
  trans=[]
  from scitbx import matrix
  rots.append(matrix.sqr((1,0,0,0,1,0,0,0,1),))
  trans.append(matrix.col((0,0,0,)))

  for i in range(n-1):
    rots.append(oper_inv*rots[-1])
    trans.append(matrix.col((0,0,0,)))

  if is_d:
    if two_fold_along_x:
      d_oper=matrix.sqr((1,0,0,0,-1,0,0,0,-1,))
    else: # along y
      d_oper=matrix.sqr((-1,0,0,0,1,0,0,0,-1,))
    new_rots=[]
    new_trans=[]
    for r,t in zip(rots,trans):
      new_rots.append(d_oper*r)
      new_trans.append(t)
    rots+=new_rots
    trans+=new_trans

  from mmtbx.ncs.ncs import ncs

  ncs_object=ncs()
  ncs_object.ncs_from_import(rot_list=rots,trans_list=trans)
  if ncs_name:
    ncs_object.set_ncs_name(ncs_name)

  return ncs_object

def remove_extra(text):
  new_text=""
  for t in text:
    if not t.lower() in "()abcdefghijklmnopqrstuvwxyz":
      new_text+=t
  return new_text

def value(str):
  try:
    return int(remove_extra(str[1:]))
  except Exception as e:
    return 0


def generate_ncs_ops(symmetry=None,
   must_be_consistent_with_space_group_number = None,
   helical_rot_deg=None,
   helical_trans_z_angstrom=None,
   op_max=None,
   two_fold_along_x=None,
   include_helical_symmetry=None,
   max_helical_ops_to_check=None,
   require_helical_or_point_group_symmetry=None,
   out=sys.stdout):
  # Generate ncs objects corresponding to common point-group symmetries in
  #  conventional orientations such as C2 D7 etc.

  ncs_list=[]
  all=False
  sym_type=None
  sym_n=None
  if symmetry.lower() in ['all','any']:
    all=True
  elif symmetry.lower() in ["i"]:
    sym_type='I'
  elif symmetry.lower() in ["o"]:
    sym_type='O'
  elif symmetry.lower() in ["t"]:
    sym_type='T'
  elif symmetry.lower().startswith("d"):
    sym_type='D'
    if len(symmetry)>1:
      sym_n=value(symmetry)
  elif symmetry.lower().startswith("c"):
    sym_type='C'
    if len(symmetry)>1:
      sym_n=value(symmetry)
  elif symmetry.lower() in ['helical','helix']:
    sym_type='helical'

  print("Sym type: %s  Sym N: %s" %(
     sym_type,sym_n), file=out)
  if sym_type is None and not all:
    from libtbx.utils import Sorry
    raise Sorry("Unknown symmetry type: '%s' " %(symmetry))

  if sym_n:
    i_start=sym_n
    i_end=sym_n
  else:
    i_start=2
    if op_max is None:
      i_end=14
    else:
      i_end=op_max

  # NOTE: the (a) (b) etc designations are arbitrary

  from mmtbx.ncs.ncs import get_ncs_from_text, \
      get_c_symmetry,get_d_symmetry,get_helical_symmetry
  if sym_type=='I' or all:
    if two_fold_along_x is None or two_fold_along_x==False:
      ncs_list.append(get_ncs_from_text(text=icosahedral_b,
        text_is_ncs_spec=True,ncs_name='I (b)'))
      ncs_list.append(get_ncs_from_text(text=icosahedral_d,
        text_is_ncs_spec=True,ncs_name='I (d)'))
      ncs_list.append(get_ncs_from_text(text=icosahedral_f,
         text_is_ncs_spec=True,
         ncs_name='I (f)'))
    if two_fold_along_x is None or two_fold_along_x==True:
      ncs_list.append(get_ncs_from_text(text=icosahedral_b,
          rotate_about_z=90,
          text_is_ncs_spec=True,ncs_name='I (a)'))
      ncs_list.append(get_ncs_from_text(text=icosahedral_d,
          text_is_ncs_spec=True,rotate_about_z=90,
           ncs_name='I (c)'))
      ncs_list.append(get_ncs_from_text(text=icosahedral_f,
          rotate_about_z=90,text_is_ncs_spec=True,
          ncs_name='I (e)'))
  if sym_type=='O' or all:
    if two_fold_along_x is None or two_fold_along_x==True:
      ncs_list.append(get_ncs_from_text(text=octahedral_a,
        text_is_ncs_spec=True,ncs_name='O (a)'))
    if two_fold_along_x is None or two_fold_along_x==False:
      ncs_list.append(get_ncs_from_text(text=octahedral_a,
        rotate_about_z=45,
        text_is_ncs_spec=True,ncs_name='O (b)'))
  if sym_type=='T' or all:
    if two_fold_along_x is None or two_fold_along_x==False:
      ncs_list.append(get_ncs_from_text(text=tetrahedral_a,
        text_is_ncs_spec=True,ncs_name='T (a)'))
    if two_fold_along_x is None or two_fold_along_x==True:
      ncs_list.append(get_ncs_from_text(text=tetrahedral_a,
        # rotate_about_y=54.73563863,
        # rotate_about_z=-45,
        rotate_about_y=45,
        text_is_ncs_spec=True,ncs_name='T (b)'))
    ncs_list.append(get_ncs_from_text(text=tetrahedral_b,
           text_is_ncs_spec=True,ncs_name='T (c)'))

  if sym_type=='C' or all:
    for i in range(i_start,i_end+1):
      ncs_list.append(get_c_symmetry(n=i,ncs_name='C%d ' %(i)))
  if sym_type=='D' or all:
    for i in range(i_start,i_end+1):
      if two_fold_along_x is None or two_fold_along_x==True:
        ncs_list.append(get_d_symmetry(n=i,two_fold_along_x=True,
        ncs_name='D%d (a)' %(i)))
      if two_fold_along_x is None or two_fold_along_x==False:
        ncs_list.append(get_d_symmetry(n=i,two_fold_along_x=False,
        ncs_name='D%d (b)' %(i)))

  #  Pare down ncs_list if must_be_consistent_with_space_group_number is set
  if must_be_consistent_with_space_group_number:
    ncs_list=remove_ncs_not_consistent_with_space_group_number(
       must_be_consistent_with_space_group_number,ncs_list)

  if sym_type=='helical' or (
      all and include_helical_symmetry):
     if helical_rot_deg is not None and helical_trans_z_angstrom is not None:
      ncs_list.append(get_helical_symmetry(
       helical_rot_deg=helical_rot_deg,
       helical_trans_z_angstrom=helical_trans_z_angstrom,
       max_ops=max_helical_ops_to_check))

  return ncs_list

def remove_ncs_not_consistent_with_space_group_number(sg_number,ncs_list):
  ''' remove ncs ojbect that are not consistent with space_group number
     sg_number
   NOTE: allows ncs that has higher symmetry than sg_number
  '''

  from cctbx import crystal
  from cctbx import sgtbx
  from cctbx import uctbx
  sg = sgtbx.space_group_info(sg_number)
  uc = uctbx.unit_cell((10.,10.,10.,90.,90.,90.))
  cs = crystal.symmetry(unit_cell=uc ,space_group_info = sg)
  ncs_from_cs = crystal_symmetry_to_ncs(cs)
  # Make sure all ops of ncs_from_cs are in each ncs used
  new_ncs_list =[]
  for ncs_obj in ncs_list:
    if ncs_from_cs.is_similar_ncs_object(ncs_obj,abs_tol_t=10000):
      new_ncs_list.append(ncs_obj)
  ncs_list = new_ncs_list
  return ncs_list

# Symmetry for icosahedron in 3 settings


icosahedral_f=\
"""

Summary of NCS information
Mon Jul  2 11:08:24 2018
/Users/terwill/Downloads/view/ncs_text

source_info icosahedral_f.dat




new_ncs_group
new_operator

rota_matrix    1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth  -14.5127   20.8478  102.7355
new_operator

rota_matrix    0.5000    0.8090   -0.3090
rota_matrix   -0.8090    0.3090   -0.5000
rota_matrix   -0.3090    0.5000    0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -55.8696   46.0690   77.1756
new_operator

rota_matrix   -0.3090    0.5000   -0.8090
rota_matrix   -0.5000   -0.8090   -0.3090
rota_matrix   -0.8090    0.3090    0.5000
tran_orth     0.0000   -0.0000    0.0000

center_orth  -89.0540    7.6245   56.6665
new_operator

rota_matrix   -0.3090   -0.5000   -0.8090
rota_matrix    0.5000   -0.8090    0.3090
rota_matrix   -0.8090   -0.3090    0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -68.2062  -41.3569   69.5511
new_operator

rota_matrix    0.5000   -0.8090   -0.3090
rota_matrix    0.8090    0.3090    0.5000
rota_matrix   -0.3090   -0.5000    0.8090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth  -22.1372  -33.1844   98.0233
new_operator

rota_matrix   -1.0000    0.0000    0.0000
rota_matrix    0.0000   -1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth   14.5127  -20.8478  102.7355
new_operator

rota_matrix   -0.5000   -0.8090   -0.3090
rota_matrix    0.8090   -0.3090   -0.5000
rota_matrix    0.3090   -0.5000    0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   55.8696  -46.0690   77.1756
new_operator

rota_matrix    0.3090   -0.5000   -0.8090
rota_matrix    0.5000    0.8090   -0.3090
rota_matrix    0.8090   -0.3090    0.5000
tran_orth     0.0000   -0.0000    0.0000

center_orth   89.0540   -7.6245   56.6665
new_operator

rota_matrix    0.3090    0.5000   -0.8090
rota_matrix   -0.5000    0.8090    0.3090
rota_matrix    0.8090    0.3090    0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth   68.2062   41.3569   69.5511
new_operator

rota_matrix   -0.5000    0.8090   -0.3090
rota_matrix   -0.8090   -0.3090    0.5000
rota_matrix    0.3090    0.5000    0.8090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   22.1372   33.1844   98.0233
new_operator

rota_matrix    1.0000    0.0000    0.0000
rota_matrix    0.0000   -1.0000    0.0000
rota_matrix    0.0000    0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth  -14.5127  -20.8478  -102.7355
new_operator

rota_matrix    0.5000   -0.8090    0.3090
rota_matrix   -0.8090   -0.3090    0.5000
rota_matrix   -0.3090   -0.5000   -0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -55.8696  -46.0690  -77.1756
new_operator

rota_matrix   -0.3090   -0.5000    0.8090
rota_matrix   -0.5000    0.8090    0.3090
rota_matrix   -0.8090   -0.3090   -0.5000
tran_orth     0.0000   -0.0000    0.0000

center_orth  -89.0540   -7.6245  -56.6665
new_operator

rota_matrix   -0.3090    0.5000    0.8090
rota_matrix    0.5000    0.8090   -0.3090
rota_matrix   -0.8090    0.3090   -0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -68.2062   41.3569  -69.5511
new_operator

rota_matrix    0.5000    0.8090    0.3090
rota_matrix    0.8090   -0.3090   -0.5000
rota_matrix   -0.3090    0.5000   -0.8090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth  -22.1372   33.1844  -98.0233
new_operator

rota_matrix   -1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth   14.5127   20.8478  -102.7355
new_operator

rota_matrix   -0.5000    0.8090    0.3090
rota_matrix    0.8090    0.3090    0.5000
rota_matrix    0.3090    0.5000   -0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   55.8696   46.0690  -77.1756
new_operator

rota_matrix    0.3090    0.5000    0.8090
rota_matrix    0.5000   -0.8090    0.3090
rota_matrix    0.8090    0.3090   -0.5000
tran_orth     0.0000   -0.0000    0.0000

center_orth   89.0540    7.6245  -56.6665
new_operator

rota_matrix    0.3090   -0.5000    0.8090
rota_matrix   -0.5000   -0.8090   -0.3090
rota_matrix    0.8090   -0.3090   -0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth   68.2062  -41.3569  -69.5511
new_operator

rota_matrix   -0.5000   -0.8090    0.3090
rota_matrix   -0.8090    0.3090   -0.5000
rota_matrix    0.3090   -0.5000   -0.8090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   22.1372  -33.1844  -98.0233
new_operator

rota_matrix   -0.0000   -0.0000   -1.0000
rota_matrix   -1.0000    0.0000   -0.0000
rota_matrix    0.0000    1.0000   -0.0000
tran_orth     0.0000   -0.0000    0.0000

center_orth  -20.8478  102.7355   14.5127
new_operator

rota_matrix   -0.8090   -0.3090   -0.5000
rota_matrix   -0.3090   -0.5000    0.8090
rota_matrix   -0.5000    0.8090    0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -46.0690   77.1756   55.8696
new_operator

rota_matrix   -0.5000   -0.8090    0.3090
rota_matrix    0.8090   -0.3090    0.5000
rota_matrix   -0.3090    0.5000    0.8090
tran_orth     0.0000   -0.0000    0.0000

center_orth   -7.6245   56.6665   89.0540
new_operator

rota_matrix    0.5000   -0.8090    0.3090
rota_matrix    0.8090    0.3090   -0.5000
rota_matrix    0.3090    0.5000    0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   41.3569   69.5511   68.2062
new_operator

rota_matrix    0.8090   -0.3090   -0.5000
rota_matrix   -0.3090    0.5000   -0.8090
rota_matrix    0.5000    0.8090    0.3090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   33.1844   98.0233   22.1372
new_operator

rota_matrix    0.0000    0.0000    1.0000
rota_matrix    1.0000    0.0000    0.0000
rota_matrix   -0.0000    1.0000    0.0000
tran_orth     0.0000   -0.0000    0.0000

center_orth   20.8478  102.7355  -14.5127
new_operator

rota_matrix    0.8090   -0.3090    0.5000
rota_matrix    0.3090   -0.5000   -0.8090
rota_matrix    0.5000    0.8090   -0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   46.0690   77.1756  -55.8696
new_operator

rota_matrix    0.5000   -0.8090   -0.3090
rota_matrix   -0.8090   -0.3090   -0.5000
rota_matrix    0.3090    0.5000   -0.8090
tran_orth     0.0000   -0.0000    0.0000

center_orth    7.6245   56.6665  -89.0540
new_operator

rota_matrix   -0.5000   -0.8090   -0.3090
rota_matrix   -0.8090    0.3090    0.5000
rota_matrix   -0.3090    0.5000   -0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -41.3569   69.5511  -68.2062
new_operator

rota_matrix   -0.8090   -0.3090    0.5000
rota_matrix    0.3090    0.5000    0.8090
rota_matrix   -0.5000    0.8090   -0.3090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth  -33.1844   98.0233  -22.1372
new_operator

rota_matrix   -0.0000   -0.0000   -1.0000
rota_matrix    1.0000   -0.0000   -0.0000
rota_matrix   -0.0000   -1.0000    0.0000
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   20.8478  -102.7355   14.5127
new_operator

rota_matrix    0.8090    0.3090   -0.5000
rota_matrix    0.3090    0.5000    0.8090
rota_matrix    0.5000   -0.8090    0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   46.0690  -77.1756   55.8696
new_operator

rota_matrix    0.5000    0.8090    0.3090
rota_matrix   -0.8090    0.3090    0.5000
rota_matrix    0.3090   -0.5000    0.8090
tran_orth     0.0000   -0.0000    0.0000

center_orth    7.6245  -56.6665   89.0540
new_operator

rota_matrix   -0.5000    0.8090    0.3090
rota_matrix   -0.8090   -0.3090   -0.5000
rota_matrix   -0.3090   -0.5000    0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -41.3569  -69.5511   68.2062
new_operator

rota_matrix   -0.8090    0.3090   -0.5000
rota_matrix    0.3090   -0.5000   -0.8090
rota_matrix   -0.5000   -0.8090    0.3090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth  -33.1844  -98.0233   22.1372
new_operator

rota_matrix   -0.0000    0.0000    1.0000
rota_matrix   -1.0000   -0.0000   -0.0000
rota_matrix    0.0000   -1.0000   -0.0000
tran_orth    -0.0000   -0.0000    0.0000

center_orth  -20.8478  -102.7355  -14.5127
new_operator

rota_matrix   -0.8090    0.3090    0.5000
rota_matrix   -0.3090    0.5000   -0.8090
rota_matrix   -0.5000   -0.8090   -0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -46.0690  -77.1756  -55.8696
new_operator

rota_matrix   -0.5000    0.8090   -0.3090
rota_matrix    0.8090    0.3090   -0.5000
rota_matrix   -0.3090   -0.5000   -0.8090
tran_orth     0.0000   -0.0000    0.0000

