mirror of
https://github.com/triqs/dft_tools
synced 2024-11-09 07:33:47 +01:00
227 lines
6.0 KiB
Fortran
227 lines
6.0 KiB
Fortran
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SUBROUTINE u4ind(u_out,rcl,l,N,TM)
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IMPLICIT NONE
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INTEGER,INTENT(in) :: l,N
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COMPLEX*16, DIMENSION(N,N), INTENT(in) :: TM !Transformation Matrix
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DOUBLE PRECISION, DIMENSION(2*l+1,2*l+1,2*l+1,2*l+1) :: uc
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!double precision, dimension(N,N,N,N), intent(out) :: u_out
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COMPLEX*16, DIMENSION(N,N,N,N), INTENT(out) :: u_out
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DOUBLE PRECISION, DIMENSION(N,N,N,N) :: u_tmp
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DOUBLE PRECISION, DIMENSION(l+1), INTENT(in) :: rcl
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INTEGER :: mmax,k,k2p1,ms1,ms2,ms3,ms4,ms5,ms6,ms7,ms8
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INTEGER :: sp,ms1sig,ms2sig,ms3sig,ms4sig
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INTEGER :: xk,xm1,xm2,xm3,xm,xm4
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DOUBLE PRECISION :: cgk0,cgk1,cgk2,yor(7,7),yoi(7,7)
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COMPLEX*16 :: am1,am2,am3,am4
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!external cgk, ctormt
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!WRITE(*,*)l,N
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mmax=2*l+1
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IF ((N==mmax).OR.(N==2*mmax)) THEN
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! dimensions are fine:
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uc=0.d0
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DO k = 0, 2*l, 2
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k2p1 = k/2 + 1
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cgk0 = cgk(l,0,k,0,l,0)
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DO ms1 = 1,mmax
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xm1 = (ms1-l-1)
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DO ms2 = 1,mmax
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xm2 = (ms2-l-1)
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DO ms3 = 1,mmax
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xm3 = (ms3-l-1)
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xm = xm1 - xm3
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DO ms4 = 1,mmax
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IF ((ms1+ms2-ms3-ms4).NE.0) CYCLE
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xm4 = (ms4-l-1)
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cgk1 = cgk(l,xm3,k,xm,l,xm1)
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cgk2 = cgk(l,xm2,k,xm,l,xm4)
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uc(ms1,ms2,ms3,ms4) = uc(ms1,ms2,ms3,ms4) + rcl(k2p1)*cgk0*cgk0*cgk1*cgk2
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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u_tmp = 0.d0
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sp = (N/mmax)-1
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! Now construct the big u matrix:
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! expand in spins:
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DO ms1=1,mmax
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DO ms1sig =0,sp
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DO ms2=1,mmax
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DO ms2sig=0,sp
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DO ms3 = 1,mmax
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DO ms3sig = 0,sp
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DO ms4 = 1,mmax
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DO ms4sig = 0,sp
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IF ((ms1sig==ms3sig).AND.(ms2sig==ms4sig)) THEN
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u_tmp(ms1sig*mmax+ms1,ms2sig*mmax+ms2,ms3sig*mmax+ms3,ms4sig*mmax+ms4) = uc(ms1,ms2,ms3,ms4)
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ENDIF
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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!call ctormt()
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! Transformation:
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!write(*,*)'TEST'
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u_out = 0.d0
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DO ms1=1,N
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DO ms2=1,N
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DO ms3=1,N
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DO ms4=1,N
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DO ms5=1,N
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am1 = CONJG(TM(ms1,ms5)) !cmplx(yor(ms1,ms5),-yoi(ms1,ms5))
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DO ms6=1,N
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am2 = CONJG(TM(ms2,ms6)) !cmplx(yor(ms2,ms6),-yoi(ms2,ms6))
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DO ms7=1,N
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am3 = TM(ms3,ms7) !cmplx(yor(ms3,ms7),yoi(ms3,ms7))
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DO ms8=1,N
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am4 = TM(ms4,ms8) !cmplx(yor(ms4,ms8),yoi(ms4,ms8))
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u_out(ms1,ms2,ms3,ms4) = u_out(ms1,ms2,ms3,ms4) + am1*am2*am3*am4 * u_tmp(ms5,ms6,ms7,ms8)
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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!if (abs(u_out(ms1,ms2,ms3,ms4))>0.0001d0) then
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! write(*,*)ms1,ms2,ms3,ms4, u_out(ms1,ms2,ms3,ms4)
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!endif
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ENDDO
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ENDDO
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ENDDO
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ENDDO
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ELSE
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WRITE(*,*)"N and l does not fit together: N=2l+1 or 2*(2l+1)!"
