c ******************************************************************************
c
c TRIQS: a Toolbox for Research in Interacting Quantum Systems
c
c Copyright (C) 2011 by L. Pourovskii, V. Vildosola, C. Martins, M. Aichhorn
c
c TRIQS is free software: you can redistribute it and/or modify it under the
c terms of the GNU General Public License as published by the Free Software
c Foundation, either version 3 of the License, or (at your option) any later
c version.
c
c TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
c WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
c FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
c details.
c
c You should have received a copy of the GNU General Public License along with
c TRIQS. If not, see .
c
c *****************************************************************************/
SUBROUTINE set_projections(e1,e2)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine sets up the projection matrices in the energy %%
C %% window [e1,e2].Two types of projection can be defined : %%
C %% - The projectors for the correlated orbital %%
C %% only. (orb = iatom,is,m) %%
C %% (They are stored in the table pr_crorb) %%
C %% - The Theta projectors for all the orbitals %%
C %% (They are stored in the table pr_orb) %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
C
USE almblm_data
USE common_data
USE prnt
USE projections
USE reps
USE symm
IMPLICIT NONE
C
REAL(KIND=8) :: e1, e2
INTEGER :: iorb, icrorb, ik, is, ib, m, l, lm, nbbot, nbtop
INTEGER :: isrt, n, ilo, iatom, i, imu, jatom, jorb,isym, jcrorb
LOGICAL :: included,param
COMPLEX(KIND=8), DIMENSION(:), ALLOCATABLE :: coeff
COMPLEX(KIND=8), DIMENSION(:,:), ALLOCATABLE :: tmp_mat
COMPLEX(KIND=8), DIMENSION(:,:), ALLOCATABLE :: tmp_matbis
COMPLEX(KIND=8), DIMENSION(:,:,:), ALLOCATABLE :: tmp_matn
C
C
C
WRITE(buf,'(a)')'Creation of the projectors...'
CALL printout(0)
C
C
C ======================================================================
C Selection of the bands which lie in the chosen energy window [e1;e2] :
C ======================================================================
C
kp(:,:)%included=.FALSE.
C the field kp%included = boolean which is .TRUE. when there is at least one band
C at this k-point whose energy eignevalue is in the energy window.
DO is=1,ns
DO ik=1,nk
included=.FALSE.
DO ib=kp(ik,is)%nbmin,kp(ik,is)%nbmax
IF(.NOT.included.AND.kp(ik,is)%eband(ib) > e1.AND.
& kp(ik,is)%eband(ib).LE.e2) THEN
C If the energy eigenvalue E of the band ib at the k-point ik is such that e1 < E =< e2,
C then all the band with ib1>ib must be "included" in the computation and kp%nb_bot is initialized at the value ib.
included=.TRUE.
kp(ik,is)%nb_bot=ib
ELSEIF(included.AND.kp(ik,is)%eband(ib) > e2) THEN
C If the energy eigenvalue E of the current band ib at the k-point ik is such that E > e2 and all the previous
C band are "included", then the field kp%included = .TRUE. and kp%nb_top = ib-1 (the index of the previous band)
kp(ik,is)%nb_top=ib-1
kp(ik,is)%included=.TRUE.
EXIT
C The loop on the band ib is stopped, since all the bands after ib have an energy > that of ib.
ELSEIF(ib==kp(ik,is)%nbmax.AND.kp(ik,is)%eband(ib)
& > e1.AND.kp(ik,is)%eband(ib).LE.e2) THEN
C If the energy eigenvalue E of the last band ib=kp%nbmax at the k-point ik is such that e1 < E =< e2 and all the
C previous bands are "included", then the band ib must be "included" and kp%nb_bot is initialized at the value kp%nbmax.
kp(ik,is)%nb_top=ib
kp(ik,is)%included=.TRUE.
ENDIF
C If the eigenvalues of the bands at the k-point ik are < e1 and included=.FALSE.
C of if the eigenvalues of the bands at the k-point ik are in the energy window [e1,e2] and included=.TRUE.,
C nothing is done...
ENDDO ! End of the ib loop
C If all the eigenvalues of the bands at the k-point ik are not in the window,
C then kp%included remains at the value .FALSE. and the field kp%nb_top and kp%nb_bot are set to 0.
IF (.not.kp(ik,is)%included) THEN
kp(ik,is)%nb_bot=0
kp(ik,is)%nb_top=0
ENDIF
ENDDO ! End of the ik loop
ENDDO ! End of the is loop
C ---------------------------------------------------------------------------------------
C Checking of the input files if spin-polarized inputs and SO is taken into account:
C There should not be any difference between up and dn limits for each k-point.
