profval.f

C LEVEL 7      SUBROUTINE PROFVAL()
        real*4 function Profval( Eta , Gamma , S_L , D_L , TwoTH , 
     1   TwoTH0 , dPRdT, dPRdG, dPRdE , dPRdS , dPRdD , Use_Asym )
c
c 115.19 bugfix jpw 15-oct-2001
c
c Returns value of Profile
c   Eta is the mixing coefficient between Gaussian and Lorentzian
c   Gamma is the FWHM
c   S_L is source width/detector distance
c   D_L is detector width/detector distance
c   TwoTH is point at which to evaluate the profile
c   TwoTH0 is two theta value for peak
c   dPRdT is derivative of profile wrt TwoTH0
c   dPRdG is derivative of profile wrt Gamma
c   dPRdE is derivative of profile wrt Eta
c   dPRdS is derivative of profile wrt S_L
c   dPRdD is derivative of profile wrt D_L
c   Use_Asym is true if asymmetry to be used
c
c
c Asymmetry due to axial divergence using the method of Finger, Cox and
c    Jephcoat, J. Appl. Cryst. 27, 892, 1992.

      implicit none
      real*4 Eta , Gamma , S_L , D_L , TwoTH 
      real*4 TwoTH0 , dPRdT, dPRdG, dPRdE , dPRdS , dPRdD
      logical Use_Asym
      integer*4 NTERMS(14)/6,10,20,40,60,80,100,150,200,300,400,
     1   600,800,1000/
C 115.19      integer*4 Fstterm(14)/0,3,8,18,38,68,108,158,233,333,483,
C changed first term to 1 instead of zero. 
      integer*4 Fstterm(14)/1,3,8,18,38,68,108,158,233,333,483,
     1   683,983,1383/
      real*4 RAD/57.2957795/

      integer*4 ArrayNum , K , NGT, ngt2 , it, i
      real*4 CsTH               ! cos(theta)
      real*4 TTH                ! tan(theta)
      real*4 SnTwoTH            ! sin(twoth)
      real*4 CsTwoTH            ! cos(twoth)
      real*4 ApB                ! (S + H)/L 
      real*4 AmB                ! (S - H)/L 
      real*4 ApB2               ! (ApB) **2
      real*4 Einfl              ! 2phi value for inflection point 
      real*4 Emin               ! 2phi value for minimum 
      real*4 dEmindA            ! derivative of Emin wrt A
      real*4 tmp , tmp1 , tmp2  ! intermediate values 
      real*4 WP(1883) , XP(1883)! Storage for Gauss-Legendre weights and intervals 
      real*4 Delta              ! Angle of integration for comvolution 
      real*4 dDELTAdA           ! derivative of DELTA wrt A (S/L)
      real*4 sinDELTA           ! sine of DELTA 
      real*4 cosDELTA           ! cosine of DELTA 
      real*4 tanDELTA           ! tangent of DELTA 
      real*4 RcosDELTA          ! 1/cos(DELTA) 
      real*4 F , dFdA
      real*4 G , dGdA , dGdB , PsVoigt
      real*4 sumWG , sumWRG , sumWdGdA , sumWRdGdA ,sumWdGdB , sumWRdGdB
      real*4 sumWGdRdG , sumWGdRdE , sumWGdRdA , sumWGdRdB , sumWGdRd2t 
      real*4 stepsize 
!
! Values for the abscissas and weights of the Gauss-Legendre
!  N-point quadrature formula have been precomputed using routine
!  Gauleg from "Numerical Recipes" (Press, Flannery, Teukolsky
!  and Vetterling, 1986, Cambridge University Press,
!  ISBN 0 521 30811 9), and are stored in the DATA statements
!  for XP and WP below.
!
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      CsTH = cos(TwoTH0 * 0.5/RAD)
      if (abs(CsTH) .lt. 1.0e-15) CsTH = 1.0e-15
      TTH = sin(TwoTH0 * 0.5/RAD)/CsTH
      CsTwoTH = cos(TwoTH0/RAD)
      SnTwoTH = sin(TwoTH0/RAD)
      ApB = S_L + D_L
      AmB = S_L - D_L
      ApB2 = ApB**2
      if (((S_L .ne. 0.0) .or. (D_L .ne. 0.0)) .and. Use_Asym) then
        tmp = sqrt(1.0 + AmB**2)*CsTwoTH
        if (abs(tmp) .gt. 1.0) then
          Einfl = acos(CsTwoTH)*RAD
        else
          Einfl = acos(tmp)*RAD
        endif
        tmp2 = 1.0 + ApB2
        tmp = sqrt(tmp2 ) * CsTwoTH

