c
c Spectrometer transfer functions based on retune_dir.dat Right arm with
c Q1/Q2 as a pair 80 cm forward. SNAKE has been modified to give the "correct" 
c transverse properties
c                                 3/11/09 -jjl
c
c
c typical call: answer = function(x,5)
c INPUTS: x = 5 or more element array 
c              x(1)=x0  (meters) (used +-0.001 m for fits)
c              x(2)=theta0 (really tan(theta0))
c              x(3)=y0   (meters) (used +-0.050 m for fits)
c              x(4)=phi0 (really tan(phi0))
c              x(5)=delta (fractional value NOT percent)
c         M=5
c
c OUTPUT: units are the same as inputs
c 
c NOMENCLATURE: function name = prefix + _rf_  +suffix
c           prefixes:     x means xfinal
c                         t means thetafinal
c                         y means yfinal
c                         p means phifinal
c                         l means pathlength difference from central trajectory
c     
c           suffixes:     fp means target to focus
c                         q1ex means target to Q1 exit
c                         dent means target to Dipole entrance
c                         dext means target to dipole exit
c                         q3en means target to Q3 entrance
c                         q3ex means target to Q3 exit
c
c          _rf_ is for right forward
c
c   The Apertures:
c   Q1 exit is a circle of radius 0.1492 m (as measured by Makis)
c   Q3 entrance and exit are circles of radius 0.300 m
c   The dipole entrance and exit are trapezoids:
c     -0.40 m<x<0.40 m (+x is down) (this is a "soft" aperture in that 
c     it indicates the approximate end of the good field region but not 
c     necessarily any real physical object)
c     y=+-(0.125*(1-(1.25*x/8.40)) (smallest gap at positive x, x in m)
c Remember the functions give you meters.
     function x_rf_q1ex   (x,m)        
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 40)             
      data ncoeff/ 39/                 
      data avdat/ -0.9577920E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.21788080E-02, 0.14110222E+00, 0.64791795E-02,-0.16665950E-02,
     + -0.42156311E-03,-0.25635035E-03,-0.28816325E-03,-0.13926360E-02,
     + -0.26326993E-03, 0.57103014E-04,-0.27673959E-03,-0.30881052E-02,
     + -0.17989227E-02,-0.43230339E-04, 0.42615302E-04, 0.20986196E-04,
     +  0.96243930E-04,-0.18779467E-02,-0.13458892E-02, 0.12961795E-03,
     +  0.16441460E-03, 0.41696279E-04, 0.51606617E-05,-0.12804189E-03,
     +  0.57178455E-04,-0.65233209E-04, 0.54313277E-05,-0.97899938E-05,
     + -0.64712212E-05,-0.36653812E-04,-0.61012784E-05,-0.74189797E-04,
     + -0.36812566E-04, 0.46927333E-04,-0.11189093E-02,-0.35917119E-03,
     + -0.16356573E-04, 0.23300004E-03, 0.27800235E-04,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
c                                      
c                  function            
c                                      
      x_rf_q1ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)    *x21        *x51
     4  +coeff(  4)    *x23            
     5  +coeff(  5)    *x21*x31*x41    
     6  +coeff(  6)    *x21    *x42    
     7  +coeff(  7)    *x21        *x52
     8  +coeff(  8)    *x23*x32        
      x_rf_q1ex   =x_rf_q1ex           
     9  +coeff(  9)    *x21*x34        
     1  +coeff( 10)                *x51
     2  +coeff( 11)    *x21*x32        
     3  +coeff( 12)    *x23*x31*x41    
     4  +coeff( 13)    *x23    *x42    
     5  +coeff( 14)    *x22            
     6  +coeff( 15)*x11            *x51
     7  +coeff( 16)*x11                
     8  +coeff( 17)    *x21*x31*x41*x51
      x_rf_q1ex   =x_rf_q1ex           
     9  +coeff( 18)    *x21*x32*x42    
     1  +coeff( 19)    *x21*x31*x43    
     2  +coeff( 20)    *x23*x32    *x51
     3  +coeff( 21)    *x23    *x42*x51
     4  +coeff( 22)    *x21    *x44*x51
