mirror of
https://github.com/triqs/dft_tools
synced 2024-07-18 00:43:41 +02:00
ad8c4e75fe
Adding Elk-TRIQS interface (first iteration) This interface reads in Elk's ground-state files / projectors generated by a specific Elk interface code version (https://github.com/AlynJ/Elk_interface-TRIQS). The interface can perform charge-self consistent DFT+DMFT calculations using the aforementioned Elk code version, including spin orbit-coupling. Hence, this is the first open source interfaced DFT code to triqs with FCSC support. The commit includes detailed documentation and tutorials on how to use this interface. Moreover, further new post-processing routines are added for Fermi surface plots and spectral functions (A(w)) from the elk inputs. The interface was tested by A. James and A. Hampel. However, this is the first iteration of the interface and should be used with care. Please report all bugs. List of changes: --------------- - sumk.py: added cacluation of charge density correction for elk (dm_type='elk'). - sumk_dft_tools.py: added new post-processing functions to calculate the Fermi surface and A(w) from the Elk inputs. - documentation and tutorial files amended for this interface. - added python tests for the Elk converter.
297 lines
10 KiB
Python
297 lines
10 KiB
Python
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##########################################################################
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#
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# TRIQS: a Toolbox for Research in Interacting Quantum Systems
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#
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# Copyright (C) 2019 by A. D. N. James, M. Zingl and M. Aichhorn
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#
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# TRIQS is free software: you can redistribute it and/or modify it under the
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# terms of the GNU General Public License as published by the Free Software
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# Foundation, either version 3 of the License, or (at your option) any later
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# version.
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#
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# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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# details.
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#
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# You should have received a copy of the GNU General Public License along with
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# TRIQS. If not, see <http://www.gnu.org/licenses/>.
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#
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##########################################################################
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from types import *
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import numpy
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import os.path
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from locale import atof
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class ElkConverterTools:
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"""
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Conversion Tools required to help covert Elk outputs into the TRIQS format.
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"""
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def __init__(self):
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pass
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def rotaxang(self,rot):
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"""
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This routine determines the axis of rotation vector (v) and the angle of rotation (th).
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If R corresponds to an improper rotation then only the proper part is used and the determinant
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is set to -1. The rotation convention follows the "right-hand rule". See Elk's rotaxang
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routine.
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"""
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eps=1E-8
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v=numpy.zeros([3], numpy.float_)
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# find the determinant
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det=numpy.linalg.det(rot)
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if (abs(det-1.0)<eps):
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det=1.0
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elif (abs(det+1.0)<eps):
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det=-1.0
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else:
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raise "sym_converter : Invalid rotation matrix!"
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# proper rotation matrix
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rotp=det*rot
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v[0]=(rotp[1,2]-rotp[2,1])/2.0
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v[1]=(rotp[2,0]-rotp[0,2])/2.0
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v[2]=(rotp[0,1]-rotp[1,0])/2.0
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t1=numpy.sqrt(numpy.dot(v,v))
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t2=(rotp[0,0]+rotp[1,1]+rotp[2,2]-1.0)/2.0
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if (abs(abs(t2)-1.0)>eps):
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# theta not equal to 0 or pi
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th=-numpy.arctan2(t1,t2)
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v[:]=v[:]/t1
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else:
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# special case of sin(th)=0
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if(t2>eps):
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# zero angle: axis arbitrary
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th=0.0
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v[:]=1.0/numpy.sqrt(3.0)
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else:
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# rotation by pi
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th=numpy.pi
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if((rotp[0,0]>=rotp[1,1])&(rotp[0,0]>=rotp[2,2])):
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if(rotp[0,0]<(-1.0+eps)):
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mpi.report(rotp[0,0],-1.0+eps)
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raise "sym_converter : Invalid rotation matrix!"
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v[0]=numpy.sqrt(abs(rotp[0,0]+1.0)/2.0)
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v[1]=(rotp[1,0]+rotp[0,1])/(4.0*v[0])
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v[2]=(rotp[2,0]+rotp[0,2])/(4.0*v[0])
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elif((rotp[1,1]>=rotp[0,0])&(rotp[1,1]>=rotp[2,2])):
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if(rotp[1,1]<(-1.0+eps)):
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mpi.report(rotp[1,1],-1.0+eps)
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raise "sym_converter : Invalid rotation matrix!"