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ENDIF
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CONTAINS
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SUBROUTINE ctormt
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IMPLICIT NONE
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DOUBLE PRECISION :: sqtwo, sq54, sq34
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yor=0.d0
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yoi=0.d0
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sqtwo=1.d0/SQRT(2.d0)
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sq54=SQRT(5.d0)/4d0
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sq34=SQRT(3.d0)/4d0
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IF (l.EQ.0) THEN
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yor(1,1)=1.d0
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ELSEIF (l.EQ.1) THEN
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yor(1,1)= sqtwo
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yor(1,3)=-sqtwo
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yor(2,2)=1.d0
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yoi(3,1)= sqtwo
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yoi(3,3)= sqtwo
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ELSEIF (l.EQ.2) THEN
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!yoi(1,1)= sqtwo
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!yoi(1,5)=-sqtwo
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!yoi(2,2)= sqtwo
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!yoi(2,4)= sqtwo
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!yor(3,3)=1.d0
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!yor(4,2)= sqtwo
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!yor(4,4)=-sqtwo
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!yor(5,1)= sqtwo
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!yor(5,5)= sqtwo
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! Wien2K matrix:
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yor(3,1) = -sqtwo
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yor(3,5) = sqtwo
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yor(5,2) = sqtwo
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yor(5,4) = sqtwo
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yor(1,3) = 1.d0
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yor(4,2) = sqtwo
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yor(4,4) = -sqtwo
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yor(2,1) = sqtwo
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yor(2,5) = sqtwo
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ELSEIF (l.EQ.3) THEN
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yoi(1,2)=sqtwo
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yoi(1,6)=-sqtwo
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yor(2,1)=-sq54
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yor(2,3)=sq34
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yor(2,5)=-sq34
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yor(2,7)=sq54
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yoi(3,1)=-sq54
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yoi(3,3)=-sq34
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yoi(3,5)=-sq34
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yoi(3,7)=-sq54
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yor(4,4)=1.d0
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yor(5,1)=-sq34
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yor(5,3)=-sq54
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yor(5,5)=sq54
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yor(5,7)=sq34
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yoi(6,1)=sq34
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yoi(6,3)=-sq54
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yoi(6,5)=-sq54
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yoi(6,7)=sq34
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yor(7,2)=sqtwo
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yor(7,6)=sqtwo
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ENDIF
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END SUBROUTINE ctormt
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DOUBLE PRECISION FUNCTION cgk(a,al,b,be,c,ga)
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IMPLICIT NONE
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INTEGER :: a,al,b,be,c,ga
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INTEGER :: z,zmin,zmax,i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13
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DOUBLE PRECISION :: fa(0:20), fac
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fa = (/1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 12.d1, 72.d1, 504.d1,&
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4032.d1, 36288.d1, 36288.d2, 399168.d2, 4790016.d2,&
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62270208.d2, 871782912.d2, 1307674368.d3, 20922789888.d3,&
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355687428096.d3, 6402373705728.d3, 121645100408832.d3,243290200817664.d4/)
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i1=0
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i2=(a+b-c)
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i3=(a-al)
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i4=(b+be)
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i5=(c-b+al)
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i6=(c-a-be)
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zmin=MAX(i1,-i5,-i6)
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zmax=MIN(i2, i3, i4)
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cgk=0.d0
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IF (ABS(al).GT.a) RETURN
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IF (ABS(be).GT.b) RETURN
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IF (ABS(ga).GT.c) RETURN
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IF ( zmin.GT.zmax ) RETURN
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IF ( (al+be).NE.ga ) RETURN
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i7=(a-b+c)
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i8=(c+b-a)
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i9=(c+b+a)
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i10=(a+al)
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i11=(b-be)
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i12=(c+ga)
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i13=(c-ga)
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DO z=zmin,zmax
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IF (MOD(z,2)==0) THEN
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fac = 1.d0
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ELSE
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fac=-1.d0
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ENDIF
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cgk=cgk+fac/(fa(z)*fa(i2-z)*fa(i3-z)*fa(i4-z)*fa(i5+z)* fa(i6+z))
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ENDDO
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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))
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END FUNCTION cgk
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END SUBROUTINE u4ind
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