     5  +coeff( 23)    *x21*x32    *x53
     6  +coeff( 24)    *x23*x33*x41    
     7  +coeff( 25)    *x23*x31*x43*x51
     8  +coeff( 26)    *x23*x34*x42    
      x_rf_q1ex   =x_rf_q1ex           
     9  +coeff( 27)    *x21*x34*x44    
     1  +coeff( 28)        *x31*x41    
     2  +coeff( 29)            *x42    
     3  +coeff( 30)    *x22*x32        
     4  +coeff( 31)        *x34        
     5  +coeff( 32)    *x22*x31*x41    
     6  +coeff( 33)    *x22    *x42    
     7  +coeff( 34)    *x21*x32    *x51
     8  +coeff( 35)    *x21*x33*x41    
      x_rf_q1ex   =x_rf_q1ex           
     9  +coeff( 36)    *x21    *x44    
     1  +coeff( 37)*x11*x22            
     2  +coeff( 38)    *x23*x31*x41*x51
     3  +coeff( 39)    *x23        *x53
c                                      
      return                           
      end                              
      function t_rf_q1ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 15)             
      data ncoeff/ 14/                 
      data avdat/  0.9256746E-04/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.25427787E-03,-0.17188324E-01,-0.87265839E-03, 0.60274489E-02,
     + -0.10612020E-02,-0.12768088E-02,-0.75777736E-03,-0.16519318E-02,
     + -0.67057268E-03,-0.26154166E-03, 0.52478201E-04,-0.40121675E-02,
     + -0.23100956E-02, 0.34854096E-04,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      t_rf_q1ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)*x11                
     4  +coeff(  4)    *x21        *x51
     5  +coeff(  5)    *x23            
     6  +coeff(  6)    *x21*x31*x41    
     7  +coeff(  7)    *x21    *x42    
     8  +coeff(  8)    *x23*x32        
      t_rf_q1ex   =t_rf_q1ex           
     9  +coeff(  9)    *x21*x32        
     1  +coeff( 10)    *x21        *x52
     2  +coeff( 11)                *x51
     3  +coeff( 12)    *x23*x31*x41    
     4  +coeff( 13)    *x23    *x42    
     5  +coeff( 14)*x11            *x51
c                                      
      return                           
      end                              
      function y_rf_q1ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff(  8)             
      data ncoeff/  7/                 
      data avdat/ -0.4014544E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.56866859E-03, 0.11350179E+00, 0.12747298E+00,-0.35446617E-02,
     + -0.27220116E-02,-0.13258143E-02,-0.93502353E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x21 = x2                         
      x22 = x21*x2                     
      x31 = x3                         
      x41 = x4                         
      x51 = x5                         
c                                      
c                  function            
c                                      
      y_rf_q1ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)        *x31    *x51
     5  +coeff(  5)            *x41*x51
     6  +coeff(  6)    *x22*x31        
     7  +coeff(  7)    *x22    *x41    
c                                      
      return                           
      end                              
      function p_rf_q1ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff(  8)             
      data ncoeff/  7/                 
      data avdat/ -0.2415565E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.35239634E-03, 0.60865439E-01, 0.82966976E-01,-0.34830850E-02,
     + -0.27864336E-02,-0.16031390E-02,-0.14507399E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x21 = x2                         
      x22 = x21*x2                     
      x31 = x3                         
      x41 = x4                         
      x51 = x5                         
c                                      
c                  function            
c                                      
      p_rf_q1ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)        *x31    *x51
