430 lines
12 KiB
Fortran
430 lines
12 KiB
Fortran
!
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!=======================================================================
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!
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MODULE UTILITIES_2
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!
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USE ACCURACY_REAL
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!
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! It contains the following functions/subroutines:
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!
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! * SUBROUTINE IMAG_TO_REAL(IM,OM,NS,RE)
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! * SUBROUTINE REAL_TO_IMAG(RE,OM,NS,RE_INF,IM)
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! * SUBROUTINE EPSI_TO_EPSR(EPSI,OM,NS,EPSR)
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! * SUBROUTINE EPSR_TO_EPSI(EPSR,OM,NS,EPSI)
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! * SUBROUTINE GR_TO_SQ_3D(Q,NSIZE,MAX_R,T,RS,GR_TYPE,RH_TYPE,SQ)
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! * SUBROUTINE SQ_TO_GR_3D(R,NSIZE,MAX_X,IN_MODE,T,RS,SQ_TYPE,&
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! GQ_TYPE,EC_TYPE,GR)
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! * SUBROUTINE SQ_TO_VA_3D(NSIZE,MAX_X,IN_MODE,T,SQ_TYPE, &
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! GQ_TYPE,EC_TYPE,VA)
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!
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CONTAINS
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!
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!=======================================================================
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!
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SUBROUTINE IMAG_TO_REAL(IM,OM,NS,RE)
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!
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! This subroutine computes the real part of the function F(omega)
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! form the knowledge of the imaginary part, using the Kramers-Kronig
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! relations.
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!
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!
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!
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! Input parameters:
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!
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! * IM : array containing Im[ F(omega) ]
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! * OM : array containing omega
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! * NS : size of arrays of OM, RE and IM
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!
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!
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! Output variables :
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!
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! * RE : array containing Re[ F(omega) ]
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 23 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ZERO
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USE TRANSFORMS, ONLY : KK
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!
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IMPLICIT NONE
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!
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REAL (WP) :: IM(NS),OM(NS)
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REAL (WP) :: RE(NS),RE_INF
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!
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INTEGER :: NS
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!
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! Calling the Kramers-Kronig subroutine
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!
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RE_INF=ZERO ! unused inside KK
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CALL KK('I2R',NS,OM,RE,RE_INF,IM) ! for 'I2R'
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!
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RETURN
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!
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END
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!
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!=======================================================================
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!
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SUBROUTINE REAL_TO_IMAG(RE,OM,NS,RE_INF,IM)
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!
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! This subroutine computes the imaginary part of the function F(omega)
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! form the knowledge of the real part, using the Kramers-Kronig
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! relations.
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!
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!
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!
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! Input parameters:
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!
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! * RE : array containing Re[ F(omega) ]
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! * OM : array containing omega
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! * NS : size of arrays of OM, RE and IM
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! * RE_INF : value of Re[ F(omega --> + infinity) ]
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!
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!
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! Output variables :
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!
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! * IM : array containing Im[ F(omega) ]
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 23 Jun 2020
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!
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!
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USE TRANSFORMS, ONLY : KK
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!
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IMPLICIT NONE
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!
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REAL (WP) :: RE(NS),OM(NS)
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REAL (WP) :: IM(NS),RE_INF
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!
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INTEGER :: NS
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!
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! Calling the Kramers-Kronig subroutine
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!
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CALL KK('R2I',NS,OM,RE,RE_INF,IM) !
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!
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END SUBROUTINE REAL_TO_IMAG
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!
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!=======================================================================
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!
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SUBROUTINE EPSI_TO_EPSR(EPSI,OM,NS,EPSR)
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!
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! This subroutine computes the real part of the dielectric function
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! form the knowledge of the imaginary part, using the Kramers-Kronig
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! relations.
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!
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!
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!
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! Input parameters:
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!
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! * EPSI : array containing Im[ EPS(q,omega) ] for a given q
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! * OM : array containing omega
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! * NS : size of arrays of OM, EPSR and EPSI
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!
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!
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! Output variables :
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!
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! * EPSR : array containing Re[ EPS(q,omega) ] for a given q
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE REAL_NUMBERS, ONLY : ONE
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USE TRANSFORMS, ONLY : KK
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!