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v[1]=numpy.sqrt(abs(rotp[1,1]+1.0)/2.0)
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v[2]=(rotp[2,1]+rotp[1,2])/(4.0*v[1])
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v[0]=(rotp[0,1]+rotp[1,0])/(4.0*v[1])
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else:
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if(rotp[2,2]<(-1.0+eps)):
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mpi.report(rotp[2,2],-1.0+eps)
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raise "sym_converter : Invalid rotation matrix!"
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v[2]=numpy.sqrt(abs(rotp[2,2]+1.0)/2.0)
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v[0]=(rotp[0,2]+rotp[2,0])/(4.0*v[2])
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v[1]=(rotp[1,2]+rotp[2,1])/(4.0*v[2])
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# return theta and v
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return v,th
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def axangsu2(self,v,th):
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"""
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Calculate the rotation SU(2) matrix - see Elk's axangsu2 routine.
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"""
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su2=numpy.zeros([2,2], numpy.complex_)
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t1=numpy.sqrt(numpy.dot(v,v))
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if(t1<1E-8):
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raise "sym_converter : zero length axis vector!"
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# normalise the vector
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t1=1.0/t1
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x=v[0]*t1; y=v[1]*t1; z=v[2]*t1
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#calculate the SU(2) matrix
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cs=numpy.cos(0.5*th)
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sn=numpy.sin(0.5*th)
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su2[0,0]=cs-z*sn*1j
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su2[0,1]=-y*sn-x*sn*1j
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su2[1,0]=y*sn-x*sn*1j
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su2[1,1]=cs+z*sn*1j
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#return the SU(2) matrix
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return su2
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def v3frac(self,v,eps):
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"""
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This finds the fractional part of 3-vector v components. This uses the
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same method as in Elk (version 6.2.8) r3fac subroutine.
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"""
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v[0]=v[0]-numpy.floor(v[0])
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if(v[0] < 0): v[0]+=1
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if((1-v[0]) < eps): v[0]=0
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if(v[0] < eps): v[0]=0
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v[1]=v[1]-numpy.floor(v[1])
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if(v[1] < 0): v[1]+=1
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if((1-v[1]) < eps): v[1]=0
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if(v[1] < eps): v[1]=0
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v[2]=v[2]-numpy.floor(v[2])
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if(v[2] < 0): v[2]+=1
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if((1-v[2]) < eps): v[2]=0
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if(v[2] < eps): v[2]=0
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return v
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def gen_perm(self,nsym,ns,na,natmtot,symmat,tr,atpos,epslat=1E-6):
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"""
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Generate the atom permutations per symmetry.
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"""
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perm=[]
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iea=[]
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for isym in range(nsym):
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iea.append(numpy.zeros([natmtot,ns], numpy.int_))
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#loop over species
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for js in range(ns):
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#loop over species atoms
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v=numpy.zeros([3,na[js]], numpy.float_)
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v2=numpy.zeros(3, numpy.float_)
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for ia in range(na[js]):
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v[:,ia]=self.v3frac(atpos[js][ia][0:3],epslat)
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for ia in range(na[js]):
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v2[:]=numpy.matmul(symmat[isym][:,:],(atpos[js][ia][0:3]+tr[isym]))
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v2[:]=self.v3frac(v2,epslat)
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for ja in range(na[js]):
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t1=sum(abs(v[:,ja]-v2[:])) #check
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if(t1 < epslat):
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iea[isym][ja,js]=ia
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break
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#put iea into perm format
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for isym in range(nsym):
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perm.append([])
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ja=0
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prv_atms=0
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for js in range(ns):
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for ia in range(na[js]):
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perm[isym].append(iea[isym][ia,js]+prv_atms+1)
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ja+=1
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prv_atms+=na[js]
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#output perm
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return perm
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def symlat_to_complex_harmonics(self,nsym,n_shells,symlat,shells):
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"""
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This calculates the Elk (crystal) symmetries in complex spherical harmonics
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This follows the methodology used in Elk's rotzflm, ylmrot and ylmroty routines.
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"""
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#need SciPy routines to get Euler angles - need version 1.4+
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#from scipy.spatial.transform import Rotation as R
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symmat=[]
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rot=numpy.identity(3, numpy.float_)
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angi=numpy.zeros(3, numpy.float_)
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#loop over symmetries
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for isym in range(nsym):
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symmat.append([])
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for ish in range(n_shells):
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l=shells[ish]['l']
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symmat[isym].append(numpy.zeros([2*l+1, 2*l+1], numpy.complex_))
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#get determinant
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det=numpy.linalg.det(symlat[isym])
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p=1
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#p is -1 for improper symmetries
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if(det<0.0): p=-1
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rot[:,:]=p*symlat[isym][:,:]
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#r=R.from_matrix(rot)
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#get the y-convention Euler angles as used by Elk.