C Printing a Warning if this is not the case.
C -------------------
C
IF (ifSP.AND.ifSO) THEN
param=.TRUE.
DO ik=1,nk
param=param.AND.(kp(ik,1)%included.eqv.kp(ik,2)%included)
param=param.AND.(kp(ik,1)%nb_bot==kp(ik,2)%nb_bot)
param=param.AND.(kp(ik,1)%nb_top==kp(ik,2)%nb_top)
IF (.not.param) EXIT
C For a valid compoutation, the same k-points must be included for up and dn states,
C and the upper and lower limits must be the same in both case.
ENDDO
IF (.not.param) THEN
WRITE(buf,'(a,a)')'A Spin-orbit computation for this',
& ' compound is not possible with these input files.'
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
ENDIF
ENDIF
C ---------------------------------------------------------------------------------------
C
C
C ==================================================================
C Orthonormalization of the radial wave functions for each orbital :
C ==================================================================
C
C This step is essential for setting the Theta projectors.
IF(.NOT.ALLOCATED(norm_radf)) THEN
ALLOCATE(norm_radf(norb))
C norm_radf is a table of "ortfunc" elements, its size ranges from 1 to norb.
DO iorb=1,norb
l=orb(iorb)%l
isrt=orb(iorb)%sort
norm_radf(iorb)%n=nLO(l,isrt)+2
n=norm_radf(iorb)%n
ALLOCATE(norm_radf(iorb)%s12(n,n,ns))
C norm_radf%n = size of the matrix s12
C norm_radf%s12 = matrix of size n*n (one for spin up, one for spin down, if necessary)
DO is=1,ns
norm_radf(iorb)%s12(1:n,1:n,is)=0d0
norm_radf(iorb)%s12(1,1,is)=1d0
norm_radf(iorb)%s12(2,2,is)=u_dot_norm(l,isrt,is)
C Initialization of the matrix norm_radf%s12 for each orbital (l,isrt).
C We remind tha it is assumed that nLO has the value 0 or 1 only !!
DO ilo=1,nLO(l,isrt)
norm_radf(iorb)%s12(2+ilo,2+ilo,is)=1d0
norm_radf(iorb)%s12(2+ilo,1,is)=
= ovl_LO_u(ilo,l,isrt,is)
norm_radf(iorb)%s12(1,2+ilo,is)=
= ovl_LO_u(ilo,l,isrt,is)
norm_radf(iorb)%s12(2+ilo,2,is)=
= ovl_LO_udot(ilo,l,isrt,is)
norm_radf(iorb)%s12(2,2+ilo,is)=
= ovl_LO_udot(ilo,l,isrt,is)
ENDDO
C Computation of the square root of norm_radf:
CALL orthogonal_r(norm_radf(iorb)%
& s12(1:n,1:n,is),n,.FALSE.)
C the field norm_radf%s12 is finally the C matrix described in the tutorial (or in equation (3.63) in my thesis)
ENDDO
ENDDO
ENDIF
C
C =====================================
C Creation of the projection matrices :
C =====================================
C
IF(.NOT.ALLOCATED(pr_orb)) THEN
ALLOCATE(pr_crorb(ncrorb,nk,ns))
ALLOCATE(pr_orb(norb,nk,ns))
ENDIF
C pr_crorb = table of "proj_mat" elements for the correlated orbitals (size from 1 to ncrorb, from 1 to nk, from 1 to ns)
C pr_orb = table of "proj_mat_n" elements for all the orbitals (size from 1 to norb, from 1 to nk, from 1 to ns)
DO is=1,ns
DO ik=1,nk
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,is)%included) CYCLE
C ------------------------------------------------
C Wannier Projectors for the correlated orbitals :
C ------------------------------------------------
DO icrorb=1,ncrorb
l=crorb(icrorb)%l
iatom=crorb(icrorb)%atom
isrt=crorb(icrorb)%sort
C Case of l=0 :
C -------------
IF (l==0) THEN
IF(ALLOCATED(pr_crorb(icrorb,ik,is)%mat)) THEN
DEALLOCATE(pr_crorb(icrorb,ik,is)%mat)
ENDIF
ALLOCATE(pr_crorb(icrorb,ik,is)%
% mat(1,kp(ik,is)%nb_bot:kp(ik,is)%nb_top))
C pr_crorb%mat = the projection matrix with 1 line and (nb_top-nb_bot) columns
DO ib=kp(ik,is)%nb_bot,kp(ik,is)%nb_top
pr_crorb(icrorb,ik,is)%mat(1,ib)=
= kp(ik,is)%Alm(1,iatom,ib)
DO ilo=1,nLO(l,isrt)
pr_crorb(icrorb,ik,is)%mat(1,ib)=
= pr_crorb(icrorb,ik,is)%mat(1,ib)+
+ kp(ik,is)%Clm(ilo,1,iatom,ib)*
* ovl_LO_u(ilo,l,isrt,is)
ENDDO ! End of the ilo loop
ENDDO ! End of the ib loop
C prcrorb(icrorb,ik,is)%mat(1,ib)= = Alm+Clm*ovl_LO_u
C
C Case of any other l :
C ---------------------
ELSE
lm=l*l
C Since the correlated orbital is the l orbital, the elements range from l*l+1 to (l+1)^2
C the sum from 0 to (l-1) of m (from -l to l) is l^2.