center_orth   -7.6245  -56.6665  -89.0540
new_operator

rota_matrix    0.5000    0.8090   -0.3090
rota_matrix    0.8090   -0.3090    0.5000
rota_matrix    0.3090   -0.5000   -0.8090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   41.3569  -69.5511  -68.2062
new_operator

rota_matrix    0.8090    0.3090    0.5000
rota_matrix   -0.3090   -0.5000    0.8090
rota_matrix    0.5000   -0.8090   -0.3090
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   33.1844  -98.0233  -22.1372
new_operator

rota_matrix   -0.0000   -1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
rota_matrix   -1.0000    0.0000    0.0000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -102.7355   14.5127   20.8478
new_operator

rota_matrix    0.3090   -0.5000    0.8090
rota_matrix    0.5000    0.8090    0.3090
rota_matrix   -0.8090    0.3090    0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -77.1756   55.8696   46.0690
new_operator

rota_matrix    0.8090    0.3090    0.5000
rota_matrix    0.3090    0.5000   -0.8090
rota_matrix   -0.5000    0.8090    0.3090
tran_orth     0.0000   -0.0000    0.0000

center_orth  -56.6665   89.0540    7.6245
new_operator

rota_matrix    0.8090    0.3090   -0.5000
rota_matrix   -0.3090   -0.5000   -0.8090
rota_matrix   -0.5000    0.8090   -0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -69.5511   68.2062  -41.3569
new_operator

rota_matrix    0.3090   -0.5000   -0.8090
rota_matrix   -0.5000   -0.8090    0.3090
rota_matrix   -0.8090    0.3090   -0.5000
tran_orth    -0.0000   -0.0000   -0.0000

center_orth  -98.0233   22.1372  -33.1844
new_operator

rota_matrix   -0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000   -1.0000
rota_matrix   -1.0000   -0.0000   -0.0000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -102.7355  -14.5127  -20.8478
new_operator

rota_matrix    0.3090    0.5000   -0.8090
rota_matrix    0.5000   -0.8090   -0.3090
rota_matrix   -0.8090   -0.3090   -0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -77.1756  -55.8696  -46.0690
new_operator

rota_matrix    0.8090   -0.3090   -0.5000
rota_matrix    0.3090   -0.5000    0.8090
rota_matrix   -0.5000   -0.8090   -0.3090
tran_orth     0.0000   -0.0000    0.0000

center_orth  -56.6665  -89.0540   -7.6245
new_operator

rota_matrix    0.8090   -0.3090    0.5000
rota_matrix   -0.3090    0.5000    0.8090
rota_matrix   -0.5000   -0.8090    0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth  -69.5511  -68.2062   41.3569
new_operator

rota_matrix    0.3090    0.5000    0.8090
rota_matrix   -0.5000    0.8090   -0.3090
rota_matrix   -0.8090   -0.3090    0.5000
tran_orth    -0.0000   -0.0000   -0.0000

center_orth  -98.0233  -22.1372   33.1844
new_operator

rota_matrix    0.0000   -1.0000    0.0000
rota_matrix   -0.0000   -0.0000   -1.0000
rota_matrix    1.0000    0.0000   -0.0000
tran_orth    -0.0000    0.0000   -0.0000

center_orth  102.7355   14.5127  -20.8478
new_operator

rota_matrix   -0.3090   -0.5000   -0.8090
rota_matrix   -0.5000    0.8090   -0.3090
rota_matrix    0.8090    0.3090   -0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth   77.1756   55.8696  -46.0690
new_operator

rota_matrix   -0.8090    0.3090   -0.5000
rota_matrix   -0.3090    0.5000    0.8090
rota_matrix    0.5000    0.8090   -0.3090
tran_orth     0.0000   -0.0000    0.0000

center_orth   56.6665   89.0540   -7.6245
new_operator

rota_matrix   -0.8090    0.3090    0.5000
rota_matrix    0.3090   -0.5000    0.8090
rota_matrix    0.5000    0.8090    0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   69.5511   68.2062   41.3569
new_operator

rota_matrix   -0.3090   -0.5000    0.8090
rota_matrix    0.5000   -0.8090   -0.3090
rota_matrix    0.8090    0.3090    0.5000
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   98.0233   22.1372   33.1844
new_operator

rota_matrix   -0.0000    1.0000    0.0000
rota_matrix   -0.0000   -0.0000    1.0000
rota_matrix    1.0000    0.0000    0.0000
tran_orth     0.0000    0.0000    0.0000

center_orth  102.7355  -14.5127   20.8478
new_operator

rota_matrix   -0.3090    0.5000    0.8090
rota_matrix   -0.5000   -0.8090    0.3090
rota_matrix    0.8090   -0.3090    0.5000
tran_orth    -0.0000    0.0000   -0.0000

center_orth   77.1756  -55.8696   46.0690
new_operator

rota_matrix   -0.8090   -0.3090    0.5000
rota_matrix   -0.3090   -0.5000   -0.8090
rota_matrix    0.5000   -0.8090    0.3090
tran_orth     0.0000   -0.0000    0.0000

center_orth   56.6665  -89.0540    7.6245
new_operator

rota_matrix   -0.8090   -0.3090   -0.5000
rota_matrix    0.3090    0.5000   -0.8090
rota_matrix    0.5000   -0.8090   -0.3090
tran_orth    -0.0000    0.0000   -0.0000

center_orth   69.5511  -68.2062  -41.3569
new_operator

rota_matrix   -0.3090    0.5000   -0.8090
rota_matrix    0.5000    0.8090    0.3090
rota_matrix    0.8090   -0.3090   -0.5000
tran_orth    -0.0000   -0.0000   -0.0000

center_orth   98.0233  -22.1372  -33.1844


"""
icosahedral_d=\
"""

Summary of NCS information
Mon Jul  2 11:08:15 2018
/Users/terwill/Downloads/view/ncs_text

source_info icosahedral_d.dat




new_ncs_group
new_operator

rota_matrix    1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6708    0.1625    0.7236
rota_matrix   -0.6882    0.5000    0.5257
rota_matrix   -0.2764   -0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1382   -0.4253    0.8944
rota_matrix   -0.9511   -0.3090    0.0000
rota_matrix    0.2764   -0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1382   -0.9511    0.2764
rota_matrix   -0.4253   -0.3090   -0.8507
rota_matrix    0.8944    0.0000   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6708   -0.6882   -0.2764
rota_matrix    0.1625    0.5000   -0.8507
rota_matrix    0.7236    0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4472    0.0000    0.8944
rota_matrix    0.0000   -1.0000    0.0000
rota_matrix    0.8944    0.0000   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.9472   -0.1625    0.2764
rota_matrix    0.1625   -0.5000   -0.8507
rota_matrix    0.2764    0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8618    0.4253   -0.2764
rota_matrix   -0.4253    0.3090   -0.8507
rota_matrix   -0.2764    0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3090    0.9511    0.0000
rota_matrix   -0.9511    0.3090    0.0000
rota_matrix    0.0000   -0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.0528    0.6882    0.7236
rota_matrix   -0.6882   -0.5000    0.5257
rota_matrix    0.7236   -0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -1.0000   -0.0000   -0.0000
rota_matrix   -0.0000    1.0000    0.0000
rota_matrix   -0.0000    0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6708    0.1625   -0.7236
rota_matrix    0.6882    0.5000   -0.5257
rota_matrix    0.2764   -0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1382   -0.4253   -0.8944
rota_matrix    0.9511   -0.3090   -0.0000
rota_matrix   -0.2764   -0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1382   -0.9511   -0.2764
rota_matrix    0.4253   -0.3090    0.8507
rota_matrix   -0.8944    0.0000    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6708   -0.6882    0.2764
rota_matrix   -0.1625    0.5000    0.8507
rota_matrix   -0.7236    0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4472   -0.0000   -0.8944
rota_matrix   -0.0000   -1.0000    0.0000
rota_matrix   -0.8944    0.0000    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.9472   -0.1625   -0.2764
rota_matrix   -0.1625   -0.5000    0.8507
rota_matrix   -0.2764    0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8618    0.4253    0.2764
rota_matrix    0.4253    0.3090    0.8507
rota_matrix    0.2764    0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3090    0.9511   -0.0000
rota_matrix    0.9511    0.3090   -0.0000
rota_matrix   -0.0000   -0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.0528    0.6882   -0.7236
rota_matrix    0.6882   -0.5000   -0.5257
rota_matrix   -0.7236   -0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4472    0.5257    0.7236
rota_matrix   -0.8507   -0.0000   -0.5257
rota_matrix   -0.2764   -0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6382   -0.2629    0.7236
rota_matrix   -0.2629   -0.8090   -0.5257
rota_matrix    0.7236   -0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.0528   -0.6882    0.7236
rota_matrix    0.6882   -0.5000   -0.5257
rota_matrix    0.7236    0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6708   -0.1625    0.7236
rota_matrix    0.6882    0.5000   -0.5257
rota_matrix   -0.2764    0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618    0.5878    0.7236
rota_matrix   -0.2629    0.8090   -0.5257
rota_matrix   -0.8944   -0.0000    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4472   -0.5257    0.7236
rota_matrix    0.8507    0.0000    0.5257
rota_matrix   -0.2764    0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618    0.2629    0.8944
rota_matrix    0.5878    0.8090   -0.0000
rota_matrix   -0.7236    0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6708    0.6882    0.2764
rota_matrix    0.1625    0.5000   -0.8507
rota_matrix   -0.7236   -0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.9472    0.1625   -0.2764
rota_matrix    0.1625   -0.5000   -0.8507
rota_matrix   -0.2764   -0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8090   -0.5878    0.0000
rota_matrix    0.5878   -0.8090   -0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4472   -0.5257   -0.7236
rota_matrix   -0.8507   -0.0000   -0.5257
rota_matrix    0.2764    0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618    0.2629   -0.8944
rota_matrix   -0.5878    0.8090    0.0000
rota_matrix    0.7236    0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6708    0.6882   -0.2764
rota_matrix   -0.1625    0.5000    0.8507
rota_matrix    0.7236   -0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.9472    0.1625    0.2764
rota_matrix   -0.1625   -0.5000    0.8507
rota_matrix    0.2764   -0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8090   -0.5878   -0.0000
rota_matrix   -0.5878   -0.8090    0.0000
rota_matrix   -0.0000    0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4472    0.5257   -0.7236
rota_matrix    0.8507    0.0000    0.5257
rota_matrix    0.2764   -0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6382   -0.2629   -0.7236
rota_matrix    0.2629   -0.8090    0.5257
rota_matrix   -0.7236   -0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.0528   -0.6882   -0.7236
rota_matrix   -0.6882   -0.5000    0.5257
rota_matrix   -0.7236    0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6708   -0.1625   -0.7236
rota_matrix   -0.6882    0.5000    0.5257
rota_matrix    0.2764    0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618    0.5878   -0.7236
rota_matrix    0.2629    0.8090    0.5257
rota_matrix    0.8944   -0.0000   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4472   -0.8507   -0.2764
rota_matrix    0.5257   -0.0000   -0.8507
rota_matrix    0.7236   -0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3090   -0.9511    0.0000
rota_matrix    0.9511    0.3090   -0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618   -0.5878    0.7236
rota_matrix    0.2629    0.8090    0.5257
rota_matrix   -0.8944    0.0000    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618   -0.2629    0.8944
rota_matrix   -0.5878    0.8090    0.0000
rota_matrix   -0.7236   -0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8618   -0.4253    0.2764
rota_matrix   -0.4253    0.3090   -0.8507
rota_matrix    0.2764   -0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4472   -0.8507    0.2764
rota_matrix   -0.5257   -0.0000    0.8507
rota_matrix   -0.7236   -0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3090   -0.9511   -0.0000
rota_matrix   -0.9511    0.3090    0.0000
rota_matrix   -0.0000    0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618   -0.5878   -0.7236
rota_matrix   -0.2629    0.8090   -0.5257
rota_matrix    0.8944    0.0000   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618   -0.2629   -0.8944
rota_matrix    0.5878    0.8090   -0.0000
rota_matrix    0.7236   -0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8618   -0.4253   -0.2764
rota_matrix    0.4253    0.3090    0.8507
rota_matrix   -0.2764   -0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4472    0.8507    0.2764
rota_matrix    0.5257    0.0000   -0.8507
rota_matrix   -0.7236    0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1382    0.9511   -0.2764
rota_matrix   -0.4253   -0.3090   -0.8507
rota_matrix   -0.8944   -0.0000    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8090    0.5878    0.0000
rota_matrix   -0.5878   -0.8090    0.0000
rota_matrix    0.0000   -0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6382    0.2629    0.7236
rota_matrix    0.2629   -0.8090    0.5257
rota_matrix    0.7236    0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1382    0.4253    0.8944
rota_matrix    0.9511   -0.3090   -0.0000
rota_matrix    0.2764    0.8507   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4472    0.8507   -0.2764
rota_matrix   -0.5257    0.0000    0.8507
rota_matrix    0.7236    0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1382    0.9511    0.2764
rota_matrix    0.4253   -0.3090    0.8507
rota_matrix    0.8944   -0.0000   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8090    0.5878   -0.0000
rota_matrix    0.5878   -0.8090   -0.0000
rota_matrix   -0.0000   -0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6382    0.2629   -0.7236
rota_matrix   -0.2629   -0.8090   -0.5257
rota_matrix   -0.7236    0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1382    0.4253   -0.8944
rota_matrix   -0.9511   -0.3090    0.0000
rota_matrix   -0.2764    0.8507    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000


"""
tetrahedral_a=\
"""
new_operator
rota_matrix  1.000  0.000  0.000
rota_matrix  0.000  1.000  0.000
rota_matrix  0.000  0.000  1.000
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.833  0.289  -0.471
rota_matrix  -0.288  -0.500  -0.816
rota_matrix  -0.472  0.816  -0.334
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.668  -0.577  -0.471
rota_matrix  -0.578  0.003  0.816
rota_matrix  -0.469  0.817  -0.335
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.166  0.290  0.943
rota_matrix  0.867  0.499  -0.001
rota_matrix  -0.471  0.817  -0.334
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.500  0.866  -0.000
rota_matrix  -0.866  -0.500  0.000
rota_matrix  0.000  0.001  1.000
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.667  0.577  -0.471
rota_matrix  0.578  0.000  -0.816
rota_matrix  -0.471  -0.817  -0.333
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.833  -0.290  -0.471
rota_matrix  0.287  -0.501  0.816
rota_matrix  -0.473  -0.815  -0.335
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.168  -0.288  0.943
rota_matrix  -0.866  0.501  -0.001
rota_matrix  -0.472  -0.816  -0.334
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.500  -0.866  0.000
rota_matrix  0.866  -0.500  0.001
rota_matrix  -0.000  0.000  1.000
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.166  -0.866  -0.471
rota_matrix  -0.289  0.500  -0.817
rota_matrix  0.943  0.000  -0.333
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.165  0.866  -0.471
rota_matrix  0.291  0.499  0.816
rota_matrix  0.942  -0.002  -0.335
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.334  -0.001  0.943
rota_matrix  -0.001  -1.000  -0.001
rota_matrix  0.943  -0.001  -0.334
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
"""