c If S_L or D_L are zero, set Einfl = 2theta 
    
        if ((S_L .eq. 0.0) .or. (D_L .eq. 0.0)) Einfl = TwoTH0
        if (abs(tmp) .le. 1.0) then
          Emin = acos(tmp) * RAD
          tmp1 = tmp2 * (1.0 - tmp2 * CsTwoTH**2)
        else
          tmp1 = 0.0
          if (tmp .gt. 0.0) then
            Emin = 0.0
          else
            Emin = 180.0
          endif
        endif
        if ((tmp1 .gt. 0.0) .and. (abs(tmp) .le. 1.0)) then
          dEmindA = -ApB * CsTwoTH/sqrt(tmp1)
        else
          dEmindA = 0.0
        endif
        ArrayNum = 1
        K = 400.0 * (TwoTH0 - Emin)   ! Calculate number of terms needed 
C From LWF - number of terms must be such that the interval between 2phi(min) and 2theta
C is in steps no larger than 0.005
C        stepsize = (twoth0-emin)/float(K)
        stepsize = 1.0/400.0 ! This seems to be always the case apart from rounding K
        if(stepsize .gt. gamma/10.0) then
           stepsize = gamma/10.0
           K = (twoth0-emin)/stepsize
        endif
        do while ((ArrayNum .lt. 14) .and. (K .gt. NTERMS(ArrayNum)))
          ArrayNum = ArrayNum + 1
        enddo
        NGT = nterms(ArrayNum)              ! Save number of terms 
        ngt2 = ngt / 2
c Clear terms needed for summations 
        sumWG = 0.0
        sumWRG = 0.0
        sumWdGdA = 0.0
        sumWRdGdA = 0.0
        sumWdGdB = 0.0
        sumWRdGdB = 0.0
        sumWGdRd2t = 0.0
        sumWGdRdG = 0.0
        sumWGdRdE = 0.0
        sumWGdRdA = 0.0
        sumWGdRdB = 0.0
c Compute the convolution integral 
        it = fstterm(arraynum)-ngt2
        do K = ngt2 , NGT 
          delta = Emin + (TwoTH0 - Emin) * xp(K + it)
          dDeltadA = (1.0 - xp(k+it) ) * dEmindA
          sinDELTA = sin(Delta/RAD)
          cosDELTA = cos(Delta/RAD)
          if (abs(cosDELTA) .lt. 1.0e-15) cosDELTA = 1.0e-15
          RcosDELTA = 1.0 / cosDELTA
          tanDELTA = tan(Delta/RAD)
          tmp = cosDELTA**2 - CsTwoTH**2
          if (tmp .gt. 0.0) then
            tmp1 = sqrt(tmp)
            F = abs(CsTwoTH) / tmp1
            dFdA = cosDELTA * CsTwoTH * sinDELTA * dDELTAdA 
     1         / (tmp1 * tmp1 * tmp1)
          else
            F = 0.0
            dFdA = 0.0
          endif
c  calculate G(Delta,2theta) , FCJ eq. 7a and 7b 
          if ( abs(Delta - Emin) .gt. abs(Einfl - Emin)) then
            if (S_L .gt. D_L) then
!
! N.B. this is the only place where d()/dA <> d()/dB
!
              G = 2.0 * D_L * F * RcosDELTA
              dGdA = 2.0 * D_L * RcosDELTA * (dFdA + 
     1                F*tanDELTA*dDELTAdA)
              dGdB = dGdA + 2.0 * F * RcosDELTA
            else
              G = 2.0 * S_L * F * RcosDELTA
              dGdB = 2.0 * S_L * RcosDELTA
     1                  *(dFdA + F * tanDELTA * dDELTAdA)
              dGdA = dGdB + 2.0 * F * RcosDELTA
            endif
          else
            G = (-1.0 + ApB * F) * RcosDELTA
            dGdA = RcosDELTA * (F - tanDELTA * dDELTAdA + ApB * dFdA
     1               + ApB * F * tanDELTA * dDELTAdA)
            dGdB = dGdA
          endif
          tmp = PsVoigt(TwoTh-DELTA+TwoTH0,TwoTH0,eta,Gamma,dPRdT
     1          ,dPRdG,dPRdE)
          sumWG = sumWG + wp(k+it) * G
          sumWRG = sumWRG + wp(k+it) * G * tmp
          sumWdGdA = sumWdGdA + wp(k+it) * dGdA
          sumWdGdB = sumWdGdB + wp(k+it) * dGdB
          sumWRdGdA = sumWRdGdA + wp(k+it) * dGdA * tmp
          sumWRdGdB = sumWRdGdB + wp(k+it) * dGdB * tmp 
          sumWGdRd2t = sumWGdRd2t + wp(k+it) * G * dPRdT
          sumWGdRdG = sumWGdRdG + wp(k+it) * G * dPRdG
          sumWGdRdE = sumWGdRdE + wp(k+it) * G * dPRdE
          sumWGdRdA = sumWGdRdA + wp(k+it) * G * dPRdT * dDELTAdA * RAD
        enddo
        if (sumWG .eq. 0.0) sumWG = 1.0
        Profval = sumWRG / sumWG
        dPRdT = sumWGdRd2t/ sumWG
        dPRdG = sumWGdRdG / sumWG
        dPRdE = sumWGdRdE / sumWG
        dPRdS = (sumWRdGdA + sumWGdRdA) / sumWG - sumWRG *
     1          sumWdGdA / sumWG**2