IF(ALLOCATED(pr_crorb(icrorb,ik,is)%mat)) THEN
DEALLOCATE(pr_crorb(icrorb,ik,is)%mat)
ENDIF
ALLOCATE(pr_crorb(icrorb,ik,is)%
% mat(-l:l,kp(ik,is)%nb_bot:kp(ik,is)%nb_top))
C pr_crorb%mat = the projection matrix with (2*l+1) lines and (nb_top-nb_bot) columns
DO m=-l,l
lm=lm+1
DO ib=kp(ik,is)%nb_bot,kp(ik,is)%nb_top
pr_crorb(icrorb,ik,is)%mat(m,ib)=
= kp(ik,is)%Alm(lm,iatom,ib)
DO ilo=1,nLO(l,isrt)
pr_crorb(icrorb,ik,is)%mat(m,ib)=
= pr_crorb(icrorb,ik,is)%mat(m,ib)+
+ kp(ik,is)%Clm(ilo,lm,iatom,ib)*
* ovl_LO_u(ilo,l,isrt,is)
ENDDO ! End of the ilo loop
ENDDO ! End of the ib loop
ENDDO ! End of the m loop
C prcrorb(icrorb,ik,is)%mat(m,ib)= = Alm+Clm*ovl_LO_u
ENDIF ! End of the if l=0 if-then-else
ENDDO ! End of the icrorb loop
C
C ---------------------------------------
C Theta Projectors for all the orbitals :
C ---------------------------------------
DO iorb=1,norb
l=orb(iorb)%l
n=norm_radf(iorb)%n
iatom=orb(iorb)%atom
C Case of l=0 :
C -------------
IF (l==0) THEN
IF(ALLOCATED(pr_orb(iorb,ik,is)%matn)) THEN
DEALLOCATE(pr_orb(iorb,ik,is)%matn)
ENDIF
ALLOCATE(pr_orb(iorb,ik,is)%
% matn(1,kp(ik,is)%nb_bot:kp(ik,is)%nb_top,n))
ALLOCATE(coeff(1:n))
C pr_orb%matn = the projection matrix with 1 line and (nb_top-nb_bot) columns for the n (size of s12) coefficients
C coeff = table of size n which will contain the decomposition of the Bloch state |psi_ik,ib,is>
C as in equation 22 of the tutorial (Alm, Blm, and Clm )
DO ib=kp(ik,is)%nb_bot,kp(ik,is)%nb_top
coeff(1)=kp(ik,is)%Alm(1,iatom,ib)
coeff(2)=kp(ik,is)%Blm(1,iatom,ib)
coeff(3:n)=kp(ik,is)%Clm(1:n-2,1,iatom,ib)
coeff=MATMUL(coeff,norm_radf(iorb)%s12(1:n,1:n,is))
C coeff = coefficients c_(j,lm) of the decomposition of the state |psi> in the orthogonalized basis |phi_j>
C as defined in the tutorial (equation 25)
pr_orb(iorb,ik,is)%matn(1,ib,1:n)=coeff(1:n)
ENDDO
DEALLOCATE(coeff)
C pr_orb(iorb,ik,is)%matn(m,ib,1:n) is then the Theta projector as defined in equation 26 of the tutorial.
C
C Case of any other l :
C ---------------------
ELSE
lm=l*l
C As the orbital is the l orbital, the elements range from l*l+1 to (l+1)^2
C the sum from 0 to (l-1) of m (from -l to l) is l^2.