tetrahedral_b=\
"""
new_operator
rota_matrix  1.000  0.000  0.000
rota_matrix  0.000  1.000  0.000
rota_matrix  0.000  0.000  1.000
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -1.000  0.001  0.001
rota_matrix  0.001  0.333  0.943
rota_matrix  0.000  0.943  -0.333
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.499  0.288  0.818
rota_matrix  0.867  -0.166  -0.470
rota_matrix  0.001  0.943  -0.333
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.498  -0.287  -0.818
rota_matrix  -0.867  -0.167  -0.469
rota_matrix  -0.002  0.943  -0.332
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.500  0.866  -0.000
rota_matrix  -0.866  -0.500  -0.000
rota_matrix  -0.000  0.000  1.000
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.499  -0.866  0.001
rota_matrix  -0.289  -0.166  0.943
rota_matrix  -0.817  -0.471  -0.334
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.498  0.287  0.818
rota_matrix  -0.289  0.834  -0.469
rota_matrix  -0.817  -0.471  -0.332
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.000  0.574  -0.819
rota_matrix  0.578  -0.668  -0.469
rota_matrix  -0.816  -0.473  -0.332
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.500  -0.866  0.000
rota_matrix  0.866  -0.500  -0.000
rota_matrix  0.000  -0.000  1.000
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  0.501  0.866  0.001
rota_matrix  0.289  -0.168  0.943
rota_matrix  0.816  -0.472  -0.334
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.000  -0.577  0.817
rota_matrix  -0.578  -0.667  -0.470
rota_matrix  0.816  -0.472  -0.333
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
new_operator
rota_matrix  -0.498  -0.288  -0.818
rota_matrix  0.289  0.834  -0.470
rota_matrix  0.818  -0.470  -0.332
tran_orth  0.000  0.000  0.000
center_orth  0.000  0.000  0.000
"""
octahedral_a=\
"""
new_operator
rota_matrix  1.0  0.0  0.0
rota_matrix  0.0  1.0  0.0
rota_matrix  0.0  0.0  1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  -1.0  -0.0
rota_matrix  1.0  0.0  0.0
rota_matrix  -0.0  -0.0  1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -1.0  0.0  -0.0
rota_matrix  -0.0  -1.0  0.0
rota_matrix  -0.0  0.0  1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  1.0  -0.0
rota_matrix  -0.0  -0.0  -1.0
rota_matrix  -1.0  0.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  -0.0  1.0
rota_matrix  -0.0  1.0  0.0
rota_matrix  -1.0  -0.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -1.0  0.0  -0.0
rota_matrix  0.0  -0.0  -1.0
rota_matrix  -0.0  -1.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  0.0  -1.0
rota_matrix  1.0  -0.0  -0.0
rota_matrix  -0.0  -1.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  1.0  -0.0
rota_matrix  -1.0  -0.0  0.0
rota_matrix  0.0  0.0  1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  -1.0  -0.0
rota_matrix  0.0  0.0  -1.0
rota_matrix  1.0  -0.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  1.0  -0.0  -0.0
rota_matrix  -0.0  0.0  -1.0
rota_matrix  0.0  1.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  -0.0  1.0
rota_matrix  0.0  -1.0  -0.0
rota_matrix  1.0  0.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  -0.0  1.0
rota_matrix  1.0  0.0  0.0
rota_matrix  -0.0  1.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  0.0  -1.0
rota_matrix  -0.0  -1.0  -0.0
rota_matrix  -1.0  0.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  -1.0  0.0
rota_matrix  -0.0  0.0  1.0
rota_matrix  -1.0  -0.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  1.0  0.0
rota_matrix  0.0  -0.0  1.0
rota_matrix  1.0  0.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  -0.0  -1.0
rota_matrix  -1.0  0.0  -0.0
rota_matrix  0.0  1.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -1.0  -0.0  0.0
rota_matrix  0.0  0.0  1.0
rota_matrix  -0.0  1.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  1.0  0.0  0.0
rota_matrix  0.0  -1.0  -0.0
rota_matrix  0.0  0.0  -1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  1.0  0.0
rota_matrix  1.0  -0.0  -0.0
rota_matrix  -0.0  0.0  -1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -1.0  0.0  0.0
rota_matrix  0.0  1.0  -0.0
rota_matrix  -0.0  -0.0  -1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  0.0  -1.0  0.0
rota_matrix  -1.0  -0.0  -0.0
rota_matrix  0.0  -0.0  -1.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  1.0  0.0  0.0
rota_matrix  -0.0  -0.0  1.0
rota_matrix  0.0  -1.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  0.0  -1.0
rota_matrix  0.0  1.0  0.0
rota_matrix  1.0  -0.0  -0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
new_operator
rota_matrix  -0.0  0.0  1.0
rota_matrix  -1.0  -0.0  -0.0
rota_matrix  0.0  -1.0  0.0
tran_orth  0.0  0.0  0.0
center_orth  0.0  0.0  0.0
"""

icosahedral_b=\
"""

Summary of NCS information
Mon Jul  2 11:07:59 2018
/Users/terwill/Downloads/view/ncs_text

source_info icosahedral_b.dat




new_ncs_group
new_operator

rota_matrix    1.0000   -0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000   -0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3090    0.9511   -0.0001
rota_matrix   -0.9511    0.3090   -0.0002
rota_matrix   -0.0001    0.0002    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8090    0.5878   -0.0003
rota_matrix   -0.5878   -0.8090   -0.0001
rota_matrix   -0.0003    0.0001    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8090   -0.5878   -0.0003
rota_matrix    0.5878   -0.8090    0.0001
rota_matrix   -0.0003   -0.0001    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3090   -0.9511   -0.0001
rota_matrix    0.9511    0.3090    0.0002
rota_matrix   -0.0001   -0.0002    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.9473   -0.1623    0.2761
rota_matrix   -0.1623   -0.5000   -0.8507
rota_matrix    0.2761   -0.8507    0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4471   -0.5256   -0.7238
rota_matrix    0.8508    0.0000   -0.5256
rota_matrix    0.2762   -0.8508    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6709   -0.1623   -0.7236
rota_matrix    0.6881    0.5000    0.5259
rota_matrix    0.2764   -0.8507    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8617    0.4255    0.2765
rota_matrix   -0.4255    0.3090    0.8506
rota_matrix    0.2765   -0.8506    0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1384    0.4255    0.8943
rota_matrix   -0.9511   -0.3090   -0.0002
rota_matrix    0.2763   -0.8506    0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8617   -0.4255   -0.2765
rota_matrix   -0.4255    0.3090    0.8506
rota_matrix   -0.2765    0.8506   -0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6709    0.1623    0.7236
rota_matrix    0.6881    0.5000    0.5259
rota_matrix   -0.2764    0.8507   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4471    0.5256    0.7238
rota_matrix    0.8508    0.0000   -0.5256
rota_matrix   -0.2762    0.8508   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.9473    0.1623   -0.2761
rota_matrix   -0.1623   -0.5000   -0.8507
rota_matrix   -0.2761    0.8507   -0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1384   -0.4255   -0.8943
rota_matrix   -0.9511   -0.3090   -0.0002
rota_matrix   -0.2763    0.8506   -0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8090    0.5878    0.0003
rota_matrix    0.5878   -0.8090    0.0001
rota_matrix    0.0003    0.0001   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8090   -0.5878    0.0003
rota_matrix   -0.5878   -0.8090   -0.0001
rota_matrix    0.0003   -0.0001   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3090   -0.9511    0.0001
rota_matrix   -0.9511    0.3090   -0.0002
rota_matrix    0.0001   -0.0002   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3090    0.9511    0.0001
rota_matrix    0.9511    0.3090    0.0002
rota_matrix    0.0001    0.0002   -1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1384    0.9511    0.2763
rota_matrix   -0.4255   -0.3090    0.8506
rota_matrix    0.8943    0.0002    0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4476    0.0000    0.8943
rota_matrix    0.0000   -1.0000   -0.0000
rota_matrix    0.8943   -0.0000    0.4476
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1384   -0.9511    0.2763
rota_matrix    0.4255   -0.3090   -0.8506
rota_matrix    0.8943   -0.0002    0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618   -0.5878   -0.7236
rota_matrix    0.2630    0.8090   -0.5257
rota_matrix    0.8944   -0.0001    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618    0.5878   -0.7236
rota_matrix   -0.2630    0.8090    0.5257
rota_matrix    0.8944    0.0001    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4471   -0.8508   -0.2762
rota_matrix   -0.5256    0.0000   -0.8508
rota_matrix    0.7238    0.5256   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618   -0.2630   -0.8944
rota_matrix   -0.5878    0.8090   -0.0001
rota_matrix    0.7236    0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6709    0.6881   -0.2764
rota_matrix    0.1623    0.5000    0.8507
rota_matrix    0.7236    0.5259   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.0531    0.6881    0.7237
rota_matrix    0.6881   -0.5000    0.5259
rota_matrix    0.7237    0.5259   -0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6379   -0.2630    0.7238
rota_matrix    0.2630   -0.8090   -0.5257
rota_matrix    0.7238    0.5257   -0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.0531   -0.6881   -0.7237
rota_matrix    0.6881   -0.5000    0.5259
rota_matrix   -0.7237   -0.5259    0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6709   -0.6881    0.2764
rota_matrix    0.1623    0.5000    0.8507
rota_matrix   -0.7236   -0.5259    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618    0.2630    0.8944
rota_matrix   -0.5878    0.8090   -0.0001
rota_matrix   -0.7236   -0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4471    0.8508    0.2762
rota_matrix   -0.5256    0.0000   -0.8508
rota_matrix   -0.7238   -0.5256    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6379    0.2630   -0.7238
rota_matrix    0.2630   -0.8090   -0.5257
rota_matrix   -0.7238   -0.5257    0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618    0.5878    0.7236
rota_matrix    0.2630    0.8090   -0.5257
rota_matrix   -0.8944    0.0001   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1384    0.9511   -0.2763
rota_matrix    0.4255   -0.3090   -0.8506
rota_matrix   -0.8943    0.0002   -0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4476   -0.0000   -0.8943
rota_matrix   -0.0000   -1.0000    0.0000
rota_matrix   -0.8943    0.0000   -0.4476
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1384   -0.9511   -0.2763
rota_matrix   -0.4255   -0.3090    0.8506
rota_matrix   -0.8943   -0.0002   -0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618   -0.5878    0.7236
rota_matrix   -0.2630    0.8090    0.5257
rota_matrix   -0.8944   -0.0001   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.1384   -0.4255    0.8943
rota_matrix    0.9511   -0.3090    0.0002
rota_matrix    0.2763    0.8506    0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.8617   -0.4255    0.2765
rota_matrix    0.4255    0.3090   -0.8506
rota_matrix    0.2765    0.8506    0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6709    0.1623   -0.7236
rota_matrix   -0.6881    0.5000   -0.5259
rota_matrix    0.2764    0.8507    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4471    0.5256   -0.7238
rota_matrix   -0.8508    0.0000    0.5256
rota_matrix    0.2762    0.8508    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.9473    0.1623    0.2761
rota_matrix    0.1623   -0.5000    0.8507
rota_matrix    0.2761    0.8507    0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.0531    0.6881   -0.7237
rota_matrix   -0.6881   -0.5000   -0.5259
rota_matrix   -0.7237    0.5259    0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6379   -0.2630   -0.7238
rota_matrix   -0.2630   -0.8090    0.5257
rota_matrix   -0.7238    0.5257    0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.4471   -0.8508    0.2762
rota_matrix    0.5256    0.0000    0.8508
rota_matrix   -0.7238    0.5256    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3618   -0.2630    0.8944
rota_matrix    0.5878    0.8090    0.0001
rota_matrix   -0.7236    0.5257    0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6709    0.6881    0.2764
rota_matrix   -0.1623    0.5000   -0.8507
rota_matrix   -0.7236    0.5259    0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.3618    0.2630   -0.8944
rota_matrix    0.5878    0.8090    0.0001
rota_matrix    0.7236   -0.5257   -0.4472
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4471    0.8508   -0.2762
rota_matrix    0.5256    0.0000    0.8508
rota_matrix    0.7238   -0.5256   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.6379    0.2630    0.7238
rota_matrix   -0.2630   -0.8090    0.5257
rota_matrix    0.7238   -0.5257   -0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.0531   -0.6881    0.7237
rota_matrix   -0.6881   -0.5000   -0.5259
rota_matrix    0.7237   -0.5259   -0.4469
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6709   -0.6881   -0.2764
rota_matrix   -0.1623    0.5000   -0.8507
rota_matrix    0.7236   -0.5259   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.4471   -0.5256    0.7238
rota_matrix   -0.8508    0.0000    0.5256
rota_matrix   -0.2762   -0.8508   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.6709   -0.1623    0.7236
rota_matrix   -0.6881    0.5000   -0.5259
rota_matrix   -0.2764   -0.8507   -0.4471
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix   -0.8617    0.4255   -0.2765
rota_matrix    0.4255    0.3090   -0.8506
rota_matrix   -0.2765   -0.8506   -0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.1384    0.4255   -0.8943
rota_matrix    0.9511   -0.3090    0.0002
rota_matrix   -0.2763   -0.8506   -0.4474
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000
new_operator

rota_matrix    0.9473   -0.1623   -0.2761
rota_matrix    0.1623   -0.5000    0.8507
rota_matrix   -0.2761   -0.8507   -0.4473
tran_orth     0.0000    0.0000    0.0000

center_orth    0.0000    0.0000    0.0000


"""


class ncs_group:  # one group of NCS operators and center and where it applies
  def __init__(self, ncs_rota_matr=None, center_orth=None, trans_orth=None,
      chain_residue_id=None,source_of_ncs_info=None,rmsd_list=None,
      ncs_domain_pdb=None,
      residues_in_common_list=None,cc=None,note=None,
       exclude_h=None,exclude_d=None):
    self._chain_residue_id=chain_residue_id  # just one of these
    self._rmsd_list=rmsd_list
    self._residues_in_common_list=residues_in_common_list
    self._centers=center_orth
    self._translations_orth=trans_orth
    self._rota_matrices=ncs_rota_matr
    if self._centers is not None:
      self._n_ncs_oper=len(self._centers)
    elif self._rmsd_list is not None:
      self._n_ncs_oper=len(self._rmsd_list)
    else:
      self._n_ncs_oper=0
    self._source_of_ncs_info=source_of_ncs_info
    self._ncs_domain_pdb=ncs_domain_pdb
    self._cc=cc
    self._note=note
    self._exclude_h=exclude_h
    self._exclude_d=exclude_d
    self._have_helical_symmetry=False
    self._have_point_group_symmetry=False

  def __repr__(self):
    return "NCS group with %s ops" %(self._n_ncs_oper)

  def apply_cob_to_vector(self,vector=None,
         change_of_basis_operator=None,
         coordinate_offset=None,
         unit_cell=None,new_unit_cell=None):
    if coordinate_offset is not None:
      from scitbx.math import  matrix
      new_vector=matrix.col(vector)+matrix.col(coordinate_offset)
    elif change_of_basis_operator:
      frac=unit_cell.fractionalize(vector)
      new_frac = change_of_basis_operator.c() * frac
      new_vector=new_unit_cell.orthogonalize(new_frac)
    return new_vector


  def copy_rot_trans(self,list_of_matrices,list_of_translations,
      change_of_basis_operator=None,
      coordinate_offset=None,
      scale_factor=None,
      unit_cell=None,new_unit_cell=None):
    # if change_of_basis_operator is None, then return copy of what we have
    from scitbx.math import  matrix
    new_list_of_matrices=[]
    new_list_of_translations=[]
    if change_of_basis_operator is not None:
      a=  matrix.sqr(new_unit_cell.orthogonalization_matrix()) \
        * change_of_basis_operator.c().as_rational().r \
        * matrix.sqr(unit_cell.fractionalization_matrix())
      a_inv=a.inverse()
    else:
      a=None
    for ncs_r,ncs_t in zip(list_of_matrices,list_of_translations):
      if scale_factor is not None:
        # expand by scale_factor about (0,0,0). Affects all translations
        new_list_of_matrices.append(deepcopy(ncs_r))
        new_list_of_translations.append(scale_factor*matrix.col(ncs_t))
      elif change_of_basis_operator is None and coordinate_offset is None:
        new_list_of_matrices.append(deepcopy(ncs_r))
        new_list_of_translations.append(deepcopy(ncs_t))
      elif coordinate_offset is not None:
        # TT 2015-11-02 special case of below where cob is just a translation
        # R' =  R
        # T' =  T + t - R t
        new_list_of_matrices.append(deepcopy(ncs_r))  # these are the same
        from scitbx import matrix
        delta = ncs_r * matrix.col(coordinate_offset)
        t_prime=matrix.col(ncs_t) + \
          matrix.col(coordinate_offset) - matrix.col(delta)
        new_list_of_translations.append(t_prime)

      else:
        # tt 2011-10-02
        # Formula for conversion of NCS rotation matrix and translation
        # relating two points in coordinate system to a second coordinate system
        # The change-of-basis operator is new_x = a x + t
        # The NCS operator is y = R x + T (in original coordinate system)
        # Then if NCS operator in new coordinate system is y' = R' x' + T':
        # R' = a R a_inv
        # T' = a T + t - a R a_inv t = transformed T minus R' * t
        #
        # Derivation:
        # x' and y' (values in new coordinate system) can be written:
        #   x'=a x + t
        #   y'=a y + t
        # Or rewriting:
        #   x= a_inv (x' - t)
        #   y= a_inv (y' - t)
        # Then as y = R x + T  (in original coordinate system), we can say:
        #   a_inv (y' - t) = R (a_inv (x' - t) ) + T
        # Or...
        #   y' = [a R a_inv] x' - [a R a_inv ] t + t + a t
        # So that:
        #   R' = a R a_inv
        #   T' = a T + t - a R a_inv t = transformed T minus R' * t