     5  +coeff(  5)            *x41*x51
     6  +coeff(  6)    *x22*x31        
     7  +coeff(  7)    *x22    *x41    
c                                      
      return                           
      end                              
      function l_rf_q1ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 14)             
      data ncoeff/ 13/                 
      data avdat/ -0.3279555E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.32755209E-02,-0.14357080E-03,-0.79903784E-05,-0.11368580E-04,
     +  0.35717301E-06,-0.82960594E-02,-0.16269361E-02,-0.46965852E-02,
     + -0.39669508E-02, 0.42071915E-03,-0.11934397E-05, 0.19326439E-03,
     +  0.21510830E-03,                
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
c                                      
c                  function            
c                                      
      l_rf_q1ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)            *x41    
     4  +coeff(  4)                *x51
     5  +coeff(  5)*x11                
     6  +coeff(  6)    *x22            
     7  +coeff(  7)        *x32        
     8  +coeff(  8)        *x31*x41    
      l_rf_q1ex   =l_rf_q1ex           
     9  +coeff(  9)            *x42    
     1  +coeff( 10)        *x31*x41*x51
     2  +coeff( 11)        *x32*x42*x51
     3  +coeff( 12)        *x32    *x51
     4  +coeff( 13)            *x42*x51
c                                      
      return                           
      end                              
      function x_rf_dent   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 91)             
      data ncoeff/ 90/                 
      data avdat/  0.5179330E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.15408091E-02,-0.11816246E+00,-0.23176301E-01, 0.30879299E-02,
     +  0.30657558E-02, 0.56751836E-02, 0.18897792E-02, 0.14023345E-02,
     +  0.16663171E-02, 0.95952610E-02, 0.23597828E-02, 0.27090230E-03,
     +  0.10881169E-02, 0.11984827E-02,-0.22074312E-03, 0.22256650E-01,
     +  0.12824249E-01,-0.25269133E-03,-0.53177751E-03,-0.18151953E-03,
     +  0.17505318E-01, 0.12778126E-01,-0.98249724E-03,-0.30456466E-03,
     + -0.12519564E-03,-0.28283635E-03, 0.42008035E-03, 0.10497656E-01,
     +  0.34436933E-02,-0.11289171E-03,-0.32617176E-04, 0.10640113E-03,
     + -0.35969703E-03,-0.36278396E-03,-0.27030852E-03,-0.11379861E-03,
     +  0.80405545E-04,-0.76644059E-03,-0.18008668E-02,-0.86072221E-03,
     + -0.40447549E-05,-0.29428429E-04, 0.55116743E-04, 0.11327337E-03,
     +  0.48051763E-04,-0.14806380E-02,-0.77802053E-03,-0.25138983E-04,
     +  0.14150278E-03, 0.17172695E-03, 0.28138261E-03,-0.25784293E-04,
     +  0.33348108E-04,-0.16112861E-03,-0.12736829E-03,-0.27152558E-03,
     +  0.17937385E-03,-0.60271565E-03, 0.22585240E-03, 0.96095846E-05,
     + -0.52646177E-04,-0.61204068E-04,-0.12043581E-03, 0.24631954E-03,
     + -0.19685975E-04, 0.91041715E-04,-0.32927561E-04, 0.45277546E-04,
     + -0.35084136E-04,-0.41672200E-04,-0.18182560E-03, 0.55077675E-04,
     +  0.73241492E-04, 0.12855133E-03, 0.12449808E-03, 0.28326638E-04,
     +  0.25349227E-04, 0.46078640E-04, 0.32011900E-04,-0.71483388E-04,
     + -0.12628488E-03,-0.10278954E-03,-0.12867364E-04,-0.10513134E-02,
     + -0.10217794E-03,-0.18011819E-02,-0.12170505E-02, 0.13598455E-04,
     + -0.12252641E-03, 0.25492482E-04,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      x_rf_dent   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)    *x21        *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x23            
     7  +coeff(  7)    *x21*x31*x41    
     8  +coeff(  8)    *x21    *x42    
      x_rf_dent   =x_rf_dent           
     9  +coeff(  9)    *x21        *x52
     1  +coeff( 10)    *x23*x32        
     2  +coeff( 11)    *x21*x34        
     3  +coeff( 12)    *x23*x33*x41    