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#ang=r.as_euler('zyz')
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ang=self.zyz_euler(rot)
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#Elk uses inverse rotations, i.e. the function is being rotated, not the spherical harmonics
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angi[0]=-ang[2]
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angi[1]=-ang[1]
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angi[2]=-ang[0]
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#calculate the symmetry in the complex spherical harmonic basis.
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d = self.ylmrot(p,angi,l)
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symmat[isym][ish][:,:] = d[:,:]
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#return the complex spherical harmonic
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return symmat
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def zyz_euler(self,rot):
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"""
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This calculates the Euler angles of matrix rot in the y-convention.
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See Elk's roteuler routine.
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This will be made redundent when TRIQS uses scipy version 1.4+
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"""
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eps=1E-8
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pi=numpy.pi
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ang=numpy.zeros(3, numpy.float_)
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#get the Euler angles
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if((abs(rot[2,0])>eps) or (abs(rot[2,1])>eps)):
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ang[0]=numpy.arctan2(rot[2,1],rot[2,0])
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if(abs(rot[2,0])>abs(rot[2,1])):
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ang[1]=numpy.arctan2(rot[2,0]/numpy.cos(ang[0]),rot[2,2])
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else:
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ang[1]=numpy.arctan2(rot[2,1]/numpy.sin(ang[0]),rot[2,2])
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ang[2]=numpy.arctan2(rot[1,2],-rot[0,2])
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else:
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ang[0]=numpy.arctan2(rot[0,1],rot[0,0])
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if(rot[2,2]>0.0):
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ang[1]=0.0
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ang[2]=0.0
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else:
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ang[1]=pi
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ang[2]=pi
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#return Euler angles
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return ang
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def ylmrot(self,p,angi,l):
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"""
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calculates the rotation matrix in complex spherical harmonics for l.
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THIS HAS ONLY BEEN TESTED FOR l=2.
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"""
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d=numpy.identity(2*l+1, numpy.complex_)
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# generate the rotation matrix about the y-axis
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dy=self.ylmroty(angi[1],l)
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# apply inversion to odd l values if required
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if(p==-1):
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if(l % 2.0 != 0):
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dy*=-1
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# rotation by alpha and gamma
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for m1 in range(-l,l+1,1):
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lm1=l+m1
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for m2 in range(-l,l+1,1):
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lm2=l+m2
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t1=-m1*angi[0]-m2*angi[2]
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d[lm1,lm2]=dy[lm1,lm2]*(numpy.cos(t1)+1j*numpy.sin(t1))
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#return the rotation matrix
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return d
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def ylmroty(self,beta,l):
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"""
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returns the rotation matrix around the y-axis with angle beta.
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This uses the same real matrix formual as in Elk - see Elk's manual for ylmroty description
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"""
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#import the factorial function - needed for later versions of scipy (needs testing)
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from scipy import special as spec
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#calculates the rotation matrix in complex spherical harmonics for l
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dy=numpy.identity(2*l+1, numpy.float_)
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#sine and cosine of beta
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cb=numpy.cos(beta/2.0)
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sb=numpy.sin(beta/2.0)
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# generate the rotaion operator for m-components of input l
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for m1 in range(-l,l+1,1):
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for m2 in range(-l,l+1,1):
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sm=0.0
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minlm=numpy.amin([l+m1, l-m2]) + 1
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for k in range(minlm):
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if(((l+m1-k)>=0) and ((l-m2-k)>=0) and ((m2-m1+k)>=0)):
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j=2*(l-k)+m1-m2
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if(j==0):
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t1=1.0
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else:
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t1=cb**j
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j=2*k+m2-m1
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if(j!=0):
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t1=t1*sb**j
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t2=t1/(spec.factorial(k)*spec.factorial(l+m1-k)*spec.factorial(l-m2-k)*spec.factorial(m2-m1+k))
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if(k % 2.0 != 0):
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t2=-t2
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sm+=t2
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t1=numpy.sqrt(spec.factorial(l+m1)*spec.factorial(l-m1)*spec.factorial(l+m2)*spec.factorial(l-m2))
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dy[m1+l,m2+l]=t1*sm
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#return y-rotation matrix
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return dy
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