        # matrices are a ncs_r a_inv
        ncs_r_prime=a * ncs_r * a_inv
        new_list_of_matrices.append(ncs_r_prime)

        # translation vectors are partly a * ncs_t + t (the cob operator)
        frac=unit_cell.fractionalize(ncs_t)
        new_frac = change_of_basis_operator.c() * frac
        new_ncs_t=new_unit_cell.orthogonalize(new_frac)
        # translation vectors depend on the change of basis and the rotation
        # as well as the change-of-basis operator
        t_as_col=change_of_basis_operator.c().t().as_rational().as_float()
        # the basis translation in orig coordinate system
        cob_trans=unit_cell.orthogonalize(t_as_col)
        # correction for the basis translation in new coordinate system
        delta = ncs_r_prime * cob_trans
        t_prime=matrix.col(new_ncs_t) - matrix.col(delta)
        new_list_of_translations.append(t_prime)

    return new_list_of_matrices,new_list_of_translations

  def copy_vector_list(self,list_of_vectors,
      change_of_basis_operator=None,
      coordinate_offset=None,
      scale_factor=None,
         unit_cell=None,new_unit_cell=None):
    from scitbx.math import  matrix
    new_vector_list=[]
    for vector in list_of_vectors:
      if scale_factor is not None:
        new_vector=scale_factor*matrix.col(vector)
      elif change_of_basis_operator is None and coordinate_offset is None:
        new_vector=deepcopy(vector)
      else:
        new_vector=self.apply_cob_to_vector(vector=vector,
          change_of_basis_operator=change_of_basis_operator,
          coordinate_offset=coordinate_offset,
           unit_cell=unit_cell,new_unit_cell=new_unit_cell)
      new_vector_list.append(new_vector)
    return new_vector_list

  def deep_copy(self,change_of_basis_operator=None,unit_cell=None,
      coordinate_offset=None,
      new_unit_cell=None,
      scale_factor=None,
      extract_point_group_symmetry=None,
      ops_to_keep=None,
      hierarchy_to_match_order=None):  # make full copy;
    # optionally apply change-of-basis operator (requires old, new unit cells)
    # optionally apply coordinate_offset (adding coordinate_offset to coords)
    # optionally sort operators to match order in hierarchy
    # optionally apply scale factor (magnification)
    # optionally keep only ops_to_keep operators
    # optionaly extract point group symmetry

    # Can do only one of the above five things at most
    assert [change_of_basis_operator,scale_factor,
      coordinate_offset,ops_to_keep,hierarchy_to_match_order,
      extract_point_group_symmetry].count(None)>=4

    if hierarchy_to_match_order and self._chain_residue_id is not None:
      return self.deep_copy_order(
         hierarchy_to_match_order=hierarchy_to_match_order)

    if ops_to_keep is not None:
      return self.deep_copy_ops_to_keep(ops_to_keep=ops_to_keep)

    if extract_point_group_symmetry:
      return self.extract_point_group_symmetry()

    from mmtbx.ncs.ncs import ncs
    new=ncs_group()
    new._chain_residue_id=self._chain_residue_id
    new._rmsd_list=deepcopy(self._rmsd_list)
    new._residues_in_common_list=deepcopy(self._residues_in_common_list)

    # centers simply get affected by the change of basis operator if present
    #   or scale_factor
    new._centers=self.copy_vector_list(self._centers,
      change_of_basis_operator=change_of_basis_operator,
      coordinate_offset=coordinate_offset,
      scale_factor=scale_factor,
         unit_cell=unit_cell,new_unit_cell=new_unit_cell)

    # matrices and translations may need to be adjusted if change of basis set
    #  Scale_factor applied to translations
    new._rota_matrices,new._translations_orth=self.copy_rot_trans(
       self._rota_matrices,self._translations_orth,
         scale_factor=scale_factor,
         coordinate_offset=coordinate_offset,
         unit_cell=unit_cell,new_unit_cell=new_unit_cell)

    new._n_ncs_oper=deepcopy(self._n_ncs_oper)
    new._source_of_ncs_info=self._source_of_ncs_info
    new._ncs_domain_pdb=deepcopy(self._ncs_domain_pdb)
    new._cc=deepcopy(self._cc)
    new._note=deepcopy(self._note)
    new._exclude_h=self._exclude_h
    new._exclude_d=self._exclude_d
    return new

  def deep_copy_ops_to_keep(self,ops_to_keep=None):
    # keep only ops_to_keep operators
    assert ops_to_keep is not None

    new=self.deep_copy() # exact copy.  Now remove all except ops_to_keep

    new._n_ncs_oper=0
    new._rota_matrices=[]
    new._rota_matrices_inv=[]
    new._translations_orth=[]
    new._translations_orth_inv=[]
    new._residues_in_common_list=[]
    new._centers=[]

    new._rmsd_list=[]
    new._residues_in_common_list=[]

    if self._chain_residue_id:
      [group,residue_range_list]=self._chain_residue_id
    else:
      group=self._n_ncs_oper*[None]
      residue_range_list=self._n_ncs_oper*[None]
    new_residue_range_list=[]
    new_group=[]

    for i in range(self._n_ncs_oper):
      if i in ops_to_keep:
        new._n_ncs_oper+=1
        new._rota_matrices.append(self.rota_matrices()[i])
        new._rota_matrices_inv.append(self.rota_matrices_inv()[i])
        new._translations_orth.append(self.translations_orth()[i])
        new._translations_orth_inv.append(self.translations_orth_inv()[i])
        new._rmsd_list.append(self._rmsd_list[i])
        new._residues_in_common_list.append(self._residues_in_common_list[i])
        new._centers.append(self._centers[i])
        new_residue_range_list.append(residue_range_list[i])
        new_group.append(group[i])

    if self._chain_residue_id:
      new._chain_residue_id=[new_group,new_residue_range_list]
    else:
      new._chain_residue_id=None
    return new

  def get_order_dict(self,hierarchy_to_match_order=None):
    self.chain_id_from_index={}
    self.index_from_chain_id={}
    i=0
    for m in hierarchy_to_match_order.models()[:1]:
      for chain in m.chains():
        id=remove_single_quotes(chain.id)
        self.chain_id_from_index[i]=id
        self.index_from_chain_id[id]=i
        i+=1

  def get_new_group(self,hierarchy_to_match_order=None):
    # change the order of the operators to match hierarchy
    self.get_order_dict(hierarchy_to_match_order=hierarchy_to_match_order)

    # figure out what is the new order of groups
    sort_list=[]
    [group,residue_range_list] = self._chain_residue_id
    for x in group:
      id=self.index_from_chain_id.get(x)
      assert id is not None
      sort_list.append([id,x])
    sort_list.sort(key=itemgetter(0))
    new_group=[]
    for [id,x] in sort_list:
      new_group.append(x)

    # Identify which operator is the new first one
    first_chain_id=new_group[0]
    i=0
    first_op=None
    for chain_id in group:
      if chain_id==first_chain_id:
        first_op=i
      i+=1
    assert first_op is not None
    return new_group,first_op

  def deep_copy_order(self,hierarchy_to_match_order=None):  # make full copy;
    assert self._chain_residue_id is not None

    # Get the new order of chain IDs
    new_group,first_op=self.get_new_group(
      hierarchy_to_match_order=hierarchy_to_match_order)

    from mmtbx.ncs.ncs import ncs
    new=ncs_group()
    new._chain_residue_id=self._chain_residue_id
    new._rmsd_list=deepcopy(self._rmsd_list)
    new._residues_in_common_list=deepcopy(self._residues_in_common_list)

    # now adjust all the operators so that the reference is first_op
    # operator j maps copy j on to copy 0.
    # we want operator j to map copy j onto copy first_op. First map to
    #  copy 0 then map copy 0 to copy first_op
    #  Rx + T =  Rinv_fo (Rj x + Tj) + Tinv_fo
    #  ==> R= Rinv_fo Rj   T = Rinv_fo Tj + Tinv_fo
    # check: if fo=0 then Rinv_fo=U Tinv_fo=0 -> R=Rj and T=Tj ok.

    # centers are the same
    new._centers=deepcopy(self._centers)
    new._rota_matrices=[]
    new._translations_orth=[]
    r_first_op_inv=self._rota_matrices[first_op].inverse()
    t_first_op_inv=-1.*r_first_op_inv*self._translations_orth[first_op]

    for r,t in zip(self._rota_matrices,self._translations_orth):
      new_r=r_first_op_inv*r
      new_t=r_first_op_inv*t + t_first_op_inv

      new._rota_matrices.append(new_r)
      new._translations_orth.append(new_t)
    new._n_ncs_oper=deepcopy(self._n_ncs_oper)
    new._source_of_ncs_info=self._source_of_ncs_info
    new._ncs_domain_pdb=deepcopy(self._ncs_domain_pdb)
    new._cc=deepcopy(self._cc)
    new._note=deepcopy(self._note)
    new._exclude_h=self._exclude_h
    new._exclude_d=self._exclude_d

    # Now just change the order of everything
    translations_orth=[]
    rota_matrices=[]
    centers=[]
    rmsd_list=[]
    residues_in_common_list=[]
    group=[]
    residue_range_list=[]
    # NOTE: [group,residue_range_list] = new._chain_residue_id

    for chain_id in new_group:
      for t,r,c,rmsd,res_in_common,g,res_range in zip(
          new._translations_orth,
          new._rota_matrices,
          new._centers,
          new._rmsd_list,
          new._residues_in_common_list,
          new._chain_residue_id[0],
          new._chain_residue_id[1]):
        if g==chain_id: # this is the one
          translations_orth.append(t)
          rota_matrices.append(r)
          centers.append(c)
          rmsd_list.append(rmsd)
          residues_in_common_list.append(res_in_common)
          group.append(g)
          residue_range_list.append(res_range)

    new._translations_orth=translations_orth
    new._rota_matrices=rota_matrices
    new._centers=centers
    new._rmsd_list=rmsd_list  # NOTE will not be correct perhaps leave out
    new._residues_in_common_list=residues_in_common_list
    new._chain_residue_id=[group,residue_range_list]

    assert group==new_group
    chain_residue_id=[group,residue_range_list]
    return new


  def display_summary(self,verbose=None):
    text=""
    text+="\nSummary of NCS group with "+str(self.n_ncs_oper())+" operators:"
    i=0
    if verbose:
      if self._chain_residue_id:
        text+="\nID of chain/residue where these apply: "+\
           str(self._chain_residue_id)
      if self._rmsd_list and self._chain_residue_id:
        text+="\nRMSD (A) from chain "+str(self._chain_residue_id[0][0])+':'+\
         self.print_list(self._rmsd_list)
      if self._residues_in_common_list and self._chain_residue_id:
        text+="\nNumber of residues matching chain "+\
            str(self._chain_residue_id[0][0])+':'+\
             str(self._residues_in_common_list)
      if self._source_of_ncs_info:
        text+="\nSource of NCS info: "+str(self._source_of_ncs_info)
      if self._ncs_domain_pdb:
        text+="\nNCS domains represented by: "+str(self._ncs_domain_pdb)
      if self._cc:
        text+="\nCorrelation of NCS: "+str(self._cc)
      if self._note:
        text+="\nNOTE: "+str(self._note)
      for center,trans_orth,ncs_rota_matr in zip (
         self._centers, self._translations_orth,self._rota_matrices):
        if center is None: continue
        i+=1
        text+="\n\nOPERATOR "+str(i)
        text+="\nCENTER: "+" %8.4f  %8.4f  %8.4f" %tuple(center)
        r = ncs_rota_matr.elems
        text+="\n\nROTA 1: "+" %8.4f  %8.4f  %8.4f" %tuple(r[0:3])
        text+="\nROTA 2: "+" %8.4f  %8.4f  %8.4f" %tuple(r[3:6])
        text+="\nROTA 3: "+" %8.4f  %8.4f  %8.4f" %tuple(r[6:9])
        text+="\nTRANS:  "+" %8.4f  %8.4f  %8.4f" %tuple(trans_orth)
      text+="\n"
    return text

  def format_group_specification(self):
    if not self._chain_residue_id or len(self._chain_residue_id)<2:
      return ""

    # Need to test for existence because we might have operators or
    # chain specifications but not both

    if self._chain_residue_id is not None:
      [group,residue_range_list] = self._chain_residue_id
    else:
      group=self.n_ncs_oper()*[None]
      residue_range_list=self.n_ncs_oper()*[None]

    if self._centers is not None:
      [centers, translations_orth,rota_matrices]=\
         [self._centers, self._translations_orth,self._rota_matrices]
    else:
      centers=self.n_ncs_oper()*[None]
      translations_orth=self.n_ncs_oper()*[None]
      rota_matrices=self.n_ncs_oper()*[None]

    if self._rmsd_list is not None:
       rmsd_list=self._rmsd_list
    else:
      rmsd_list=self.n_ncs_oper()*[None]

    if self._residues_in_common_list is not None:
       residues_in_common_list=self._residues_in_common_list
    else:
      residues_in_common_list=self.n_ncs_oper()*[None]

    text="\nnew_ncs_group\n"
    if self._cc is not None: text+="NCS_CC "+str(self._cc)+"\n"
    if self._note is not None: text+="NOTE "+str(self._note)+"\n"
    if self._ncs_domain_pdb is not None:
      text+="  NCS_DOMAIN_PDB "+str(self._ncs_domain_pdb)+"\n"

    count=0
    for id,residue_ranges, center,trans_orth,ncs_rota_matr, \
        rmsd,common in zip (
        group,residue_range_list,
        centers, translations_orth,rota_matrices,
        rmsd_list,residues_in_common_list):
     count+=1
     text+='new_operator\n'
     if center is not None:
       for j in range(3):
         text+="\nrota_matrix "+" %8.4f  %8.4f  %8.4f" %tuple(
          ncs_rota_matr.elems[j*3:j*3+3])
       text+="\ntran_orth  "+" %8.4f  %8.4f  %8.4f" %tuple(trans_orth)
       text+="\n"
       text+="\ncenter_orth "+" %8.4f  %8.4f  %8.4f" %tuple(center)
       text+="\n"

     if id is not None: text+="CHAIN "+str(id)+ "\n"
     if rmsd is not None: text+="RMSD "+str(rmsd)+ "\n"
     if common is not None: text+="MATCHING "+str(common)+ "\n"

     if residue_ranges is not None and residue_ranges:
       for residue_range in residue_ranges:
         text+="  RESSEQ "
         text+=str(residue_range[0])+":"+str(residue_range[1])+"\n"
       text+="\n"
    return text

  def format_for_phenix_refine(self, prefix="pdb_interpretation.ncs_group"):
    if not self._chain_residue_id or len(self._chain_residue_id)<2:
      return ""
    exclude=""
    if self._exclude_h: exclude+=" and (not element H) "
    if self._exclude_d: exclude+=" and (not element D) "
    [group,residue_range_list] = self._chain_residue_id
    count=0
    text = []
    for id,residue_ranges in zip (group,residue_range_list):
      count+=1
      if count==1:
        text.append("%s {"%prefix)
        l = "  reference = chain '{}'".format(id)
      else:
        l = "  selection = chain '{}'".format(id)
      if residue_ranges:
        first=True
        for residue_range in residue_ranges:
          if first:
            first=False
            l += " and (resseq "
          else:
            l += " or resseq  "
          l += str(residue_range[0])+":"+str(residue_range[1])
        l += " ) " + exclude
      text.append(l)
    text.append("}")
    text = '\n'.join(text)
    return text

  def format_for_biomt(self,crystal_number=None,skip_identity_if_first=False,
       ncs_domain_pdb=True):

    serial_number=0
    from iotbx.mtrix_biomt import container

    result=container()
    for t,r in zip (
       self.translations_orth_inv(),self.rota_matrices_inv()):
      serial_number+=1
      result.add(r,t,serial_number, coordinates_present=False)

    return result.format_BIOMT_pdb_string()

