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 zz_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 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, allow_negative_z_translation = False): 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 = sorted(sort_z_translations, key = lambda s: s[0]) #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 allow_negative_z_translation and n_minus_one>n_plus_one: sorted_indices.reverse() self._helix_z_translation= -1 * delta else: 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 delta_rot = t1 - t0 if delta_rot > 180: delta_rot = delta_rot - 360 if delta_rot <= -180: delta_rot = delta_rot + 360 return delta_rot 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())