IF(ALLOCATED(pr_orb(iorb,ik,is)%matn)) THEN
DEALLOCATE(pr_orb(iorb,ik,is)%matn)
ENDIF
ALLOCATE(pr_orb(iorb,ik,is)%
% matn(-l:l,kp(ik,is)%nb_bot:kp(ik,is)%nb_top,n))
ALLOCATE(coeff(1:n))
C pr_orb%matn = the projection matrix with (2*l+1) lines and (nb_top-nb_bot) columns for the n (size of s12) coefficients
C coeff = table of size n which will contain the decomposition of the Bloch state |psi_ik,ib,is>
C as in equation 22 of the tutorial (Alm, Blm, and Clm )
DO m=-l,l
lm=lm+1
DO ib=kp(ik,is)%nb_bot,kp(ik,is)%nb_top
coeff(1)=kp(ik,is)%Alm(lm,iatom,ib)
coeff(2)=kp(ik,is)%Blm(lm,iatom,ib)
coeff(3:n)=kp(ik,is)%Clm(1:n-2,lm,iatom,ib)
coeff=MATMUL(coeff,
& norm_radf(iorb)%s12(1:n,1:n,is))
C coeff = coefficients c_(j,lm) of the decomposition of the state |psi> in the orthogonalized basis |phi_j>
C as defined in the tutorial (equation 25)
pr_orb(iorb,ik,is)%matn(m,ib,1:n)=coeff(1:n)
ENDDO
ENDDO ! End of the m loop
DEALLOCATE(coeff)
C pr_orb(iorb,ik,is)%matn(m,ib,1:n) is then the Theta projector as defined in equation 26 of the tutorial.
ENDIF ! End of the if l=0 if-then-else
ENDDO ! End of the iorb loop
C
ENDDO ! End of the loop on ik
ENDDO ! End of the loop on is
C
C
C ==========================================================================
C Multiplication of the projection matrices by the local rotation matrices :
C ==========================================================================
C
C ------------------------------------------------
C Wannier Projectors for the correlated orbitals :
C ------------------------------------------------
C
DO jcrorb=1,ncrorb
jatom=crorb(jcrorb)%atom
isrt=crorb(jcrorb)%sort
l=crorb(jcrorb)%l
C
C The case l=0 is a particular case of "non-mixing" basis.
C --------------------------------------------------------
IF (l==0) THEN
C For the s orbital, no multiplication is needed, since the matrix representation of any rotation
C (and thus Rloc) is always 1.
DO ik=1,nk
DO is=1,ns
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,is)%included) CYCLE
nbtop=kp(ik,is)%nb_top
nbbot=kp(ik,is)%nb_bot
IF(ALLOCATED(pr_crorb(jcrorb,ik,is)%mat_rep)) THEN
DEALLOCATE(pr_crorb(jcrorb,ik,is)%mat_rep)
ENDIF
ALLOCATE(pr_crorb(jcrorb,ik,is)
& %mat_rep(1,nbbot:nbtop))
pr_crorb(jcrorb,ik,is)%mat_rep(1,nbbot:nbtop)=
= pr_crorb(jcrorb,ik,is)%mat(1,nbbot:nbtop)
C As a result, prcrorb%matrep = prcrorb%mat
ENDDO
ENDDO
C
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) )
C ---------------------------------------------------------------------------------------------------
ELSEIF (reptrans(l,isrt)%ifmixing) THEN
C If this option is used, then ifSO=.TRUE. (because of the restriction in set_ang_trans.f)
C Moreover ifSP=.TRUE. (since ifSO => ifSP in this version)
C As a result, we know that nb_bot(up)=nb_bot(dn) and nb_top(up)=nb_top(dn)
DO ik=1,nk
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,1)%included) CYCLE
nbbot=kp(ik,1)%nb_bot
nbtop=kp(ik,1)%nb_top
C In this case, the projection matrix will be stored in prcrorb%matrep with is=1.
IF(ALLOCATED(pr_crorb(jcrorb,ik,1)%mat_rep)) THEN
DEALLOCATE(pr_crorb(jcrorb,ik,1)%mat_rep)
ENDIF
ALLOCATE(pr_crorb(jcrorb,ik,1)%
% mat_rep(1:2*(2*l+1),nbbot:nbtop))
C The element prcrorb%matrep for is=2 is set to 0, since all the matrix will be stored in the matrix matrep for is=1
IF(.not.ALLOCATED(pr_crorb(jcrorb,ik,2)%mat_rep)) THEN
ALLOCATE(pr_crorb(jcrorb,ik,2)%mat_rep(1,1))
pr_crorb(jcrorb,ik,2)%mat_rep(1,1)=0.d0
ENDIF
C Creation of a matrix tmp_mat which "concatenates" up and dn parts of pr_crorb.