  def format_for_resolve(self,crystal_number=None,skip_identity_if_first=False,
       ncs_domain_pdb=True):
    text="new_ncs_group"
    if ncs_domain_pdb and self._ncs_domain_pdb is not None:
        text+="\nncs_domain_pdb "+str(self._ncs_domain_pdb)+"\n"
    i=0
    for center,trans_orth,ncs_rota_matr in zip (
       self._centers, self._translations_orth,self._rota_matrices):
      i+=1
      if i==1 and skip_identity_if_first and \
        is_identity(ncs_rota_matr,trans_orth): continue
      for j in range(3):
       text+="\nrota_matrix "+" %8.4f  %8.4f  %8.4f" %tuple(
          ncs_rota_matr[j*3:j*3+3])
      text+="\ntran_orth  "+" %8.4f  %8.4f  %8.4f" %tuple(trans_orth)
      text+="\n"
      text+="\ncenter_orth "+" %8.4f  %8.4f  %8.4f" %tuple(center)
      if crystal_number is not None:
        text+="\ncrystal_number "+str(crystal_number)
      text+="\n"
    return text

  def n_ncs_oper(self):
    return self._n_ncs_oper

  def chain_residue_id(self):
    return self._chain_residue_id

  def rmsd_list(self):
    return self._rmsd_list

  def cc(self):
    return self._cc

  def note(self):
    return self._note

  def add_rmsd_list(self,rmsd_list):
    self._rmsd_list=rmsd_list

  def add_cc(self,cc):
    self._cc=cc

  def add_note(self,note):
    self._note=note

  def residues_in_common_list(self):
    return self._residues_in_common_list

  def add_residues_in_common_list(self,residues_in_common_list):
    self._residues_in_common_list=residues_in_common_list

  def add_chain_residue_id(self,chain_residue_id):
    self._chain_residue_id=chain_residue_id


  def centers(self):
    return self._centers

  def translations_orth(self):
    return self._translations_orth

  def rota_matrices(self):
    return self._rota_matrices

  def translations_orth_inv(self):
    if not hasattr(self,"_translations_orth_inv"):
      self.get_inverses()
    return self._translations_orth_inv

  def rota_matrices_inv(self):
    if not hasattr(self,"_rota_matrices_inv"):
      self.get_inverses()
    return self._rota_matrices_inv

  def delete_inv(self):
    if hasattr(self,"_rota_matrices_inv"):
      del self._rota_matrices_inv
    if hasattr(self,"_translations_orth_inv"):
      del self._translations_orth_inv

  def adjust_magnification(self,magnification=None):
    if not magnification or magnification==1:
      return # nothing to do

    self._translations_orth=self.copy_vector_list(self._translations_orth,
      scale_factor=magnification)
    self._centers=self.copy_vector_list(self._centers,
      scale_factor=magnification)

    self.get_inverses()

  def invert_matrices(self):
    self.get_inverses()
    # move the inverses to std
    self._translations_orth=deepcopy(self._translations_orth_inv)
    self._rota_matrices=deepcopy(self._rota_matrices_inv)
    self.get_inverses()

  def rotate_matrices(self,rot=None):
    translations_orth_rot=deepcopy(self._translations_orth)
    rota_matrices_rot=deepcopy(self._rota_matrices)

    self._translations_orth=[]
    self._rota_matrices=[]

    # create r_rot, t_rot such that r_rot x + t_rot is the same as
    #       rot * ( r [rot_inv x ] + t) : rotate x to orig, apply, r t, rotate back
    # r_rot(x)+t_rot ==  rot * ( r [rot_inv x ] + t)
    #  So:  t_rot=rot t
    #       r_rot=rot r rot_inv

    rot_inv=rot.inverse()
    for r,t in zip(rota_matrices_rot,translations_orth_rot):
      r_rot=rot *(r*rot_inv)
      t_rot=rot*t
      self._rota_matrices.append(r_rot)
      self._translations_orth.append(t_rot)
    self.get_inverses()

  def get_inverses(self):
    self._translations_orth_inv=[]
    self._rota_matrices_inv=[]
    for r,t in zip(self.rota_matrices(),self.translations_orth()):
      r_inv=r.inverse()
      t_inv=-1.*r_inv*t
      self._rota_matrices_inv.append(r_inv)
      self._translations_orth_inv.append(t_inv)

  def rotations_translations_forward_euler(self):
    # note usual rt is from molecule j to molecule 1. Here it is opposite.
    from scitbx.math import euler_angles
    rotations_forward_euler=[]
    translations_forward_euler=[]
    for r,t in zip(self._rota_matrices,self._translations_orth):
      r_inv=r.inverse()
      t_inv=-1.*r_inv*t
      r_inv_euler=euler_angles.zyz_angles(r_inv)
      rotations_forward_euler.append(r_inv_euler)
      translations_forward_euler.append(t_inv)
    return rotations_forward_euler,translations_forward_euler

  def source_of_ncs_info(self):
    return self._source_of_ncs_info

  def ncs_domain_pdb(self):
    return self._ncs_domain_pdb

  def print_list(self,list_of_real):
    text=""
    for number in list_of_real:
     text+="  "+str(self.round(number,2))
    return text

  def round(self,value,n_digit):  # round off value to n_digit digits
    if type(value) == type(1):
       return self.round(float(value),n_digit)
    if type(value) != type(1.0):
       return self.round(0.0,1)

    if n_digit == 0:
      rounder=1
    else:
      rounder=10**n_digit
    if value >= 0:
      rounded=float(int(0.5+value*rounder))/rounder
    else:
      value1=-1.*value
      rounded=float(int(0.5+value1*rounder))/rounder
      rounded=-1.*rounded
    return rounded

  def extract_point_group_symmetry(self,
   tol_r=None,
   abs_tol_t=None,
   rel_tol_t=None):
    # sequentially remove operators until pg symmetry is achieved or none
    # are left
   ops_to_keep=[self.identity_op_id()]
   n_ops=len(self.rota_matrices_inv())
   for test_op in range(n_ops):
     if test_op in ops_to_keep: continue
     test_ops_to_keep=ops_to_keep+[test_op]
     new_group=self.deep_copy(
         ops_to_keep=test_ops_to_keep)
     if new_group.is_point_group_symmetry(
         tol_r=default_tol_r,
         abs_tol_t=default_abs_tol_t,
         rel_tol_t=default_rel_tol_t,
         symmetry_to_match=self):  # test_op keeps us in the original set
       ops_to_keep.append(test_op)
   new_group=self.deep_copy(
         ops_to_keep=ops_to_keep)
   if new_group.is_point_group_symmetry(
         tol_r=default_tol_r,
         abs_tol_t=default_abs_tol_t,
         rel_tol_t=default_rel_tol_t):
     return new_group
   else:
     return None

  def is_similar_ncs_group(self, other,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t,
   allow_self_contained_in_other = True):
    '''
     return True if all operations of self match one of other
    '''

    if (not allow_self_contained_in_other) and \
       len(self.rota_matrices_inv()) != len(other.rota_matrices_inv()):
      return False

    if len(self.rota_matrices_inv()) < 1:
      return False

    for r,t in zip(self.rota_matrices_inv(),self.translations_orth_inv()):
        is_similar=False
        for r2,t2 in zip(other.rota_matrices_inv(),
           other.translations_orth_inv()):
          if is_same_transform(r,t,r2,t2,tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t):
            is_similar=True
            break
        if not is_similar:
          return False
    return True

  def sort_by_z_translation(self,tol_z=0.01):
    n=len(self.rota_matrices_inv())
    z_translations=[]
    sort_z_translations=[]
    for i1 in range(n): # figure out if translation is along z
      z_translations.append(self.translations_orth_inv()[i1][2])
      sort_z_translations.append([self.translations_orth_inv()[i1][2],i1])
    rota_matrices_sav=deepcopy(self._rota_matrices)
    translations_orth_sav=deepcopy(self._translations_orth)

    # sort the z-translations to reorder the matrices. Could be backwards
    sort_z_translations.sort()
    sorted_indices=[]
    sorted_z=[]
    n_plus_one=0
    n_minus_one=0
    delta=None
    all_same_delta=True
    for z,i1 in sort_z_translations:
      if sorted_indices:
        if i1==sorted_indices[-1]+1: n_plus_one+=1
        if i1==sorted_indices[-1]-1: n_minus_one+=1
        delta_z=z-sorted_z[-1]
        if delta is None:
          delta=delta_z
        elif abs(delta-delta_z)>tol_z:
          is_helical=False # XX not used
      sorted_indices.append(i1)
      sorted_z.append(z)
    if n_minus_one>n_plus_one:
      sorted_indices.reverse()
    self._helix_z_translation=delta

    # Reorder the operators:
    self._rota_matrices=len(rota_matrices_sav)*[None]
    self._translations_orth=len(rota_matrices_sav)*[None]
    for i1,i2 in zip(sorted_indices,range(n)):
      self._rota_matrices[i2]=rota_matrices_sav[i1]
      self._translations_orth[i2]=translations_orth_sav[i1]
    self.delete_inv() # remove the inv matrices/rotations so they regenerate
    if len(self._rota_matrices)<2:
      self._helix_theta=None
    else:
      self._helix_theta=self.get_theta_along_z(
        self._rota_matrices[0],self._rota_matrices[1])
    self.get_inverses()
    return sorted_indices

  def get_trans_along_z(self,t0,t1):
    return t1[2]-t0[2]

  def get_theta_along_z(self,m0,m1):
    import math
    cost=m0[0]
    sint=m0[1]
    t0=180.*math.atan2(sint,cost)/3.14159
    cost=m1[0]
    sint=m1[1]
    t1=180.*math.atan2(sint,cost)/3.14159
    return t1 - t0

  def is_helical_along_z(self,tol_z=0.01,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t):
    # This assumes the operators are in order, but allow special case
    #   where the identity operator is placed at the beginning but belongs
    #   at the end
    # Also assumes the axis of helical symmetry is parallel to the Z-axis.
    #   and returns False if not

    # For helical symmetry sequential application of operators moves up or
    #  down the list by an index depending on the indices of the operators.
    if len(self.rota_matrices_inv()) < 2:
      return False
    if self.is_point_group_symmetry(tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t):
      return False

    n=len(self.rota_matrices_inv())
    if n < 3:
      return False

    is_helical=True
    rota_matrices_sav=deepcopy(self._rota_matrices)
    translations_orth_sav=deepcopy(self._translations_orth)

    sorted_indices=self.sort_by_z_translation(tol_z=tol_z)

    offset_list=[]
    n_missing_list=[]
    self.helix_oper_forwards=None
    self.helix_oper_reverse=None
    self.helix_oper_identity=None
    for i1 in range(n): # figure out offset made by this self.helix_operator
      offset,n_missing=self.oper_adds_offset(i1,tol_r=tol_r,
          abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t)
      offset_list.append(offset)
      n_missing_list.append(n_missing)
      if offset==1:self.helix_oper_forwards=sorted_indices[i1]
      if offset==-1:self.helix_oper_reverse=sorted_indices[i1]
      if offset==0:self.helix_oper_identity=sorted_indices[i1]
    # offset_list should be one instance of each value and will be 0 at the
    #  operator that is unity
    if None in offset_list:
      is_helical=False

    if is_helical:
      ii=offset_list.index(0)
      if not is_identity(
          self.rota_matrices_inv()[ii],self.translations_orth_inv()[ii]):
        is_helical=False

    if is_helical:
      for i1 in range(n):
        if n_missing_list[i1] != abs(i1-ii):
          is_helical=False
          break
    if is_helical:
      offset_list.sort()
      start_value=offset_list[0]
      expected_list=list(range(start_value,start_value+n))
      if offset_list != expected_list:
        is_helical=False
    # restore
    sys.stdout.flush()
    self._rota_matrices=rota_matrices_sav
    self._translations_orth=translations_orth_sav
    self.delete_inv() # remove the inv matrices/rotations so they regenerate
    if is_helical:
      self._have_helical_symmetry=True
      self.tol_z=tol_z
      self.tol_r=tol_r
      self.abs_tol_t=abs_tol_t
      self.rel_tol_t=rel_tol_t
      return True
    else:
      return False

  def get_forwards_reverse_helix(self,r1=None,t1=None,r2=None,t2=None):
    # get the forwards and reverse transforms, deciding which is which based
    # on the order of operators supplied for r1 t1 and r2 t2
    assert self._have_helical_symmetry
    for dir in ['forwards','reverse']:
      if dir=='forwards':
        r_forwards,t_forwards=self.helix_rt_forwards()
        r_reverse,t_reverse=self.helix_rt_reverse()
      else:
        r_forwards,t_forwards=self.helix_rt_reverse()
        r_reverse,t_reverse=self.helix_rt_forwards()

      # apply to n-1 and see if we get n:
      new_r = r_forwards*r1
      new_t= (r_forwards* t1) + t_forwards
      if is_same_transform(new_r,new_t,r2,t2,
         tol_r=self.tol_r,
         abs_tol_t=self.abs_tol_t,
         rel_tol_t=self.rel_tol_t):
        return r_forwards,t_forwards,r_reverse,t_reverse
    from libtbx.utils import Sorry
    raise Sorry(
     "Unable to find forward and reverse operators for this helical symmetry")

  def get_helix_parameters(self,tol_z=default_tol_z):
    from libtbx import group_args
    helix_z_translation=self.get_helix_z_translation()
    helix_theta=self.get_helix_theta()
    if helix_z_translation is not None and helix_theta is not None:
      return group_args(helix_z_translation=helix_z_translation,
        helix_theta=helix_theta)

  def extend_helix_operators(self,z_range=None,tol_z=default_tol_z,
      max_operators=None):
    assert self._have_helical_symmetry
    # extend the operators to go from -z_range to z_range
    rota_matrices_inv_sav=deepcopy(self.rota_matrices_inv())
    translations_orth_inv_sav=deepcopy(self.translations_orth_inv())
    # only apply centers if some existing ones are not zero
    have_non_zero_c=False
    from scitbx import matrix
    for c in self._centers:
      if list(c)!=[0,0,0]:
        have_non_zero_c=True
        break

    sort_list=[]
    for r,t,c in zip(rota_matrices_inv_sav,translations_orth_inv_sav,self._centers):
      z_value=t[2]
      sort_list.append([z_value,r,t,c])
    sort_list.sort(key=itemgetter(0))
    z_first,r_first,t_first,c_first=sort_list[0]
    z_last,r_last,t_last,c_last=sort_list[-1]
    z_next_to_last,r_next_to_last,t_next_to_last,c_next_to_last=sort_list[-2]
    z_translation=self.get_helix_z_translation()
    if not z_translation:
      from libtbx.utils import Sorry
      raise Sorry("Cannot apply extension of helical NCS operators with no"+
        " Z-translation")

    # Figure out which direction to add single shifts to each end
    r_forwards,t_forwards,r_reverse,t_reverse=self.get_forwards_reverse_helix(
      r1=r_next_to_last,t1=t_next_to_last,r2=r_last,t2=t_last)

    if max_operators:
      max_new_each_direction=max(0,
          (1+max_operators-len(rota_matrices_inv_sav))//2)
    else:
      max_new_each_direction=None

    # Add on at end until we get to z_max (or z_min if z_translation<0)
    r_list=[r_last]
    t_list=[t_last]
    c_list=[c_last]
    while 1:
      new_r = r_forwards*r_list[-1]
      new_t= (r_forwards * t_list[-1]) + t_forwards
      new_c= (r_forwards*c_list[-1])+t_forwards
      if max_new_each_direction and len(c_list)>=max_new_each_direction:
        break
      elif is_in_range(new_t[2],-z_range,z_range):
        r_list.append(new_r)
        t_list.append(new_t)
        c_list.append(new_c)
      else:
        break
    rota_matrices_inv=rota_matrices_inv_sav+r_list[1:]
    translations_orth_inv=translations_orth_inv_sav+t_list[1:]
    centers=self._centers+c_list[1:]