     4  +coeff( 13)    *x21*x32        
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)                *x51
     7  +coeff( 16)    *x23*x31*x41    
     8  +coeff( 17)    *x23    *x42    
      x_rf_dent   =x_rf_dent           
     9  +coeff( 18)*x11            *x51
     1  +coeff( 19)    *x21*x31*x41*x51
     2  +coeff( 20)*x11*x21            
     3  +coeff( 21)    *x21*x32*x42    
     4  +coeff( 22)    *x21*x31*x43    
     5  +coeff( 23)    *x23*x32    *x51
     6  +coeff( 24)    *x21    *x44*x51
     7  +coeff( 25)            *x42    
     8  +coeff( 26)    *x24            
      x_rf_dent   =x_rf_dent           
     9  +coeff( 27)    *x22*x31*x41    
     1  +coeff( 28)    *x21*x33*x41    
     2  +coeff( 29)    *x21    *x44    
     3  +coeff( 30)        *x31*x41    
     4  +coeff( 31)                *x52
     5  +coeff( 32)    *x22    *x42    
     6  +coeff( 33)    *x23        *x51
     7  +coeff( 34)    *x21*x32    *x51
     8  +coeff( 35)    *x21    *x42*x51
      x_rf_dent   =x_rf_dent           
     9  +coeff( 36)    *x21        *x53
     1  +coeff( 37)*x11*x22            
     2  +coeff( 38)    *x24*x32        
     3  +coeff( 39)    *x23*x31*x41*x51
     4  +coeff( 40)    *x23    *x42*x51
     5  +coeff( 41)    *x21    *x41    
     6  +coeff( 42)            *x43    
     7  +coeff( 43)    *x23*x31        
     8  +coeff( 44)    *x22        *x52
      x_rf_dent   =x_rf_dent           
     9  +coeff( 45)    *x23        *x52
     1  +coeff( 46)    *x24*x31*x41    
     2  +coeff( 47)    *x24    *x42    
     3  +coeff( 48)*x11*x21        *x51
     4  +coeff( 49)*x11*x22*x31*x41    
     5  +coeff( 50)*x11*x22    *x42    
     6  +coeff( 51)*x11*x23    *x42    
     7  +coeff( 52)*x11*x21*x32*x42    
     8  +coeff( 53)*x11*x24        *x51
      x_rf_dent   =x_rf_dent           
     9  +coeff( 54)*x11*x23*x31    *x51
     1  +coeff( 55)*x11*x23    *x41*x51
     2  +coeff( 56)*x11*x23    *x43    
     3  +coeff( 57)*x11*x23*x34*x41    
     4  +coeff( 58)*x11*x23*x32*x44    
     5  +coeff( 59)*x11*x24    *x42*x53
     6  +coeff( 60)            *x41    
     7  +coeff( 61)    *x21    *x41*x51
     8  +coeff( 62)        *x31*x41*x51
      x_rf_dent   =x_rf_dent           
     9  +coeff( 63)            *x42*x51
     1  +coeff( 64)    *x22*x32        
     2  +coeff( 65)        *x34        
     3  +coeff( 66)    *x23    *x41    
     4  +coeff( 67)    *x21*x31    *x52
     5  +coeff( 68)                *x54
     6  +coeff( 69)        *x34    *x51
     7  +coeff( 70)    *x21*x32*x41*x51
     8  +coeff( 71)    *x21*x31*x42*x51
      x_rf_dent   =x_rf_dent           
     9  +coeff( 72)        *x32*x42*x51
     1  +coeff( 73)            *x44*x51
     2  +coeff( 74)    *x21*x32    *x52
     3  +coeff( 75)    *x21*x31*x41*x52
     4  +coeff( 76)    *x21*x31    *x53
     5  +coeff( 77)*x11    *x32        
     6  +coeff( 78)*x11*x21    *x41    
     7  +coeff( 79)*x11    *x31*x41    
     8  +coeff( 80)    *x23*x32*x41    
      x_rf_dent   =x_rf_dent           
     9  +coeff( 81)    *x22*x31*x43    
     1  +coeff( 82)    *x24    *x41*x51
     2  +coeff( 83)    *x22*x32*x41*x51
     3  +coeff( 84)    *x21*x33*x41*x51
     4  +coeff( 85)    *x22*x31*x42*x51
     5  +coeff( 86)    *x21*x32*x42*x51
     6  +coeff( 87)    *x21*x31*x43*x51
     7  +coeff( 88)*x11            *x52
     8  +coeff( 89)    *x21*x32    *x53
      x_rf_dent   =x_rf_dent           
     9  +coeff( 90)            *x43*x53
c                                      
c                                      
c  transform to TRANSPORT x            
c                                      
      x_rf_dent=-x_rf_dent*3.346065 !multiply by -cos(30)/sin(15degrees)
                                       
                                       
      return                           
      end                              
