3
0
mirror of https://github.com/triqs/dft_tools synced 2024-10-31 19:23:45 +01:00
dft_tools/fortran/vertex/vertex.f90

227 lines
6.0 KiB
Fortran
Raw Normal View History

2013-07-23 19:49:42 +02:00
SUBROUTINE u4ind(u_out,rcl,l,N,TM)
IMPLICIT NONE
INTEGER,INTENT(in) :: l,N
COMPLEX*16, DIMENSION(N,N), INTENT(in) :: TM !Transformation Matrix
DOUBLE PRECISION, DIMENSION(2*l+1,2*l+1,2*l+1,2*l+1) :: uc
!double precision, dimension(N,N,N,N), intent(out) :: u_out
COMPLEX*16, DIMENSION(N,N,N,N), INTENT(out) :: u_out
DOUBLE PRECISION, DIMENSION(N,N,N,N) :: u_tmp
DOUBLE PRECISION, DIMENSION(l+1), INTENT(in) :: rcl
INTEGER :: mmax,k,k2p1,ms1,ms2,ms3,ms4,ms5,ms6,ms7,ms8
INTEGER :: sp,ms1sig,ms2sig,ms3sig,ms4sig
INTEGER :: xk,xm1,xm2,xm3,xm,xm4
DOUBLE PRECISION :: cgk0,cgk1,cgk2,yor(7,7),yoi(7,7)
COMPLEX*16 :: am1,am2,am3,am4
!external cgk, ctormt
!WRITE(*,*)l,N
mmax=2*l+1
IF ((N==mmax).OR.(N==2*mmax)) THEN
! dimensions are fine:
uc=0.d0
DO k = 0, 2*l, 2
k2p1 = k/2 + 1
cgk0 = cgk(l,0,k,0,l,0)
DO ms1 = 1,mmax
xm1 = (ms1-l-1)
DO ms2 = 1,mmax
xm2 = (ms2-l-1)
DO ms3 = 1,mmax
xm3 = (ms3-l-1)
xm = xm1 - xm3
DO ms4 = 1,mmax
IF ((ms1+ms2-ms3-ms4).NE.0) CYCLE
xm4 = (ms4-l-1)
cgk1 = cgk(l,xm3,k,xm,l,xm1)
cgk2 = cgk(l,xm2,k,xm,l,xm4)
uc(ms1,ms2,ms3,ms4) = uc(ms1,ms2,ms3,ms4) + rcl(k2p1)*cgk0*cgk0*cgk1*cgk2
ENDDO
ENDDO
ENDDO
ENDDO
ENDDO
u_tmp = 0.d0
sp = (N/mmax)-1
! Now construct the big u matrix:
! expand in spins:
DO ms1=1,mmax
DO ms1sig =0,sp
DO ms2=1,mmax
DO ms2sig=0,sp
DO ms3 = 1,mmax
DO ms3sig = 0,sp
DO ms4 = 1,mmax
DO ms4sig = 0,sp
IF ((ms1sig==ms3sig).AND.(ms2sig==ms4sig)) THEN
u_tmp(ms1sig*mmax+ms1,ms2sig*mmax+ms2,ms3sig*mmax+ms3,ms4sig*mmax+ms4) = uc(ms1,ms2,ms3,ms4)
ENDIF
ENDDO
ENDDO
ENDDO
ENDDO
ENDDO
ENDDO
ENDDO
ENDDO
!call ctormt()
! Transformation:
!write(*,*)'TEST'
u_out = 0.d0
DO ms1=1,N
DO ms2=1,N
DO ms3=1,N
DO ms4=1,N
DO ms5=1,N
am1 = CONJG(TM(ms1,ms5)) !cmplx(yor(ms1,ms5),-yoi(ms1,ms5))
DO ms6=1,N
am2 = CONJG(TM(ms2,ms6)) !cmplx(yor(ms2,ms6),-yoi(ms2,ms6))
DO ms7=1,N
am3 = TM(ms3,ms7) !cmplx(yor(ms3,ms7),yoi(ms3,ms7))
DO ms8=1,N
am4 = TM(ms4,ms8) !cmplx(yor(ms4,ms8),yoi(ms4,ms8))
u_out(ms1,ms2,ms3,ms4) = u_out(ms1,ms2,ms3,ms4) + am1*am2*am3*am4 * u_tmp(ms5,ms6,ms7,ms8)
ENDDO
ENDDO
ENDDO
ENDDO
!if (abs(u_out(ms1,ms2,ms3,ms4))>0.0001d0) then
! write(*,*)ms1,ms2,ms3,ms4, u_out(ms1,ms2,ms3,ms4)
!endif
ENDDO
ENDDO
ENDDO
ENDDO
ELSE
WRITE(*,*)"N and l does not fit together: N=2l+1 or 2*(2l+1)!"