    # and for other end
    r_list=[r_first]
    t_list=[t_first]
    c_list=[c_first]
    while 1:
      new_r = r_reverse*r_list[-1]
      new_t= (r_reverse * t_list[-1]) + t_reverse
      new_c= (r_reverse*c_list[-1])+t_reverse
      if max_new_each_direction and len(c_list)>=max_new_each_direction:
        break
      elif is_in_range(new_t[2],-z_range,z_range):
        r_list.append(new_r)
        t_list.append(new_t)
        c_list.append(new_c)
      else:
        break
    rota_matrices_inv+=r_list[1:]
    translations_orth_inv+=t_list[1:]
    centers+=c_list[1:]
    # Now we have a new set...invert and save them
    self._n_ncs_oper=len(rota_matrices_inv)
    self._rota_matrices=[]
    self._translations_orth=[]
    self._centers=[]
    for r_inv,t_inv,c in zip(rota_matrices_inv,translations_orth_inv,centers):
      r_std=r_inv.inverse()
      t_std=-1.*r_std*t_inv
      self._rota_matrices.append(r_std)
      self._translations_orth.append(t_std)
      if have_non_zero_c:
        self._centers.append(c)
      else:
        self._centers.append(matrix.col((0,0,0)))

    if self._rmsd_list:
      self._rmsd_list=len(rota_matrices_inv)*[None]
    if self._residues_in_common_list:
       self._residues_in_common_list=len(rota_matrices_inv)*[None]

    if self._chain_residue_id:
       self._chain_residue_id= [
        len(rota_matrices_inv)*[None],
        len(rota_matrices_inv)*[[]]
         ]

    self.delete_inv()
    self.get_inverses()

    # And reorder them now...
    self.sort_by_z_translation(tol_z=tol_z)

  def get_helix_z_translation(self):
    assert self._have_helical_symmetry
    if hasattr(self,'_helix_z_translation'):
      return self._helix_z_translation
    return None

  def is_point_group_symmetry(self,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t,
   symmetry_to_match=None):
    # return True if any 2 sequential operations is a member of the
    #  set.  Test by sequentially applying all pairs of
    # operators and verifying that the result is a member of the set

    # Allow checking self operators vs some other symmetry object if desired:

    if len(self.rota_matrices_inv()) < 2:
      return False

    if symmetry_to_match is None:
      symmetry_to_match=self

    for r,t in zip(self.rota_matrices_inv(),self.translations_orth_inv()):
      for r1,t1 in zip(self.rota_matrices_inv(),self.translations_orth_inv()):
        new_r = r1 * r
        new_t = (r1 * t) + t1
        is_similar=False
        for r2,t2 in zip(symmetry_to_match.rota_matrices_inv(),
           symmetry_to_match.translations_orth_inv()):
          if is_same_transform(new_r,new_t,r2,t2,tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t):
            is_similar=True
            break
        if not is_similar:
          return False
    self._have_point_group_symmetry=True
    self.tol_r=tol_r
    self.abs_tol_t=abs_tol_t
    self.rel_tol_t=rel_tol_t
    return True

  def sort_by_z_translation(self,tol_z=0.01):
    n=len(self.rota_matrices_inv())
    z_translations=[]
    sort_z_translations=[]
    for i1 in range(n): # figure out if translation is along z
      z_translations.append(self.translations_orth_inv()[i1][2])
      sort_z_translations.append([self.translations_orth_inv()[i1][2],i1])
    rota_matrices_sav=deepcopy(self._rota_matrices)
    translations_orth_sav=deepcopy(self._translations_orth)

    # sort the z-translations to reorder the matrices. Could be backwards
    sort_z_translations.sort()
    sorted_indices=[]
    sorted_z=[]
    n_plus_one=0
    n_minus_one=0
    delta=None
    all_same_delta=True
    for z,i1 in sort_z_translations:
      if sorted_indices:
        if i1==sorted_indices[-1]+1: n_plus_one+=1
        if i1==sorted_indices[-1]-1: n_minus_one+=1
        delta_z=z-sorted_z[-1]
        if delta is None:
          delta=delta_z
        elif abs(delta-delta_z)>tol_z:
          is_helical=False # XX not used
      sorted_indices.append(i1)
      sorted_z.append(z)
    if n_minus_one>n_plus_one:
      sorted_indices.reverse()
    self._helix_z_translation=delta

    # Reorder the operators:
    self._rota_matrices=len(rota_matrices_sav)*[None]
    self._translations_orth=len(rota_matrices_sav)*[None]
    for i1,i2 in zip(sorted_indices,range(n)):
      self._rota_matrices[i2]=rota_matrices_sav[i1]
      self._translations_orth[i2]=translations_orth_sav[i1]
    self.delete_inv() # remove the inv matrices/rotations so they regenerate
    if len(self._rota_matrices)<2:
      self._helix_theta=None
    else:
      self._helix_theta=self.get_theta_along_z(
        self._rota_matrices[0],self._rota_matrices[1])
    self.get_inverses()
    return sorted_indices

  def get_trans_along_z(self,t0,t1):
    return t1[2]-t0[2]

  def get_theta_along_z(self,m0,m1):
    import math
    cost=m0[0]
    sint=m0[1]
    t0=180.*math.atan2(sint,cost)/3.14159
    cost=m1[0]
    sint=m1[1]
    t1=180.*math.atan2(sint,cost)/3.14159
    return t1 - t0

  def is_helical_along_z(self,tol_z=0.01,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t):
    # This assumes the operators are in order, but allow special case
    #   where the identity operator is placed at the beginning but belongs
    #   at the end
    # Also assumes the axis of helical symmetry is parallel to the Z-axis.
    #   and returns False if not

    # For helical symmetry sequential application of operators moves up or
    #  down the list by an index depending on the indices of the operators.
    if len(self.rota_matrices_inv()) < 2:
      return False
    if self.is_point_group_symmetry(tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t):
      return False

    n=len(self.rota_matrices_inv())
    if n < 3:
      return False

    is_helical=True
    rota_matrices_sav=deepcopy(self._rota_matrices)
    translations_orth_sav=deepcopy(self._translations_orth)

    sorted_indices=self.sort_by_z_translation(tol_z=tol_z)

    offset_list=[]
    n_missing_list=[]
    self.helix_oper_forwards=None
    self.helix_oper_reverse=None
    self.helix_oper_identity=None
    for i1 in range(n): # figure out offset made by this self.helix_operator
      offset,n_missing=self.oper_adds_offset(i1,tol_r=tol_r,
          abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t)
      offset_list.append(offset)
      n_missing_list.append(n_missing)
      if offset==1:self.helix_oper_forwards=sorted_indices[i1]
      if offset==-1:self.helix_oper_reverse=sorted_indices[i1]
      if offset==0:self.helix_oper_identity=sorted_indices[i1]
    # offset_list should be one instance of each value and will be 0 at the
    #  operator that is unity
    if None in offset_list:
      is_helical=False

    if is_helical:
      ii=offset_list.index(0)
      if not is_identity(
          self.rota_matrices_inv()[ii],self.translations_orth_inv()[ii]):
        is_helical=False

    if is_helical:
      for i1 in range(n):
        if n_missing_list[i1] != abs(i1-ii):
          is_helical=False
          break
    if is_helical:
      offset_list.sort()
      start_value=offset_list[0]
      expected_list=list(range(start_value,start_value+n))
      if offset_list != expected_list:
        is_helical=False
    # restore
    sys.stdout.flush()
    self._rota_matrices=rota_matrices_sav
    self._translations_orth=translations_orth_sav
    self.delete_inv() # remove the inv matrices/rotations so they regenerate
    if is_helical:
      self._have_helical_symmetry=True
      self.tol_z=tol_z
      self.tol_r=tol_r
      self.abs_tol_t=abs_tol_t
      self.rel_tol_t=rel_tol_t
      return True
    else:
      return False

  def get_forwards_reverse_helix(self,r1=None,t1=None,r2=None,t2=None):
    # get the forwards and reverse transforms, deciding which is which based
    # on the order of operators supplied for r1 t1 and r2 t2
    assert self._have_helical_symmetry
    for dir in ['forwards','reverse']:
      if dir=='forwards':
        r_forwards,t_forwards=self.helix_rt_forwards()
        r_reverse,t_reverse=self.helix_rt_reverse()
      else:
        r_forwards,t_forwards=self.helix_rt_reverse()
        r_reverse,t_reverse=self.helix_rt_forwards()

      # apply to n-1 and see if we get n:
      new_r = r_forwards*r1
      new_t= (r_forwards* t1) + t_forwards
      if is_same_transform(new_r,new_t,r2,t2,
         tol_r=self.tol_r,
         abs_tol_t=self.abs_tol_t,
         rel_tol_t=self.rel_tol_t):
        return r_forwards,t_forwards,r_reverse,t_reverse
    from libtbx.utils import Sorry
    raise Sorry(
     "Unable to find forward and reverse operators for this helical symmetry")

  def get_helix_parameters(self,tol_z=default_tol_z):
    from libtbx import group_args
    helix_z_translation=self.get_helix_z_translation()
    helix_theta=self.get_helix_theta()
    if helix_z_translation is not None and helix_theta is not None:
      return group_args(helix_z_translation=helix_z_translation,
        helix_theta=helix_theta)

  def extend_helix_operators(self,z_range=None,tol_z=default_tol_z,
      max_operators=None):
    assert self._have_helical_symmetry
    # extend the operators to go from -z_range to z_range
    rota_matrices_inv_sav=deepcopy(self.rota_matrices_inv())
    translations_orth_inv_sav=deepcopy(self.translations_orth_inv())
    # only apply centers if some existing ones are not zero
    have_non_zero_c=False
    from scitbx import matrix
    for c in self._centers:
      if list(c)!=[0,0,0]:
        have_non_zero_c=True
        break

    sort_list=[]
    for r,t,c in zip(rota_matrices_inv_sav,translations_orth_inv_sav,self._centers):
      z_value=t[2]
      sort_list.append([z_value,r,t,c])
    sort_list.sort(key=itemgetter(0))
    z_first,r_first,t_first,c_first=sort_list[0]
    z_last,r_last,t_last,c_last=sort_list[-1]
    z_next_to_last,r_next_to_last,t_next_to_last,c_next_to_last=sort_list[-2]
    z_translation=self.get_helix_z_translation()
    if not z_translation:
      from libtbx.utils import Sorry
      raise Sorry("Cannot apply extension of helical NCS operators with no"+
        " Z-translation")

    # Figure out which direction to add single shifts to each end
    r_forwards,t_forwards,r_reverse,t_reverse=self.get_forwards_reverse_helix(
      r1=r_next_to_last,t1=t_next_to_last,r2=r_last,t2=t_last)

    if max_operators:
      max_new_each_direction=max(0,
          (1+max_operators-len(rota_matrices_inv_sav))//2)
    else:
      max_new_each_direction=None

    # Add on at end until we get to z_max (or z_min if z_translation<0)
    r_list=[r_last]
    t_list=[t_last]
    c_list=[c_last]
    while 1:
      new_r = r_forwards*r_list[-1]
      new_t= (r_forwards * t_list[-1]) + t_forwards
      new_c= (r_forwards*c_list[-1])+t_forwards
      if max_new_each_direction and len(c_list)>=max_new_each_direction:
        break
      elif is_in_range(new_t[2],-z_range,z_range):
        r_list.append(new_r)
        t_list.append(new_t)
        c_list.append(new_c)
      else:
        break
    rota_matrices_inv=rota_matrices_inv_sav+r_list[1:]
    translations_orth_inv=translations_orth_inv_sav+t_list[1:]
    centers=self._centers+c_list[1:]

    # and for other end
    r_list=[r_first]
    t_list=[t_first]
    c_list=[c_first]
    while 1:
      new_r = r_reverse*r_list[-1]
      new_t= (r_reverse * t_list[-1]) + t_reverse
      new_c= (r_reverse*c_list[-1])+t_reverse
      if max_new_each_direction and len(c_list)>=max_new_each_direction:
        break
      elif is_in_range(new_t[2],-z_range,z_range):
        r_list.append(new_r)
        t_list.append(new_t)
        c_list.append(new_c)
      else:
        break
    rota_matrices_inv+=r_list[1:]
    translations_orth_inv+=t_list[1:]
    centers+=c_list[1:]
    # Now we have a new set...invert and save them
    self._n_ncs_oper=len(rota_matrices_inv)
    self._rota_matrices=[]
    self._translations_orth=[]
    self._centers=[]
    for r_inv,t_inv,c in zip(rota_matrices_inv,translations_orth_inv,centers):
      r_std=r_inv.inverse()
      t_std=-1.*r_std*t_inv
      self._rota_matrices.append(r_std)
      self._translations_orth.append(t_std)
      if have_non_zero_c:
        self._centers.append(c)
      else:
        self._centers.append(matrix.col((0,0,0)))

    if self._rmsd_list:
      self._rmsd_list=len(rota_matrices_inv)*[None]
    if self._residues_in_common_list:
       self._residues_in_common_list=len(rota_matrices_inv)*[None]

    if self._chain_residue_id:
       self._chain_residue_id= [
        len(rota_matrices_inv)*[None],
        len(rota_matrices_inv)*[[]]
         ]

    self.delete_inv()
    self.get_inverses()

    # And reorder them now...
    self.sort_by_z_translation(tol_z=tol_z)

  def get_helix_z_translation(self):
    assert self._have_helical_symmetry
    if hasattr(self,'_helix_z_translation'):
      return self._helix_z_translation
    return None

  def get_helix_theta(self):
    assert self._have_helical_symmetry
    if hasattr(self,'_helix_theta'):
      return self._helix_theta
    return None

  def helix_rt_reverse(self):
    assert self._have_helical_symmetry
    # Return r and t for moving one reverse in a helix
    if not hasattr(self,'helix_oper_reverse') or not self.helix_oper_reverse:
      if not hasattr(self,'helix_oper_forwards') or \
         not self.helix_oper_forwards: # no info, quit
        return None,None
      else: # generate from forwards:
        r_forwards,t_forwards=self.helix_rt_forwards()
        r_reverse=r_forwards.inverse()
        t_reverse=-1.*r_reverse*t_forwards
        return r_reverse,t_reverse

    i1=self.helix_oper_reverse
    r1=self.rota_matrices_inv()[i1]
    t1=self.translations_orth_inv()[i1]
    return r1,t1

  def helix_rt_forwards(self):
    assert self._have_helical_symmetry
    # Return r and t for moving one forwards in a helix
    if not hasattr(self,'helix_oper_forwards') or not self.helix_oper_forwards:
      if not hasattr(self,'helix_oper_reverse') or \
         not self.helix_oper_reverse: # no info, quit
        return None,None
      else: # generate from reverse:
        r_reverse,t_reverse=self.helix_rt_reverse()
        r_forwards=r_reverse.inverse()
        t_forwards=-1.*r_forwards*t_reverse
        return r_forwards,t_forwards

    i1=self.helix_oper_forwards
    r1=self.rota_matrices_inv()[i1]
    t1=self.translations_orth_inv()[i1]
    return r1,t1

  def oper_adds_offset(self,i1,tol_r=None,abs_tol_t=None,rel_tol_t=None):
    # figure out what operator is created from operator i1 + any other one
    n=len(self.rota_matrices_inv())
    r1=self.rota_matrices_inv()[i1]
    t1=self.translations_orth_inv()[i1]
    offset_list=[]
    missing_list=[]
    for i in range(n): # apply i1+i and see what k we get (k-i should be const)
      r=self.rota_matrices_inv()[i]
      t=self.translations_orth_inv()[i]
      new_r = r1 * r
      new_t = (r1 * t) + t1
      match_offset=None
      for j in range(n):
        r2=self.rota_matrices_inv()[j]
        t2=self.translations_orth_inv()[j]
        if is_same_transform(new_r,new_t,r2,t2,
           tol_r=tol_r,
           abs_tol_t=abs_tol_t,
           rel_tol_t=rel_tol_t):
          match_offset=j-i
      if match_offset is not None:
        if not match_offset in offset_list: offset_list.append(match_offset)
      else:
        missing_list.append(i)
    if len(offset_list)==1:
      return offset_list[0],len(missing_list)
    else:
      return None,None



  def identity_op_id(self):
    # return id of identity operator
    id=0
    for center,trans_orth,ncs_rota_matr in zip (
       self._centers, self._translations_orth,self._rota_matrices):
      if is_identity(ncs_rota_matr,trans_orth):
         return id
      id+=1
    return None

  def map_inside_unit_cell(self,unit_cell=None):
    # map all the operators inside the unit cell.  Must be supplied
    assert unit_cell is not None
    if len(self._centers)==0: return

    new_centers=[]
    new_translations_orth=[]
    from scitbx.math import  matrix
    #rotation matrices do not change, just translations
    # find the identity:
    first_coordinate_offset=None
    for center,trans_orth,ncs_rota_matr in zip (
       self._centers, self._translations_orth,self._rota_matrices):
      if is_identity(ncs_rota_matr,trans_orth):
        first_coordinate_offset=matrix.col(offset_inside_cell(
          center,unit_cell=unit_cell))
        break
    if first_coordinate_offset is None:
      raise Sorry("Identity not found in NCS matrices?")
    for center,trans_orth,ncs_rota_matr in zip (
       self._centers, self._translations_orth,self._rota_matrices):
      coordinate_offset=offset_inside_cell(center,unit_cell=unit_cell)

      new_centers.append(matrix.col(center)+matrix.col(coordinate_offset))
      #  T'=T - R x_i + x_1
      delta = matrix.col(ncs_rota_matr * matrix.col(coordinate_offset))
      t_prime=matrix.col(trans_orth) - delta + first_coordinate_offset
      new_translations_orth.append(t_prime)

    self._centers=new_centers
    self._translations_orth=new_translations_orth

  def add_identity_op(self):
    if self.identity_op_id() is not None:
       return # nothing to do

    from scitbx import matrix

    self._rota_matrices.append(matrix.sqr(
      [1.,0.,0.]+[0.,1.,0.]+[0.,0.,1.]))
    self._translations_orth.append(matrix.col([0.,0.,0.]))
    self._centers.append(matrix.col([0.,0.,0.]))
    self._n_ncs_oper+=1

class ncs:
  def __init__(self,exclude_h=None,exclude_d=None):
    self._ncs_groups=[]  # each group is an ncs_group object
    self.source_info=None
    self._ncs_read=False
    self._exclude_h=exclude_h
    self._exclude_d=exclude_d
    self._ncs_obj = None
    self._ncs_name = None # an optional name like "D3"
    self._shift_cart = (0,0,0)  # shift to place object in original location

  def __repr__(self):
    text = "NCS object with %s groups: " %(len(self._ncs_groups))
    for g in self._ncs_groups:
      text+=str(g)
    return text

  def deep_copy(self,change_of_basis_operator=None,unit_cell=None,
      coordinate_offset=None,
      scale_factor=None,
      new_unit_cell=None,
      ops_to_keep=None,
      extract_point_group_symmetry=None,
      hierarchy_to_match_order=None):  # make a copy
    from mmtbx.ncs.ncs import ncs