      function t_rf_dent   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 25)             
      data ncoeff/ 24/                 
      data avdat/  0.1469749E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.98976330E-03, 0.47525182E-01, 0.75397163E-03,-0.15628338E-02,
     +  0.36171929E-02, 0.10765610E-01, 0.20843656E-02,-0.29718862E-02,
     + -0.49701319E-02,-0.31824808E-02,-0.45278131E-04,-0.32433223E-02,
     +  0.45348055E-03, 0.20326900E-02,-0.23545655E-02, 0.10185988E-02,
     + -0.90262020E-03,-0.17987404E-03,-0.78911558E-02,-0.44466602E-02,
     +  0.12752791E-03, 0.52360230E-03, 0.46066486E-03,-0.59142994E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      t_rf_dent   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)            *x42    
     8  +coeff(  8)    *x23            
      t_rf_dent   =t_rf_dent           
     9  +coeff(  9)    *x21*x31*x41    
     1  +coeff( 10)    *x21    *x42    
     2  +coeff( 11)        *x33*x41    
     3  +coeff( 12)    *x23*x32        
     4  +coeff( 13)        *x32        
     5  +coeff( 14)        *x31*x41    
     6  +coeff( 15)    *x21*x32        
     7  +coeff( 16)    *x22        *x51
     8  +coeff( 17)    *x21        *x52
      t_rf_dent   =t_rf_dent           
     9  +coeff( 18)*x11*x21            
     1  +coeff( 19)    *x23*x31*x41    
     2  +coeff( 20)    *x23    *x42    
     3  +coeff( 21)*x11            *x51
     4  +coeff( 22)        *x31*x41*x51
     5  +coeff( 23)            *x42*x51
     6  +coeff( 24)    *x24            
c                                      
      return                           
      end                              
      function y_rf_dent   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 19)             
      data ncoeff/ 18/                 
      data avdat/ -0.1182382E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.30119298E-03, 0.70650652E-01, 0.13722375E+00, 0.42594089E-02,
     +  0.32692472E-02, 0.13900683E-01, 0.20563714E-01,-0.70311632E-02,
     + -0.76445644E-02,-0.72305030E-02,-0.14899456E-02,-0.16245610E-02,
     +  0.17140443E-04,-0.43403568E-04, 0.10615952E-03,-0.16438721E-02,
     + -0.58439588E-02,-0.29991693E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x21 = x2                         
      x22 = x21*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x35 = x34*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x45 = x44*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      y_rf_dent   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)    *x21*x31        
     5  +coeff(  5)    *x21    *x41    
     6  +coeff(  6)        *x31    *x51
     7  +coeff(  7)            *x41*x51
     8  +coeff(  8)    *x22*x31        
      y_rf_dent   =y_rf_dent           
     9  +coeff(  9)    *x22    *x41    
     1  +coeff( 10)        *x31*x42    
     2  +coeff( 11)        *x31    *x52
     3  +coeff( 12)            *x41*x52
     4  +coeff( 13)        *x34*x41    
     5  +coeff( 14)            *x45    
     6  +coeff( 15)        *x35*x42    
     7  +coeff( 16)        *x33        
     8  +coeff( 17)        *x32*x41    
      y_rf_dent   =y_rf_dent           
     9  +coeff( 18)            *x43    
c                                      
      return                           
      end                              
      function p_rf_dent   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 34)             
      data ncoeff/ 33/                 
      data avdat/ -0.3474219E-04/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.33107633E-04,-0.70600331E-01,-0.50017171E-01,-0.19011008E-01,
     + -0.23095850E-01, 0.14936249E-01, 0.18329497E-01,-0.16682340E-01,
     +  0.25488420E-02,-0.11888063E-01,-0.33167535E-02,-0.36016349E-02,
     + -0.48046596E-02,-0.19210042E-03, 0.63251925E-03, 0.71152061E-03,