ALLOCATE(tmp_mat(1:2*(2*l+1),nbbot:nbtop))
tmp_mat(1:(2*l+1),nbbot:nbtop)=
= pr_crorb(jcrorb,ik,1)%mat(-l:l,nbbot:nbtop)
C The first (2l+1) lines are the spin-up part of the projection matrix prcrorb%mat.
C
C ---------------------------------------------------------------------------------------
C Interruption of the prgm if there is no dn part of pr_orb.
C -------------------------
C
IF(.not.ifSP) THEN
WRITE(buf,'(a,a,i2,a)')'The projectors on ',
& 'the dn states are required for isrt = ',isrt,
& ' but there is no spin-polarized input files.'
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
ENDIF
C ---------------------------------------------------------------------------------------
C
C The last (2l+1) lines are the spin-dn part of the projection matrix prcrorb%mat.
tmp_mat((2*l+2):2*(2*l+1),nbbot:nbtop)=
= pr_crorb(jcrorb,ik,2)%mat(-l:l,nbbot:nbtop)
C
C Multiplication by the local rotation matrix ; Up and dn parts are treated independently
C since in lapw2 (-alm) the coefficients Alm, Blm and Clm were calculated in the local frame
C but without taking into account the spinor-rotation matrix.
ALLOCATE(tmp_matbis(1:(2*l+1),nbbot:nbtop))
tmp_matbis(1:(2*l+1),nbbot:nbtop)=
= tmp_mat(1:(2*l+1),nbbot:nbtop)
CALL rot_projectmat(tmp_matbis,
& l,nbbot,nbtop,jatom,isrt)
tmp_mat(1:(2*l+1),nbbot:nbtop)=
= tmp_matbis(1:(2*l+1),nbbot:nbtop)
tmp_matbis(1:(2*l+1),nbbot:nbtop)=
= tmp_mat(2*l+2:2*(2*l+1),nbbot:nbtop)
CALL rot_projectmat(tmp_matbis,
& l,nbbot,nbtop,jatom,isrt)
tmp_mat(2*l+2:2*(2*l+1),nbbot:nbtop)=
= tmp_matbis(1:(2*l+1),nbbot:nbtop)
DEALLOCATE(tmp_matbis)
C
C Putting pr_crorb in the desired basis associated to (l,isrt)
C
pr_crorb(jcrorb,ik,1)%mat_rep(1:2*(2*l+1),nbbot:nbtop)=
= MATMUL(reptrans(l,isrt)%transmat
& (1:2*(2*l+1),1:2*(2*l+1)),
& tmp_mat(1:2*(2*l+1),nbbot:nbtop))
C pr_crorb%mat_rep = proj_{new_i} = reptrans*proj_{lm} = *proj_{lm}
DEALLOCATE(tmp_mat)
ENDDO ! End of the ik loop
C
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only)
C --------------------------------------------------------------------------------------------
ELSE
DO ik=1,nk
DO is=1,ns
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,is)%included) CYCLE
C In this case, nb_top(up) and nb_bot(up) can differ from nb_top(dn) and nb_bot(dn)
nbbot=kp(ik,is)%nb_bot
nbtop=kp(ik,is)%nb_top
IF(ALLOCATED(pr_crorb(jcrorb,ik,is)%mat_rep)) THEN
DEALLOCATE(pr_crorb(jcrorb,ik,is)%mat_rep)
ENDIF
ALLOCATE(pr_crorb(jcrorb,ik,is)
& %mat_rep(-l:l,nbbot:nbtop))
pr_crorb(jcrorb,ik,is)%mat_rep(-l:l,nbbot:nbtop)=
= pr_crorb(jcrorb,ik,is)%mat(-l:l,nbbot:nbtop)
C
C Multiplication by the local rotation matrix
C since in lapw2 (-alm) the coefficients Alm, Blm and Clm were calculated in the local frame
CALL rot_projectmat(pr_crorb(jcrorb,ik,is)
& %mat_rep(-l:l,nbbot:nbtop),l,nbbot,nbtop,jatom,isrt)
C
C Putting pr_crorb in the desired basis associated to (l,isrt)
pr_crorb(jcrorb,ik,is)%mat_rep(-l:l,nbbot:nbtop)=
= MATMUL(reptrans(l,isrt)%transmat(-l:l,-l:l),
& pr_crorb(jcrorb,ik,is)%mat_rep(-l:l,nbbot:nbtop))
C pr_crorb%mat_rep = proj_{new_i} = reptrans*proj_{lm} = *proj_{lm}
ENDDO ! End of the is loop
ENDDO ! End of the ik loop
ENDIF ! End of the if mixing if-then-else
ENDDO ! End of the jcrorb loop
C
C ---------------------------------------
C Theta Projectors for all the orbitals :
C ---------------------------------------
C
DO jorb=1,norb
jatom=orb(jorb)%atom
isrt=orb(jorb)%sort
n=norm_radf(jorb)%n
l=orb(jorb)%l
C
C The case l=0 is a particular case of "non-mixing" basis.