    # make new ncs object with same overall params as this one:
    new=ncs(exclude_h=self._exclude_h,exclude_d=self._exclude_d)
    new.source_info=self.source_info
    new._ncs_name=self._ncs_name
    new._ncs_read=self._ncs_read
    new._shift_cart=deepcopy(self._shift_cart)  # shift_cart is what was applied
    if coordinate_offset:
       new._shift_cart=tuple(
         [a+b for a,b in zip(new._shift_cart,coordinate_offset)])
    # deep_copy over all the ncs groups:
    for ncs_group in self._ncs_groups:
      new_group=ncs_group.deep_copy(
         change_of_basis_operator=change_of_basis_operator,
         coordinate_offset=coordinate_offset,
         scale_factor=scale_factor,
         unit_cell=unit_cell,new_unit_cell=new_unit_cell,
         ops_to_keep=ops_to_keep,
         extract_point_group_symmetry=extract_point_group_symmetry,
         hierarchy_to_match_order=hierarchy_to_match_order)

      new._ncs_groups.append(new_group)
    return new

  def change_of_basis(self,change_of_basis_operator=None,unit_cell=None,
      new_unit_cell=None):
    if change_of_basis_operator is None or unit_cell is None or\
        new_unit_cell is None:
       raise Sorry("For change of basis unit_cell, "+
           "new_unit_cell and operator are all required")
    return self.deep_copy(change_of_basis_operator=change_of_basis_operator,
      unit_cell=unit_cell,new_unit_cell=new_unit_cell)

  def magnification(self,scale_factor=None):
    if scale_factor is None:
       raise Sorry("For magnification a scale factor is required.")
    return self.deep_copy(scale_factor=scale_factor)

  def set_shift_cart(self,shift_cart):
    self._shift_cart=shift_cart

  def shift_cart(self):
    return self._shift_cart

  def coordinate_offset(self,coordinate_offset=None,unit_cell=None,
      new_unit_cell=None):
    if coordinate_offset is None:
       raise Sorry("For coordinate_offset an offset is required.")
    return self.deep_copy(coordinate_offset=coordinate_offset)

  def map_inside_unit_cell(self,unit_cell=None):
    # map all the operators inside the unit cell.  Must be supplied and the
    # centers for the operators must exist and not be zero
    for ncs_group in self._ncs_groups:
      ncs_group.map_inside_unit_cell(unit_cell=unit_cell)

  def ncs_read(self):
    return self._ncs_read

  def ncs_groups(self):
    return self._ncs_groups

  def identity_op_id_in_first_group(self): # identity operartor in first (usually main) NCS group
    if self._ncs_groups:
      return self._ncs_groups[0].identity_op_id()
    else:
      return None

  def ncs_oper_in_first_group(self): # copies in first (usually main) NCS group
    if self._ncs_groups:
      return self._ncs_groups[0].n_ncs_oper()
    else:
      return None

  def rotate_about_z(self,rot_deg=None,invert_matrices=True):
    # Rotate all the ops by rot_deg about z
    if invert_matrices:
      rot_deg=-rot_deg
    oper=get_rot_z(rot_deg=rot_deg)
    self.rotate_matrices(rot=oper)

  def rotate_about_y(self,rot_deg=None,invert_matrices=True):
    # Rotate all the ops by rot_deg about y
    if invert_matrices:
      rot_deg=-rot_deg
    oper=get_rot_y(rot_deg=rot_deg)
    self.rotate_matrices(rot=oper)

  def ncs_from_pdb_input_BIOMT(self,pdb_inp=None,log=None,quiet=False,
     invert_matrices=True):
    p=pdb_inp.process_BIOMT_records()
    if not p:
      print("No BIOMT records available", file=log)
      return

    self.ncs_from_import(rot_list=p.r,trans_list=p.t,invert_matrices=invert_matrices)

  def ncs_from_import(self,rot_list=None,trans_list=None,invert_matrices=True):

    self.init_ncs_group()

    for r,t in zip(rot_list,trans_list):
      self._rota_matrix=r.as_list_of_lists()
      self._trans=list(t)
      self._center=[0.,0.,0.]
      self.save_oper()

    self.save_existing_group_info()
    # Invert them (we use mapping from operator i to 1 ; biomt is 1 to i
    if invert_matrices:
      self.invert_matrices()

    self._ncs_read=True


  def select_first_ncs_group(self):
    # just keep the first ncs group and remove others:
    self._ncs_groups=self._ncs_groups[:1]
    return self

  def select_first_ncs_operator(self):
    # just keep the first ncs operator in the first group and remove others:
    self.select_first_ncs_group()
    if self._ncs_groups:
      self._ncs_groups=[self._ncs_groups[0].deep_copy(ops_to_keep=[0])] #  keep first only
    return self

  def set_unit_ncs(self):  # just make a single ncs operator

    self.init_ncs_group()

    self._rota_matrix=[[1.,0.,0.],[0.,1.,0.],[0.,0.,1.]]
    self._trans=[0.,0.,0.]
    self._center=[0.,0.,0.]
    self.save_oper()

    self.save_existing_group_info()
    self._ncs_read=True

  def read_ncs(self,file_name=None,lines=[],source_info="",log=None,quiet=False):
    if not log: log=sys.stdout
    if not quiet:
      if file_name:
        print("Reading NCS information from: ",file_name, file=log)
    if source_info:
       print(" based on ",source_info, file=log)
       self.source_info=source_info
    else:
       self.source_info=str(file_name)
    if file_name:
      if not os.path.isfile(file_name):
        raise Sorry("The file "+str(file_name)+" does not seem to exist?")
      else:
        with open(file_name) as f:
          lines=f.readlines()
    self.init_ncs_group()

    read_something=False

    for line in lines:
      if not line : continue
      spl=line.split()
      if len(spl)<1: continue
      key=spl[0].lower()
      if key=='transformations' and len(spl)>1 and \
         spl[1].lower()=='formatted':  # start all over!
         self._ncs_groups=[]
         self.init_ncs_group()
      elif key=='new_ncs_group': # start new group
        self.save_existing_group_info()
      # NOTE: new operator signified by rota_matrix or new_operator
      elif key=='new_operator':
        self.save_oper()
      elif key=='rota_matrix': # read set of rota
        if self._rota_matrix and \
            len(self._rota_matrix)==3 or len(self._rota_matrix)==0:
          self.save_oper()
        set=self.get_3_values_after_key(line)
        self._rota_matrix.append(set)

      elif key=='tran_orth': # read translation
        self._trans=self.get_3_values_after_key(line)
      elif key=='center_orth': # read translation
        self._center=self.get_3_values_after_key(line)
      elif key=='ncs_cc': # read  cc
        self._cc=self.get_1_value_after_key(line)
      elif key=='note' or key=='note:': # read anything
        self._note=" ".join(line.split()[1:])
      elif key=='chain':
        self._chain=self.get_1_char_after_key(line)
      elif key=='resseq':
        self._resseq_list.append(self.get_res_range_after_key(line))
      elif key=='rmsd':
        self._rmsd=self.get_1_value_after_key(line)
      elif key=='matching':
        self._residues_in_common=self.get_1_value_after_key(line)
      elif key=='source_info':
        self.source_info=self.get_1_char_after_key(line)
      elif key=='ncs_domain_pdb':
        self._ncs_domain_pdb=self.get_1_char_after_key(line)
      elif len(spl)==3 and spl[0]=='No' and spl[1]=='NCS' and spl[2]=='found':
        read_something=True
      else:
        pass
    self.save_existing_group_info()
    if read_something or len(self._ncs_groups) > 0:
      self._ncs_read=True
    else: # Try as biomtr
      import iotbx.pdb
      try:
        pdb_inp = iotbx.pdb.input(lines=lines,source_info=file_name)
        self.ncs_from_pdb_input_BIOMT(pdb_inp=pdb_inp,log=log,quiet=quiet)
      except Exception as e:
        pass

  def save_existing_group_info(self):

        self.save_oper()
        if self._n_ncs_oper > 0:  # save last-read ncs group.
          self.save_ncs_group()


  def get_res_range_after_key(self,line):
    spl = line.replace(':', ' ').split()
    if  len(spl)<3:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    start,end=None,None
    try:
      start=int(spl[1])
      end=int(spl[2])
    except Exception:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    return [start,end]

  def get_1_char_after_key(self,line):
    spl=line.split()
    if  len(spl)<2:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    char=None
    try:
      char=spl[1]
    except Exception:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    return char

  def get_1_value_after_key(self,line):
    spl=line.split()
    if  len(spl)<2:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    cc=None
    try:
      cc=float(spl[1])
    except Exception:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    return cc

  def get_3_values_after_key(self,line):
    spl=line.split()
    if  len(spl)<4:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    set=[]
    try:
      for item in spl[1:4]:
        set.append(float(item))
    except Exception:
      raise Sorry("Cannot interpret this NCS file"+"\n"+str(line))
    return set

  def init_ncs_group(self):
     self._n_ncs_oper=0
     self._ncs_trans_orth=[]
     self._ncs_rota_matr=[]
     self._ncs_center_orth=[]
     self.init_oper()
     self._rmsd_list=[]
     self._residues_in_common_list=[]
     self._cc=None
     self._note=None
     self._ncs_domain_pdb=None
     self._chain_residue_id=[]

     self._list_of_resseq_list=[]
     self._group=[]

  def init_oper(self):
     self._rota_matrix=[]
     self._trans=None
     self._center=None
     self._rmsd=None
     self._residues_in_common=None
     self._resseq_list=[]
     self._chain=None

  def save_oper(self):
     # decide if there is anything to save:

     have_oper=True
     for item in (self._trans,self._rota_matrix,self._center):
       if not item:
          have_oper=False
     if self._rota_matrix and len(self._rota_matrix)!=3:
          raise Sorry("Cannot interpret this NCS file (rotations not understood)")
     if self._trans and len(self._trans)!=3:
          raise Sorry("Cannot interpret this NCS file (translations not understood)")
     have_something=False
     if have_oper or self._rmsd or self._residues_in_common:
       have_something=True
     if not have_something: return
     self._n_ncs_oper+=1
     if have_oper:
       from scitbx import matrix
       self._ncs_trans_orth.append(matrix.col(self._trans))
       self._ncs_rota_matr.append(matrix.sqr(
         self._rota_matrix[0]+self._rota_matrix[1]+self._rota_matrix[2] ))
       self._ncs_center_orth.append(matrix.col(self._center))
     else:
       self._ncs_trans_orth.append(None)
       self._ncs_rota_matr.append(None)
       self._ncs_center_orth.append(None)
     self._rmsd_list.append(self._rmsd)
     self._residues_in_common_list.append(self._residues_in_common)
     self._list_of_resseq_list.append(self._resseq_list)
     self._group.append(self._chain)

     self.init_oper()

  def import_ncs_group(self,ncs_rota_matr=None,
       center_orth=None,
       trans_orth=None,
       chain_residue_id=None,
       residues_in_common_list=None,
       rmsd_list=None,
       ncs_domain_pdb=None,
       cc=None,
       source_of_ncs_info=None,
       ncs_group_object=None):

     if not ncs_group_object:
       list_length=None
       if center_orth is None and trans_orth:
         center_orth=len(trans_orth)*[(0,0,0)]
       for lst in [trans_orth,ncs_rota_matr,center_orth]:
         if not lst or len(lst)<1:
           print("Length too short:",type(lst),lst, end=' ')
           if lst is not None:
             print(len(lst))
           else:
             print("0")
           raise Sorry("The NCS operators in this file appear incomplete?")
         if not list_length: list_length=len(lst)
         if list_length!=len(lst):
           print("Length of list incorrect:",type(lst),lst,len(lst),list_length)
           raise Sorry("The NCS operators in this file appear incomplete?")
       ncs_group_object=ncs_group(
         ncs_rota_matr=ncs_rota_matr,
         center_orth=center_orth,
         trans_orth=trans_orth,
         chain_residue_id=remove_quotes_from_chain_id(chain_residue_id),
         residues_in_common_list=residues_in_common_list,
         rmsd_list=rmsd_list,
         source_of_ncs_info=source_of_ncs_info,
         ncs_domain_pdb=ncs_domain_pdb,
         cc=cc,
         exclude_h=self._exclude_h,exclude_d=self._exclude_d)
     self._ncs_groups.append(ncs_group_object)

  def save_ncs_group(self):
     # check that there is something  here:
     have_something=False
     for lst in [self._ncs_trans_orth,
         self._ncs_rota_matr,self._ncs_center_orth,
         self._residues_in_common_list,self._rmsd_list]:
        if lst and self._n_ncs_oper and \
           len(lst) != self._n_ncs_oper:
          print("Lengh of list does not match number of operators:",\
             type(lst),lst,self._n_ncs_oper)
          raise Sorry("The NCS operators in this file appear incomplete?")
        if lst is not None and len(lst)<1:
          print("Length of operators too short:",lst,len(lst))
          raise Sorry("The NCS operators in this file appear incomplete?")
        if lst is not None: have_something=True
     if not have_something: return
     self._chain_residue_id=[self._group,self._list_of_resseq_list]
     ncs_group_object=ncs_group(
       ncs_rota_matr=self._ncs_rota_matr,
       center_orth=self._ncs_center_orth,
       trans_orth=self._ncs_trans_orth,
       source_of_ncs_info=self.source_info,
       ncs_domain_pdb=self._ncs_domain_pdb, # 041309
       rmsd_list=self._rmsd_list,
       residues_in_common_list=self._residues_in_common_list,
       chain_residue_id=self._chain_residue_id,
       cc=self._cc,note=self._note)
     self._ncs_groups.append(ncs_group_object)
     self.init_ncs_group()

  def show_summary(self, verbose=True, log = None):
    return self.display_all(verbose=verbose, log = log)

  def display_all(self,verbose=True,log=None):
    if log==None:
      log=sys.stdout
    count=0
    text=""
    if self._ncs_name:
      text+="NCS TYPE: %s " %(self._ncs_name)

    for ncs_group in self._ncs_groups:
      count+=1
      text+="\n\nGROUP "+str(count)
      text+=ncs_group.display_summary(verbose=verbose)
    text+="\n\n"
    log.write(text)
    return text

  def shift_cart(self):
    if self._shift_cart:
      return self._shift_cart
    else:
      return (0,0,0)

  def shift_back_cart(self):
    return tuple([-a for a in self.shift_cart()])