     + -0.60770940E-02,-0.27835285E-02,-0.14216071E-02,-0.14477677E-02,
     +  0.25152157E-02,-0.34183296E-02, 0.36213796E-02, 0.53027766E-05,
     + -0.42506744E-03,-0.71217230E-03,-0.10254728E-02,-0.50816115E-03,
     + -0.12410177E-02,-0.43708445E-02, 0.14456220E-02, 0.65768475E-03,
     +  0.77164109E-03,                
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      p_rf_dent   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)    *x21*x31        
     5  +coeff(  5)    *x21    *x41    
     6  +coeff(  6)        *x31    *x51
     7  +coeff(  7)            *x41*x51
     8  +coeff(  8)    *x22    *x41    
      p_rf_dent   =p_rf_dent           
     9  +coeff(  9)    *x24*x31        
     1  +coeff( 10)    *x22*x31        
     2  +coeff( 11)    *x21*x31    *x51
     3  +coeff( 12)    *x21    *x41*x51
     4  +coeff( 13)    *x22    *x41*x51
     5  +coeff( 14)    *x24*x31    *x51
     6  +coeff( 15)*x11    *x31        
     7  +coeff( 16)*x11        *x41    
     8  +coeff( 17)        *x31*x42    
      p_rf_dent   =p_rf_dent           
     9  +coeff( 18)            *x43    
     1  +coeff( 19)        *x31    *x52
     2  +coeff( 20)            *x41*x52
     3  +coeff( 21)    *x23    *x41    
     4  +coeff( 22)    *x22*x31    *x51
     5  +coeff( 23)    *x24    *x41    
     6  +coeff( 24)    *x22*x32*x41    
     7  +coeff( 25)        *x34*x41    
     8  +coeff( 26)        *x33*x42    
      p_rf_dent   =p_rf_dent           
     9  +coeff( 27)        *x32*x43    
     1  +coeff( 28)        *x31*x44    
     2  +coeff( 29)        *x33        
     3  +coeff( 30)        *x32*x41    
     4  +coeff( 31)    *x23*x31        
     5  +coeff( 32)*x11*x21    *x41    
     6  +coeff( 33)*x11*x23*x31        
c                                      
      return                           
      end                              
      function l_rf_dent   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 17)             
      data ncoeff/ 16/                 
      data avdat/ -0.6919863E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.80287866E-02, 0.22805183E+00,-0.60614967E-02,-0.18203501E-01,
     +  0.45738440E-01,-0.12516228E-01,-0.11299343E-01,-0.80066463E-02,
     + -0.27422737E-01,-0.16299061E-01,-0.36509989E-02,-0.36696449E-02,
     + -0.18180502E-02,-0.44223885E-02,-0.65377261E-02,-0.10359195E-01,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      l_rf_dent   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)*x11                
     4  +coeff(  4)    *x22            
     5  +coeff(  5)    *x21        *x51
     6  +coeff(  6)    *x23            
     7  +coeff(  7)        *x31*x41    
     8  +coeff(  8)            *x42    
      l_rf_dent   =l_rf_dent           
     9  +coeff(  9)    *x21*x31*x41    
     1  +coeff( 10)    *x21    *x42    
     2  +coeff( 11)    *x22        *x51
     3  +coeff( 12)    *x21        *x52
     4  +coeff( 13)    *x22*x32        
     5  +coeff( 14)        *x34        
     6  +coeff( 15)    *x23*x32        
     7  +coeff( 16)    *x21*x34        
c                                      
      return                           
      end                              
      function x_rf_dext   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 91)             
      data ncoeff/ 90/                 
      data avdat/ -0.2288953E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.49263854E-02, 0.29074395E+00, 0.11475129E-04, 0.13384369E+00,
     +  0.12020225E-01, 0.88490799E-01,-0.94347326E-02,-0.13489027E-01,
     + -0.77606263E-02,-0.51470292E-02,-0.33077601E-01,-0.33790485E-02,
     + -0.35440952E-02,-0.52667782E-02, 0.35811232E-02,-0.22188023E-03,
     + -0.75333491E-01,-0.44303291E-01,-0.15817413E-02,-0.46030120E-02,
     + -0.16124323E-02,-0.80064457E-03,-0.24316886E-02, 0.14317376E-02,
     + -0.48844889E-03, 0.10532790E-03,-0.12520349E-02,-0.22225366E-02,