C --------------------------------------------------------
IF (l==0) THEN
C For the s orbital, no multiplication is needed, since the matrix representation of any rotation
C (and therefore Rloc) is always 1.
DO ik=1,nk
DO is=1,ns
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,is)%included) CYCLE
nbtop=kp(ik,is)%nb_top
nbbot=kp(ik,is)%nb_bot
IF(ALLOCATED(pr_orb(jorb,ik,is)%matn_rep)) THEN
DEALLOCATE(pr_orb(jorb,ik,is)%matn_rep)
ENDIF
ALLOCATE(pr_orb(jorb,ik,is)%matn_rep
& (1,nbbot:nbtop,1:n))
pr_orb(jorb,ik,is)%matn_rep(1,nbbot:nbtop,1:n)=
= pr_orb(jorb,ik,is)%matn(1,nbbot:nbtop,1:n)
C As a result, prorb%matnrep = prorb%matn
ENDDO
ENDDO
C
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) )
C ---------------------------------------------------------------------------------------------------
ELSEIF (reptrans(l,isrt)%ifmixing) THEN
C If this option is used, then ifSO=.TRUE. (restriction in set_ang_trans.f)
C Moreover ifSP=.TRUE. (since ifSO => ifSP)
C As a result, we know that nb_bot(up)=nb_bot(dn) and nb_top(up)=nb_top(dn)
DO ik=1,nk
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,1)%included) CYCLE
nbbot=kp(ik,1)%nb_bot
nbtop=kp(ik,1)%nb_top
C In this case, the projection matrix will be stored in prorb%matnrep with is=1.
IF(ALLOCATED(pr_orb(jorb,ik,1)%matn_rep)) THEN
DEALLOCATE(pr_orb(jorb,ik,1)%matn_rep)
ENDIF
ALLOCATE(pr_orb(jorb,ik,1)%
% matn_rep(1:2*(2*l+1),nbbot:nbtop,1:n))
C The element prorb%matnrep for is=2 is set to 0, since all the matrix will be stored in the matrix matnrep for is=1
IF(.not.ALLOCATED(pr_orb(jorb,ik,2)%matn_rep)) THEN
ALLOCATE(pr_orb(jorb,ik,2)%matn_rep(1,1,1))
pr_orb(jorb,ik,2)%matn_rep(1,1,1)=0.d0
ENDIF
C Creation of a matrix tmp_matn which "concatenates" up and dn parts of pr_orb
ALLOCATE(tmp_matn(1:2*(2*l+1),nbbot:nbtop,1:n))
tmp_matn(1:(2*l+1),nbbot:nbtop,1:n)=
= pr_orb(jorb,ik,1)%matn(-l:l,nbbot:nbtop,1:n)
C The first (2l+1) lines are the spin-up part of the projection matrix prorb%matn.
C
C ---------------------------------------------------------------------------------------
C Interruption of the prgm if there is no dn part of pr_orb.
C -------------------------
C
IF(.not.ifSP) THEN
WRITE(buf,'(a,a,i2,a)')'The projectors on ',
& 'the down states are required for isrt = ',isrt,
& ' but there is no spin-polarized input files.'
CALL printout(0)
WRITE(buf,'(a)')'END OF THE PRGM'
CALL printout(0)
STOP
ENDIF
C ---------------------------------------------------------------------------------------
C
C The last (2l+1) lines are the spin-dn part of the projection matrix prorb%matn.
tmp_matn(2*l+2:2*(2*l+1),nbbot:nbtop,1:n)=
= pr_orb(jorb,ik,2)%matn(-l:l,nbbot:nbtop,1:n)
C
DO i=1,n
C Multiplication by the local rotation matrix ; Up and dn parts are treated independently
C since in lapw2 (-alm) the coefficients Alm, Blm and Clm were calculated in the local frame
C but without taking into account the spinor-rotation matrix.