  def as_ncs_spec_string(self):
    '''
     shifts to original location and returns text string
    '''
    shifted_ncs=self.coordinate_offset(coordinate_offset=self.shift_back_cart())
    return shifted_ncs.format_all_for_group_specification(
         log=null_out(),quiet=True,out=null_out())

  def format_all_for_group_specification(self,log=None,quiet=True,out=None,
       file_name=None):
    if file_name is not None:
       out=open(file_name,'w')
    if out==None:
       out=sys.stdout
    if log==None:
      log=sys.stdout
    elif hasattr(out,'name'):
      print("NCS written as ncs object information to:"\
        ,out.name, file=log)
    all_text=""
    text="Summary of NCS information\n"
    import time,os
    text+=time.ctime()+"\n"
    text+=os.getcwd()+"\n\n"
    if self.source_info is not None:
      text+="source_info "+str(self.source_info)+"\n"
    if not self._ncs_groups:
      text+="No NCS found\n"
    if out is not None or not quiet: out.write("\n"+text+"\n\n")
    for ncs_group in self._ncs_groups:
      text=ncs_group.format_group_specification()
      if out is not None or not quiet: out.write("\n"+text+"\n\n")
      all_text+="\n"+text
    all_text+="\n"
    if out is not None and file_name is not None:
      out.close()
    return all_text

  def format_all_for_biomt(self,log=None,quiet=False,out=None,):
    if out==None:
       out=sys.stdout
    if log==None:
      log=sys.stdout
    else:
      print("\n\nNCS operators written in BIOMT format :",out.name, file=log)
    all_text=""
    if self._ncs_groups and len(self._ncs_groups)>1:
      print(
      "\nWARNING: BIOMT format cannot be used for more than one NCS group",
       "\nOnly writing out one NCS group",file=log)
    for ncs_group in self._ncs_groups[:1]:
      text=ncs_group.format_for_biomt()
      if not quiet: out.write("\n"+text+"\n\n")
      all_text+="\n"+text
    return all_text

  def format_all_for_resolve(self,log=None,quiet=False,out=None,
      crystal_number=None,skip_identity_if_first=False,ncs_domain_pdb=True):
    if out==None:
       out=sys.stdout
    if log==None:
      log=sys.stdout
    else:
      print("\n\nNCS operators written in format for resolve to:",out.name, file=log)
    all_text=""
    for ncs_group in self._ncs_groups:
      text=ncs_group.format_for_resolve(crystal_number=crystal_number,
         skip_identity_if_first=skip_identity_if_first,
         ncs_domain_pdb=ncs_domain_pdb)
      if not quiet: out.write("\n"+text+"\n\n")
      all_text+="\n"+text
    return all_text

  def format_all_for_phenix_refine(self,quiet=False,out=None,
        prefix="refinement.pdb_interpretation.ncs_group"):
    '''
    This function is an older version of creating phil for phenix refine,
    it is modified to replicate a new phil parameters that can handle
    selection to the level of atoms, "format_phil_for_phenix_refine".

    When it will still can be used in the older form, which allows only
    residue level selection.
    '''
    if hasattr(self._ncs_obj,'show'):
      if prefix == 'refinement.pdb_interpretation.ncs_group':
        prefix="pdb_interpretation"
      if quiet:
        out = null_out()
      elif out is None:
        out=sys.stdout
      all_text = self._ncs_obj.show(format='phil',log=null_out(),header=False)
      # all_text = convert_phil_format(all_text,to_type=prefix)
      if all_text:
        if not quiet:
          print(all_text + '\n', file=out)
      return all_text
    else:
      # this is only being used when only a spec file is provided
      if out == None:
        out=sys.stdout
      all_text=""
      for ncs_group in self._ncs_groups:
        text= ncs_group.format_for_phenix_refine(prefix=prefix)
        if text:
          if not quiet: out.write(text+'\n')
          all_text+="\n"+text
      return all_text

  def format_phil_for_phenix_refine(self,log=None,quiet=False,out=None):
    """ Writes NCS phil selection in phenix_refine format """
    if out==None: out=sys.stdout
    phil_str = self._ncs_obj.show(format='phil',log=null_out(),header=False)
    # ncs_str = convert_phil_format(phil_str,to_type="ncs")
    ncs_str = phil_str
    if ncs_str:
      if not quiet: out.write(ncs_str + '\n')
    return ncs_str

  def format_phil_for_ncs(self,log=None,quiet=False,out=None):
    """ Writes NCS phil selection in NCS format """
    if out==None: out=sys.stdout
    if log==None:
      log=sys.stdout
    else:
      msg  = "NCS phil selection written in ncs selection format to:"
      print(msg,out.name, file=log)
    phil_str = self._ncs_obj.show(format='phil',log=null_out(),header=False)
    if phil_str:
      if not quiet: out.write(phil_str + '\n')
    return phil_str

  def set_ncs_name(self,ncs_name):
    self._ncs_name=ncs_name

  def get_ncs_name(self):
    return self._ncs_name

  def add_source_info(self,source_info):
    if self.source_info is None:
       self.source_info=str(source_info)
    else:
       self.source_info+=str(source_info)

  def add_cc_list(self,cc_list):
   if len(self._ncs_groups) != len(cc_list):
     raise Sorry("Number of NCS groups does not match length of cc_list...")
   for ncs_group,cc in zip(self._ncs_groups,cc_list):
    ncs_group.add_cc(cc)

  def overall_note(self):
    overall_note=""
    for ncs_group in self._ncs_groups:
      if ncs_group._note is not None:
        overall_note+=" "+ncs_group._note
    return overall_note

  def overall_cc(self):
    cc_all=0.
    n=0
    for ncs_group in self._ncs_groups:
      if ncs_group._cc is not None:
        cc_all+=ncs_group._cc
        n+=1
    if n>0:
      cc_all=cc_all/float(n)
    else:
      cc_all=None
    return cc_all

  def overall_rmsd(self):
    rmsd_all=0.
    n=0
    for ncs_group in self._ncs_groups:
      if ncs_group.rmsd_list() is not None:
        for rmsd in ncs_group.rmsd_list():
          if rmsd:
            rmsd_all+=rmsd
            n+=1
    if n>0:
      rmsd_all=rmsd_all/float(n)
    else:
      rmsd_all=None
    return rmsd_all

  def max_operators(self):
    n_max=0
    for ncs_group in self._ncs_groups:
      if ncs_group and ncs_group.n_ncs_oper()>n_max:
        n_max=ncs_group.n_ncs_oper()
    return n_max

  def is_similar_ncs_object(self, other,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t,
   allow_self_contained_in_other = True):
    '''
      Determine if self and other are similar ncs objects
      ncs groups do not have to be in same order
    '''
    if not self._ncs_groups and not other._ncs_groups:
      return True  # nothing there for either one

    if self.shift_cart() != other.shift_cart():
      return False
    if not self._ncs_groups:
      return False
    if not other._ncs_groups:
      return False
    if len(self._ncs_groups) != len (other._ncs_groups):
      return False
    for ncs_group in self._ncs_groups:
      found=False
      for other_ncs_group in other._ncs_groups:
        if ncs_group.is_similar_ncs_group(other_ncs_group,tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t,
            allow_self_contained_in_other = allow_self_contained_in_other):
          found=True
          break
      if not found:
        return False
    return True

  def is_point_group_symmetry(self,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t):
    if not self._ncs_groups:
      return False
    for ncs_group in self._ncs_groups[:1]:
      if not ncs_group.is_point_group_symmetry(tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t):
        return False
    return True

  def adjust_magnification(self,magnification=None):
    if not self._ncs_groups:
      return self
    for ncs_group in self._ncs_groups:
      ncs_group.adjust_magnification(magnification=magnification)
    return self

  def rotate_matrices(self,rot=None):
    if not self._ncs_groups:
      return
    for ncs_group in self._ncs_groups:
      ncs_group.rotate_matrices(rot=rot)

  def invert_matrices(self):
    if not self._ncs_groups:
      return
    for ncs_group in self._ncs_groups:
      ncs_group.invert_matrices()

  def sort_by_z_translation(self,tol_z=default_tol_z):
    if not self._ncs_groups:
      return
    for ncs_group in self._ncs_groups:
      ncs_group.sort_by_z_translation(tol_z=tol_z)

  def extend_helix_operators(self,z_range=None,tol_z=default_tol_z,
      max_operators=None):
    if not self._ncs_groups:
      return
    for ncs_group in self._ncs_groups:
      ncs_group.extend_helix_operators(z_range=z_range,tol_z=tol_z,
        max_operators=max_operators)

  def get_helix_parameters(self,z_range=None,tol_z=default_tol_z,
      max_operators=None):
    if not self._ncs_groups:
      return
    # return values for group 0
    return self._ncs_groups[0].get_helix_parameters(tol_z=tol_z,)

  def is_helical_along_z(self,
   tol_r=default_tol_r,
   abs_tol_t=default_abs_tol_t,
   rel_tol_t=default_rel_tol_t):
    if not self._ncs_groups:
      return False
    for ncs_group in self._ncs_groups:
      if not ncs_group.is_helical_along_z(tol_r=tol_r,
            abs_tol_t=abs_tol_t,rel_tol_t=rel_tol_t):
        return False
    return True

  def add_identity_op(self):
    for ncs_group in self._ncs_groups:
      if ncs_group.identity_op_id() is None:
        ncs_group.add_identity_op()


  def apply_ncs_to_sites(self, sites_cart=None,ncs_obj=None,
      exclude_identity=False,ncs_id=None):

    if type(sites_cart) == type((1,2,3)): # it was a single site
      from scitbx.array_family import flex
      sites_cart = flex.vec3_double((sites_cart,))

    if not ncs_obj:
      ncs_obj = self
    from scitbx.array_family import flex
    new_sites_cart=flex.vec3_double()
    if (not ncs_obj or ncs_obj.max_operators()<=1):
      if exclude_identity:
        return new_sites_cart  # nothing as we exclude identity
      else:
        return sites_cart

    ncs_group=ncs_obj.ncs_groups()[0]
    from scitbx.matrix import col

    if ncs_id is not None:
      t=ncs_group.translations_orth_inv()[ncs_id]
      r=ncs_group.rota_matrices_inv()[ncs_id]
      for site in sites_cart:
        new_sites_cart.append(r * col(site)  + t)
      return new_sites_cart

    if exclude_identity:
      identity_op=ncs_group.identity_op_id()
    else:
      identity_op=None
    ii=-1
    for t,r in zip(
       ncs_group.translations_orth_inv(),ncs_group.rota_matrices_inv()):
      ii+=1
      if exclude_identity and ii==identity_op: continue
      for site in sites_cart:
        new_sites_cart.append(r * col(site)  + t)
    return new_sites_cart


test_ncs_info="""

new_ncs_group
NCS_CC 0.92
new_operator

rota_matrix    1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth   30.2920   -2.8923   16.6160
CHAIN A
RMSD 0.2
MATCHING 12.0
  RESSEQ 1:26

new_operator

rota_matrix   -0.9971    0.0424   -0.0635
rota_matrix   -0.0297   -0.9816   -0.1889
rota_matrix   -0.0703   -0.1864    0.9800
tran_orth    70.9461    5.2622    3.7549

center_orth   39.8735    3.8824   16.7239
CHAIN B
RMSD 0.1
MATCHING 15.0
  RESSEQ 101:126



new_ncs_group
NCS_CC 0.95
new_operator

rota_matrix    1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0001

center_orth   31.2920   -2.8923   16.6160
CHAIN A
RMSD 0.6
MATCHING 13.0
  RESSEQ 1:25

new_operator

rota_matrix   -0.9970    0.0424   -0.0635
rota_matrix   -0.0297   -0.9816   -0.1889
rota_matrix   -0.0703   -0.1864    0.9800
tran_orth    70.9461    5.2622    3.7549

center_orth   38.8735    3.8824   16.7239
CHAIN B
RMSD 0.5
MATCHING 11.0
  RESSEQ 101:124


"""

test1_ncs_info="""
new_ncs_group
new_operator

rota_matrix    1.0000    0.0000    0.0000
rota_matrix    0.0000    1.0000    0.0000
rota_matrix    0.0000    0.0000    1.0000
tran_orth     0.0000    0.0000    0.0000

center_orth   0.0000    0.0000    0.0000
new_operator

rota_matrix    0.3090    0.9500   -0.0000
rota_matrix   -0.9500    0.3090    0.0000
rota_matrix    0.0000   -0.0000    1.0000
tran_orth   -23.0000  147.0000    0.0000

center_orth   0.0000    0.0000    0.0000
"""
def euler_frac_to_rot_trans(euler_values,frac,unit_cell):
    # TT get RT in cctbx form from euler angles and fractional translation as
    #   used in phaser. Note: Specific for phaser EULER FRAC

    ncs_rota_matr_inv=scitbx.rigid_body.euler(
      euler_values[2],euler_values[1],euler_values[0],"zyz").rot_mat()
    ncs_rota_matr=ncs_rota_matr_inv.inverse()

    orth=unit_cell.orthogonalize(frac)
    trans_orth=-1.*ncs_rota_matr*orth
    return ncs_rota_matr,trans_orth
#####################################################



if __name__=="__main__":
  log=sys.stdout
  args=sys.argv[1:]
  if 'exercise' in args:
    file_name='TEST.NCS'
    f=open(file_name,'w')
    f.write(test_ncs_info)
    f.close()
    ncs_object=ncs()
    ncs_object.read_ncs(file_name,source_info=file_name)
    ncs_object.display_all()
    file2='TEST2.NCS'
    text=ncs_object.format_all_for_group_specification(file_name=file2)

    if not text or text != test_ncs_info:
     print("NOT OK ...please compare TEST.NCS (std) vs TEST2.NCS (output)")
     ff=open('txt.dat','w')
     ff.write(text)
     ff.close()
    else:

     print ("Running exercise_1")
     ncs_object=ncs()
     ncs_object.read_ncs(lines=test1_ncs_info.splitlines())
     ncs_lines=ncs_object.format_all_for_group_specification().splitlines()
     biomt_lines=ncs_object.format_all_for_biomt().splitlines()

     biomt_ncs_object=ncs()
     biomt_ncs_object.read_ncs(lines=biomt_lines)

     biomt_text=biomt_ncs_object.display_all()

     std_ncs_object=ncs()
     std_ncs_object.read_ncs(lines=ncs_lines)
     std_ncs_text=std_ncs_object.display_all()
     print ("STANDARD \n %s \n BIOMTR \n %s " %(
       std_ncs_text, biomt_text))
     for a,b in zip(std_ncs_text.splitlines(),biomt_text.splitlines()):
       assert a.strip()==b.strip()

     assert std_ncs_object.is_similar_ncs_object(biomt_ncs_object)
     new_ncs_obj=ncs()
     # Shift ncs coordinates, make ncs with both, make sure can find
     #   similarity even if order is different
     new_ncs_obj._ncs_groups=deepcopy(std_ncs_object._ncs_groups)
     offset_ncs=std_ncs_object.deep_copy(coordinate_offset=(10,10,10))
     assert not offset_ncs.is_similar_ncs_object(biomt_ncs_object)
     new_ncs_obj._ncs_groups.append(deepcopy(offset_ncs._ncs_groups[0]))
     second_ncs_obj=ncs()
     second_ncs_obj._ncs_groups=deepcopy(offset_ncs._ncs_groups)
     second_ncs_obj._ncs_groups.append(deepcopy(std_ncs_object._ncs_groups[0]))
     assert not new_ncs_obj.is_similar_ncs_object(biomt_ncs_object)
     assert new_ncs_obj.is_similar_ncs_object(second_ncs_obj)
     print("OK")

  elif len(args)>0 and args[0] and os.path.isfile(args[0]):
    ncs_object=ncs()
    ncs_object.read_ncs(args[0],source_info=args[0])
    ncs_object.display_all()
    if 1:
      file2='OUTPUT.NCS'
      text=ncs_object.format_all_for_group_specification(file_name=file2)
      print("IS point-group: ", end=' ')
      print(ncs_object.is_point_group_symmetry())
      print("IS helical:", end=' ')
      print(ncs_object.is_helical_along_z())
    if 1:
      file3='OUTPUT2.NCS'
      new_ncs_object=ncs_object.deep_copy(ops_to_keep=[0,1,6])
      text=new_ncs_object.format_all_for_group_specification(file_name=file3)
      print(text)
      print("IS point-group: ", end=' ')
      print(new_ncs_object.is_point_group_symmetry())
      print("IS helical:", end=' ')
      print(new_ncs_object.is_helical_along_z())