ENDIF
CONTAINS
SUBROUTINE ctormt
IMPLICIT NONE
DOUBLE PRECISION :: sqtwo, sq54, sq34
yor=0.d0
yoi=0.d0
sqtwo=1.d0/SQRT(2.d0)
sq54=SQRT(5.d0)/4d0
sq34=SQRT(3.d0)/4d0
IF (l.EQ.0) THEN
yor(1,1)=1.d0
ELSEIF (l.EQ.1) THEN
yor(1,1)= sqtwo
yor(1,3)=-sqtwo
yor(2,2)=1.d0
yoi(3,1)= sqtwo
yoi(3,3)= sqtwo
ELSEIF (l.EQ.2) THEN
!yoi(1,1)= sqtwo
!yoi(1,5)=-sqtwo
!yoi(2,2)= sqtwo
!yoi(2,4)= sqtwo
!yor(3,3)=1.d0
!yor(4,2)= sqtwo
!yor(4,4)=-sqtwo
!yor(5,1)= sqtwo
!yor(5,5)= sqtwo
! Wien2K matrix:
yor(3,1) = -sqtwo
yor(3,5) = sqtwo
yor(5,2) = sqtwo
yor(5,4) = sqtwo
yor(1,3) = 1.d0
yor(4,2) = sqtwo
yor(4,4) = -sqtwo
yor(2,1) = sqtwo
yor(2,5) = sqtwo
ELSEIF (l.EQ.3) THEN
yoi(1,2)=sqtwo
yoi(1,6)=-sqtwo
yor(2,1)=-sq54
yor(2,3)=sq34
yor(2,5)=-sq34
yor(2,7)=sq54
yoi(3,1)=-sq54
yoi(3,3)=-sq34
yoi(3,5)=-sq34
yoi(3,7)=-sq54
yor(4,4)=1.d0
yor(5,1)=-sq34
yor(5,3)=-sq54
yor(5,5)=sq54
yor(5,7)=sq34
yoi(6,1)=sq34
yoi(6,3)=-sq54
yoi(6,5)=-sq54
yoi(6,7)=sq34
yor(7,2)=sqtwo
yor(7,6)=sqtwo
ENDIF
END SUBROUTINE ctormt
DOUBLE PRECISION FUNCTION cgk(a,al,b,be,c,ga)
IMPLICIT NONE
INTEGER :: a,al,b,be,c,ga
INTEGER :: z,zmin,zmax,i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13
DOUBLE PRECISION :: fa(0:20), fac
fa = (/1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 12.d1, 72.d1, 504.d1,&
4032.d1, 36288.d1, 36288.d2, 399168.d2, 4790016.d2,&
62270208.d2, 871782912.d2, 1307674368.d3, 20922789888.d3,&
355687428096.d3, 6402373705728.d3, 121645100408832.d3,243290200817664.d4/)
i1=0
i2=(a+b-c)
i3=(a-al)
i4=(b+be)
i5=(c-b+al)
i6=(c-a-be)
zmin=MAX(i1,-i5,-i6)
zmax=MIN(i2, i3, i4)
cgk=0.d0
IF (ABS(al).GT.a) RETURN
IF (ABS(be).GT.b) RETURN
IF (ABS(ga).GT.c) RETURN
IF ( zmin.GT.zmax ) RETURN
IF ( (al+be).NE.ga ) RETURN
i7=(a-b+c)
i8=(c+b-a)
i9=(c+b+a)
i10=(a+al)
i11=(b-be)
i12=(c+ga)
i13=(c-ga)
DO z=zmin,zmax
IF (MOD(z,2)==0) THEN
fac = 1.d0
ELSE
fac=-1.d0
ENDIF
cgk=cgk+fac/(fa(z)*fa(i2-z)*fa(i3-z)*fa(i4-z)*fa(i5+z)* fa(i6+z))
ENDDO
cgk=cgk*SQRT(fa(i2)*fa(i7)*fa(i8)*fa(i10)*fa(i3)*fa(i4)*fa(i11)*fa(i12)*fa(i13)*(2.d0*c+1.d0)/fa(i9+1))
END FUNCTION cgk
END SUBROUTINE u4ind