        dPRdD = (sumWRdGdB + sumWGdRdA) / sumWG - sumWRG *
     1          sumWdGdB / sumWG**2
      else   ! here for no asymmetry }
        tmp = PsVoigt(TwoTH,TwoTH0,eta,Gamma,dPRdT,dPRdG,dPRdE)
        Profval = tmp
        dPRdS = 0.0
        dPRdD = 0.0
      endif
      return
      end


      real*4 function Gauss(Pos , Pos0 , Gamma , dGdT , dGdG )

c  Return value of Gaussian at 'Pos' for peak at 'Pos0' and 'Gamma'.
c  dGdT is derivative of G wrt Pos0.
c  dGdG is derivative of G wrt Gamma.

      implicit none
      real*4 Pos , Pos0 , Gamma , dGdT , dGdG
      real*4   c / 1.6651092/
      real*4  cg / 0.939437279/
      real*4  delp , temp 

      delp = Pos - Pos0
      if (abs(delp)/Gamma .gt. 6) then
        Gauss = 0.0
        dGdT = 0.0
        dGdG = 0.0
      else
        temp = cg * exp(-(delp * c /Gamma)**2)/Gamma
        Gauss = temp
        dGdG = temp * ( -1.0 + 2.0 * (delp * c/Gamma)**2) / Gamma
        dGdT = 2.0 * c**2 * delp * temp/Gamma**2
      endif
      return
      end

      real*4 function Lorentz(Pos , Pos0 , Gamma , dLdT , dLdG )

c  Return value of Lorentzian at 'Pos' for peak at 'Pos0' and 'Gamma'.
c  dLdT is derivative of L wrt Pos0.
c  dLdG is derivative of L wrt Gamma.
      implicit none      
      real*4 Pos , Pos0 , Gamma , dLdT , dLdG
      real*4 cl / 0.636619772/

      real*4  delp , denom

      delp = Pos - Pos0
      denom = 4.0 * delp**2 + Gamma**2
      Lorentz = cl * Gamma / denom
      dLdT = 8.0 * cl * Gamma * delp / denom**2
      dLdG = cl * (4.0 * delp**2 - Gamma**2) / denom**2
      return
      end
C                         
      real*4 function PsVoigt(TwoTH , TwoTH0 , eta , Gamma,
     1         dPRdT , dPRdG , dPRdE ) 
c
c   Returns value of Pseudo Voigt
c   Eta is the mixing coefficient between Gaussian and Lorentzian
c   Gamma is the FWHM
c   TwoTH is point at which to evaluate the profile
c   TwoTH0 is two theta value for peak
c   dPRdT is derivative of profile wrt TwoTH0
c   dPRdG is derivative of profile wrt Gamma
c   dPRdE is derivative of profile wrt Eta
      implicit none
      real*4 TwoTH , TwoTH0 , eta , Gamma
      real*4 dPRdT , dPRdG , dPRdE
      real*4  G,Gauss           ! Gaussian part 
      real*4  L,Lorentz         ! Lorentzian part 
      real*4 dGdT , dGdG , dLdT , dLdG
      G = Gauss(TwoTH , TwoTH0 , Gamma , dGdT , dGdG )
      L = Lorentz(TwoTH , TwoTH0 , Gamma , dLdT , dLdG )
      PsVoigt = Eta * L + (1.0 - Eta) * G
      dPRdT = Eta * dLdT + (1.0 - Eta) * dGdT
      dPRdG = Eta * dLdG + (1.0 - Eta) * dGdG
      dPRdE = L - G
      return
      end