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IMPLICIT NONE
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!
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REAL (WP) :: EPSI(NSIZE),OM(NSIZE)
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REAL (WP) :: EPSR(NSIZE),EPSR_INF
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!
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INTEGER :: NS
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!
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! Calling the Kramers-Kronig subroutine
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!
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EPSR_INF=ONE ! value of EPSR at infinity
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!
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CALL KK('I2R',NS,OM,EPSI,EPSR_INF,EPSR) !
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!
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END SUBROUTINE EPSI_TO_EPSR
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!
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!=======================================================================
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!
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SUBROUTINE EPSR_TO_EPSI(EPSR,OM,NS,EPSI)
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!
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! This subroutine computes the imaginary part of the dielectric function
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! form the knowledge of the real part, using the Kramers-Kronig
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! relations.
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!
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!
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!
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! Input parameters:
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!
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! * EPSR : array containing Re[ EPS(q,omega) ] for a given q
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! * OM : array containing omega
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! * NS : size of arrays of OM, EPSR and EPSI
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!
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!
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! Output variables :
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!
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! * EPSI : array containing Im[ EPS(q,omega) ] for a given q
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE REAL_NUMBERS, ONLY : ONE
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USE TRANSFORMS, ONLY : KK
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!
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IMPLICIT NONE
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!
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REAL (WP) :: EPSR(NSIZE),OM(NSIZE)
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REAL (WP) :: EPSI(NSIZE),EPSR_INF
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!
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INTEGER :: NS
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!
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! Calling the Kramers-Kronig subroutine
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!
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EPSR_INF=ONE ! value of EPSR at infinity
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!
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CALL KK('R2I',NS,OM,EPSR,EPSR_INF,EPSI) !
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!
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END SUBROUTINE EPSR_TO_EPSI
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!
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!=======================================================================
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!
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SUBROUTINE GR_TO_SQ_3D(Q,MAX_R,T,RS,GR_TYPE,RH_TYPE,SQ)
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!
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! This subroutine computes the 3D static structure factor S(q)
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! from the pair correlation function g(r) according to
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!
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! / + inf
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! | -i q.r
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! S(q) = 1 + n | ( g(r)-1 ) e dr
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! |
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! / 0
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!
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! / + inf
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! 4 pi n |
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! = 1 + -------- | r sin(qr) ( g(r)-1 ) dr
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! q |
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! / 0
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!
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!
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! Input parameters:
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!
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! * Q : point q where S(q) is computed
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! * MAX_R : upper integration value
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! * T : temperature in SI
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * GR_TYPE : pair correlation function type (3D)
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! * RH_TYPE : choice of pair distribution function rho_2(r) (3D)
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!
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!
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! Output variables :
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!
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! * SQ : S(q) at point q
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE REAL_NUMBERS, ONLY : ONE,FOUR
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USE PI_ETC, ONLY : PI
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE INTEGRATION, ONLY : INTEGR_L
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USE PAIR_CORRELATION, ONLY : PAIR_CORRELATION_3D
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 3) :: GR_TYPE,RH_TYPE
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!
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REAL (WP), INTENT(IN) :: Q,T,RS,MAX_R
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REAL (WP) :: GR,SQ
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REAL (WP) :: N0,R
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REAL (WP) :: INTF(NSIZE),XA(NSIZE),H,IN
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!
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INTEGER :: NMAX,K,N1,ID
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!
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! Computing the electron density
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!
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N0=RS_TO_N0('3D',RS) !
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!
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! Computing the integrand function
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!
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N1=NMAX ! index of upper bound
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DO K=1,NMAX !
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!
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XA(K)=MAX_R*FLOAT(K-1)/FLOAT(NSIZE-1) !
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R=XA(K) !
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!
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! Computing the pair correlation factor g(r)
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!
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CALL PAIR_CORRELATION_3D(R,RS,T,GR_TYPE,RH_TYPE,GR) !
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!
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INTF(K)=XA(K)*SIN(Q*XA(K))*(GR-ONE) !
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!
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END DO !
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!
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H=XA(2)-XA(1) ! step
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ID=1 !
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!
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! Computing the integral
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!