ALLOCATE(tmp_matbis(1:(2*l+1),nbbot:nbtop))
tmp_matbis(1:(2*l+1),nbbot:nbtop)=
= tmp_matn(1:(2*l+1),nbbot:nbtop,i)
CALL rot_projectmat(tmp_matbis,
& l,nbbot,nbtop,jatom,isrt)
tmp_matn(1:(2*l+1),nbbot:nbtop,i)=
= tmp_matbis(1:(2*l+1),nbbot:nbtop)
tmp_matbis(1:(2*l+1),nbbot:nbtop)=
= tmp_matn(2*l+2:2*(2*l+1),nbbot:nbtop,i)
CALL rot_projectmat(tmp_matbis,
& l,nbbot,nbtop,jatom,isrt)
tmp_matn(2*l+2:2*(2*l+1),nbbot:nbtop,i)=
= tmp_matbis(1:(2*l+1),nbbot:nbtop)
DEALLOCATE(tmp_matbis)
C Putting pr_orb in the desired basis associated to (l,isrt)
pr_orb(jorb,ik,1)%matn_rep
& (1:2*(2*l+1),nbbot:nbtop,i)=
= MATMUL(reptrans(l,isrt)%
& transmat(1:2*(2*l+1),1:2*(2*l+1)),
& tmp_matn(1:2*(2*l+1),nbbot:nbtop,i))
C pr_orb%matn_rep = proj_{new_i} = reptrans*proj_{lm} = *proj_{lm}
ENDDO ! End of the i-loop
DEALLOCATE(tmp_matn)
ENDDO ! End of the ik loop
C
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only)
C --------------------------------------------------------------------------------------------
ELSE
DO ik=1,nk
DO is=1,ns
C Only the k-points with inlcuded bands are considered for the projectors.
IF(.NOT.kp(ik,is)%included) CYCLE
C In this case, nb_top(up) and nb_bot(up) can differ from nb_top(dn) and nb_bot(dn)
nbbot=kp(ik,is)%nb_bot
nbtop=kp(ik,is)%nb_top
IF(ALLOCATED(pr_orb(jorb,ik,is)%matn_rep)) THEN
DEALLOCATE(pr_orb(jorb,ik,is)%matn_rep)
ENDIF
ALLOCATE(pr_orb(jorb,ik,is)%
& matn_rep(-l:l,nbbot:nbtop,1:n))
pr_orb(jorb,ik,is)%matn_rep(-l:l,nbbot:nbtop,1:n)=
= pr_orb(jorb,ik,is)%matn(-l:l,nbbot:nbtop,1:n)
C
DO i=1,n
C Multiplication by the local rotation matrix
C since in lapw2 (-alm) the coefficients Alm, Blm and Clm were calculated in the local frame
CALL rot_projectmat(pr_orb(jorb,ik,is)
& %matn_rep(-l:l,nbbot:nbtop,i),
& l,nbbot,nbtop,jatom,isrt)
C Putting pr_orb in the desired basis associated to (l,isrt)
pr_orb(jorb,ik,is)%matn_rep(-l:l,nbbot:nbtop,i)=
= MATMUL(reptrans(l,isrt)%transmat(-l:l,-l:l),
& pr_orb(jorb,ik,is)%matn_rep(-l:l,nbbot:nbtop,i))
C pr_orb%matn_rep = proj_{new_i} = reptrans*proj_{lm} = *proj_{lm}
ENDDO ! End of the i loop
ENDDO ! End of the is loop
ENDDO ! End of the ik loop
ENDIF ! End of the if mixing if-then-else
ENDDO ! End of the jorb loop
C
C
C =============================================================================
C Printing the projectors with k-points 1 and nk in the file fort.18 for test :
C =============================================================================
DO icrorb=1,ncrorb
iatom=crorb(icrorb)%atom
isrt=crorb(icrorb)%sort
l=crorb(icrorb)%l
WRITE(18,'()')
WRITE(18,'(a,i4)') 'icrorb = ', icrorb
WRITE(18,'(a,i4,a,i4)') 'isrt = ', isrt, ' l = ', l