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CALL INTEGR_L(INTF,H,NMAX,N1,IN,ID) !
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!
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SQ=ONE + (FOUR*PI*N0/Q) * IN !
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!
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END SUBROUTINE GR_TO_SQ_3D
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!
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!=======================================================================
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!
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SUBROUTINE SQ_TO_GR_3D(R,NMAX,MAX_X,IN_MODE,T,RS,SQ_TYPE, &
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GQ_TYPE,GR)
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!
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! This subroutine computes the 3D pair correlation function g(r)
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! from the static structure factor S(q) according to
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!
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! / + inf
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! 1 1 | i q.r
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! g(r) = 1 + --- ---------- | ( S(q)-1 ) e dq
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! n (2 pi)^d |
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! / 0
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!
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! / + inf
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! 1 1 |
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! = 1 + + --- ------------ | q sin(qr) ( S(q)-1 ) dq
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! n (2 pi)^2 r |
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! / 0
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!
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!
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! Input parameters:
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!
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! * R : point r where g(r) is computed
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! * NMAX : dimensioning of the arrays
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! * MAX_X : upper integration value
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! * IN_MODE : type of integral computed
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! * T : temperature in SI
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * SQ_TYPE : structure factor approximation (3D)
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! * GQ_TYPE : local-field correction type (3D)
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!
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!
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! Output variables :
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!
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! * GR : g(r) at point r
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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USE REAL_NUMBERS, ONLY : ONE,TWO
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USE PI_ETC, ONLY : PI2
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE SPECIFIC_INT_2, ONLY : INT_SQM1
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 4) :: GQ_TYPE
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CHARACTER (LEN = 3) :: SQ_TYPE
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!
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REAL (WP) :: R,T,RS,MAX_X
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REAL (WP) :: GR
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REAL (WP) :: IN,N0
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!
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INTEGER :: NMAX,IN_MODE,LL
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!
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IN_MODE=4 !
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LL=0 !
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!
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! Computing the integral
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!
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CALL INT_SQM1(NMAX,MAX_X,IN_MODE,RS,T,R,LL,SQ_TYPE, & !
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GQ_TYPE,IN) !
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!
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! Computing the electron density
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!
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N0=RS_TO_N0('3D',RS) !
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!
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GR=ONE + ONE/N0 * IN/(TWO*PI2*R) !
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!
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END SUBROUTINE SQ_TO_GR_3D
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!
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!=======================================================================
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!
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SUBROUTINE SQ_TO_VA_3D(NMAX,MAX_X,IN_MODE,RS,T,SQ_TYPE, &
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GQ_TYPE,VA)
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!
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! This subroutine computes the average potential energy per electron <V>
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! from the static structure factor S(q) according to
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!
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! / + inf
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! e^2 |
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! <V> = ----- | ( S(q)-1 ) dq
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! pi |
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! / 0
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!
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!
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! Input parameters:
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!
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! * NMAX : dimensioning of the arrays
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! * MAX_X : upper integration value
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! * IN_MODE : type of integral computed
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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! * SQ_TYPE : structure factor approximation (3D)
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! * GQ_TYPE : local-field correction type (3D)
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!
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!
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! Output variables :
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!
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! * VA : <V> per electron
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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USE REAL_NUMBERS, ONLY : ZERO
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USE CONSTANTS_P1, ONLY : E
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USE PI_ETC, ONLY : PI
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USE SPECIFIC_INT_2, ONLY : INT_SQM1
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 4) :: GQ_TYPE
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CHARACTER (LEN = 3) :: SQ_TYPE
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!
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REAL (WP) :: MAX_X,RS,T
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REAL (WP) :: VA
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REAL (WP) :: R,IN
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!
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INTEGER :: NMAX,IN_MODE,LL
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!
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IN_MODE=1 !
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LL=0 ! unused
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R=ZERO ! parameters
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!
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! Computing the integral
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!
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CALL INT_SQM1(NMAX,MAX_X,IN_MODE,RS,T,R,LL,SQ_TYPE, & !
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GQ_TYPE,IN) !
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!
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VA=E*E/PI * IN !
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!
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END SUBROUTINE SQ_TO_VA_3D
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!
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END MODULE UTILITIES_2
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