IF (l==0) THEN
WRITE(18,'(a,i4)') 'ik = ', 1
DO ib = kp(1,1)%nb_bot,kp(1,1)%nb_top
WRITE(18,*) pr_crorb(icrorb,1,1)%mat_rep(:,ib)
IF (ifSP)
& WRITE(18,*) pr_crorb(icrorb,1,2)%mat_rep(:,ib)
WRITE(18,'()')
ENDDO
WRITE(18,'(a,i4)') 'ik = ', nk
DO ib = kp(nk,1)%nb_bot,kp(nk,1)%nb_top
WRITE(18,*) pr_crorb(icrorb,nk,1)%mat_rep(:,ib)
IF (ifSP)
& WRITE(18,*) pr_crorb(icrorb,nk,2)%mat_rep(:,ib)
WRITE(18,'()')
ENDDO
ELSEIF (reptrans(l,isrt)%ifmixing) THEN
WRITE(18,'(a,i4)') 'ik = ', 1
DO ib = kp(1,1)%nb_bot,kp(1,1)%nb_top
WRITE(18,*) pr_crorb(icrorb,1,1)%mat_rep(:,ib)
WRITE(18,'()')
ENDDO
WRITE(18,'(a,i4)') 'ik = ', nk
DO ib = kp(nk,1)%nb_bot,kp(nk,1)%nb_top
WRITE(18,*) pr_crorb(icrorb,nk,1)%mat_rep(:,ib)
WRITE(18,'()')
ENDDO
ELSE
WRITE(18,'(a,i4)') 'ik = ', 1
DO ib = kp(1,1)%nb_bot,kp(1,1)%nb_top
WRITE(18,*) pr_crorb(icrorb,1,1)%mat_rep(:,ib)
IF (ifSP)
& WRITE(18,*) pr_crorb(icrorb,1,2)%mat_rep(:,ib)
WRITE(18,'()')
ENDDO
WRITE(18,'(a,i4)') 'ik = ', nk
DO ib = kp(nk,1)%nb_bot,kp(nk,1)%nb_top
WRITE(18,*) pr_crorb(icrorb,nk,1)%mat_rep(:,ib)
IF (ifSP)
& WRITE(18,*) pr_crorb(icrorb,nk,2)%mat_rep(:,ib)
WRITE(18,'()')
ENDDO
ENDIF
ENDDO
C
DO iorb=1,norb
iatom=orb(iorb)%atom
isrt=orb(iorb)%sort
l=orb(iorb)%l
n=norm_radf(iorb)%n
WRITE(18,'()')
WRITE(18,'(a,i4)') 'iorb = ', iorb
WRITE(18,'(a,i4,a,i4)') 'isrt = ', isrt, ' l = ', l
IF (l==0) THEN
WRITE(18,'(a,i4)') 'ik = ', 1
DO i=1,n
WRITE(18,'(i4)') i
DO ib = kp(1,1)%nb_bot,kp(1,1)%nb_top
WRITE(18,*) pr_orb(iorb,1,1)%matn_rep(:,ib,i)
IF (ifSP)
& WRITE(18,*) pr_orb(iorb,1,2)%matn_rep(:,ib,i)
WRITE(18,'()')
ENDDO
ENDDO
WRITE(18,'(a,i4)') 'ik = ', nk
DO i=1,n
WRITE(18,'(i4)') i
DO ib = kp(nk,1)%nb_bot,kp(nk,1)%nb_top
WRITE(18,*) pr_orb(iorb,nk,1)%matn_rep(:,ib,i)
IF (ifSP)
& WRITE(18,*) pr_orb(iorb,nk,2)%matn_rep(:,ib,i)
WRITE(18,'()')
ENDDO
ENDDO
ELSEIF(reptrans(l,isrt)%ifmixing) THEN
DO i=1,n
WRITE(18,'(i4)') i
DO ib = kp(1,1)%nb_bot,kp(1,1)%nb_top
WRITE(18,*) pr_orb(iorb,1,1)%matn_rep(:,ib,i)
WRITE(18,'()')
ENDDO
ENDDO
WRITE(18,'(a,i4)') 'ik = ', nk
DO i=1,n
WRITE(18,'(i4)') i
DO ib = kp(nk,1)%nb_bot,kp(nk,1)%nb_top
WRITE(18,*) pr_orb(iorb,nk,1)%matn_rep(:,ib,i)
WRITE(18,'()')
ENDDO
ENDDO
ELSE
DO i=1,n
WRITE(18,'(i4)') i
DO ib = kp(1,1)%nb_bot,kp(1,1)%nb_top
WRITE(18,*) pr_orb(iorb,1,1)%matn_rep(:,ib,i)
IF (ifSP)
& WRITE(18,*) pr_orb(iorb,1,2)%matn_rep(:,ib,i)
WRITE(18,'()')
ENDDO
ENDDO
WRITE(18,'(a,i4)') 'ik = ', nk
DO i=1,n
WRITE(18,'(i4)') i
DO ib = kp(nk,1)%nb_bot,kp(nk,1)%nb_top
WRITE(18,*) pr_orb(iorb,nk,1)%matn_rep(:,ib,i)
IF (ifSP)
& WRITE(18,*) pr_orb(iorb,nk,2)%matn_rep(:,ib,i)
WRITE(18,'()')
ENDDO
ENDDO
ENDIF
ENDDO
C
RETURN
END