     + -0.61319029E-03,-0.65795951E-01,-0.48680790E-01,-0.12832272E-02,
     + -0.47020172E-03, 0.49894322E-02, 0.17018167E-01, 0.43724649E-01,
     + -0.65541454E-03, 0.10601597E-01,-0.46533684E-03, 0.28743938E-03,
     + -0.79828268E-02, 0.57521076E-04, 0.11847362E-03,-0.17480332E-02,
     +  0.48516830E-03, 0.81278878E-03, 0.29125658E-03,-0.36247890E-01,
     + -0.13771328E-01,-0.23187522E-02, 0.29086540E-02, 0.35177007E-01,
     + -0.42565654E-04,-0.20163260E-03, 0.38036448E-03, 0.27860157E-03,
     + -0.33277861E-03,-0.86299228E-02, 0.10462598E-03, 0.11870101E-02,
     +  0.66979264E-03,-0.98111457E-04,-0.19422253E-02,-0.21571176E-03,
     + -0.12936593E-03,-0.21087762E-03,-0.51691540E-03, 0.22464248E-03,
     + -0.41147991E-03, 0.31763551E-03, 0.61742187E-03,-0.72945881E-03,
     + -0.39517377E-04,-0.13061958E-03, 0.97285789E-04,-0.17061798E-03,
     +  0.42596905E-03, 0.14870425E-03, 0.10820851E-03,-0.10071463E-03,
     +  0.26232091E-03, 0.18011784E-03, 0.21779623E-03, 0.67106169E-03,
     + -0.30087063E-03, 0.13378130E-03, 0.17747657E-03, 0.17189779E-03,
     +  0.57592842E-03,-0.59963774E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      x_rf_dext   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)                *x51
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)*x11                
     8  +coeff(  8)    *x23            
      x_rf_dext   =x_rf_dext           
     9  +coeff(  9)    *x21*x31*x41    
     1  +coeff( 10)    *x21    *x42    
     2  +coeff( 11)    *x23*x32        
     3  +coeff( 12)                *x52
     4  +coeff( 13)    *x21*x32        
     5  +coeff( 14)            *x42    
     6  +coeff( 15)    *x22        *x51
     7  +coeff( 16)        *x33*x41    
     8  +coeff( 17)    *x23*x31*x41    
      x_rf_dext   =x_rf_dext           
     9  +coeff( 18)    *x23    *x42    
     1  +coeff( 19)        *x32        
     2  +coeff( 20)        *x31*x41    
     3  +coeff( 21)            *x42*x51
     4  +coeff( 22)    *x21        *x52
     5  +coeff( 23)    *x24            
     6  +coeff( 24)    *x23        *x51
     7  +coeff( 25)*x11*x21            
     8  +coeff( 26)        *x31*x43*x51
      x_rf_dext   =x_rf_dext           
     9  +coeff( 27)        *x31*x41*x51
     1  +coeff( 28)    *x22*x31*x41    
     2  +coeff( 29)    *x22        *x52
     3  +coeff( 30)    *x21*x32*x42    
     4  +coeff( 31)    *x21*x31*x43    
     5  +coeff( 32)    *x24        *x51
     6  +coeff( 33)*x11*x22            
     7  +coeff( 34)    *x23*x34        
     8  +coeff( 35)    *x23*x33*x41    
      x_rf_dext   =x_rf_dext           
     9  +coeff( 36)    *x23*x32*x42    
     1  +coeff( 37)    *x21*x33*x43    
     2  +coeff( 38)    *x23    *x44    
     3  +coeff( 39)    *x24*x34        
     4  +coeff( 40)    *x24    *x44    
     5  +coeff( 41)    *x23*x34*x42    
     6  +coeff( 42)    *x21    *x41*x51
     7  +coeff( 43)                *x53
     8  +coeff( 44)    *x22*x32        
      x_rf_dext   =x_rf_dext           
     9  +coeff( 45)    *x21*x32    *x51
     1  +coeff( 46)    *x21*x31*x41*x51
     2  +coeff( 47)    *x21    *x42*x51
     3  +coeff( 48)    *x21*x33*x41    
     4  +coeff( 49)    *x21    *x44    
     5  +coeff( 50)    *x24    *x42    
     6  +coeff( 51)    *x21*x34*x42    
     7  +coeff( 52)    *x23*x31*x43    
     8  +coeff( 53)    *x21    *x41    
      x_rf_dext   =x_rf_dext           
     9  +coeff( 54)    *x23*x31        
     1  +coeff( 55)        *x31*x43    
     2  +coeff( 56)            *x44    
     3  +coeff( 57)        *x31*x41*x52
     4  +coeff( 58)    *x21*x34        
     5  +coeff( 59)*x11            *x51
     6  +coeff( 60)    *x22    *x42*x51
     7  +coeff( 61)    *x21*x31*x42*x51
     8  +coeff( 62)    *x24*x32        
      x_rf_dext   =x_rf_dext           
     9  +coeff( 63)    *x24*x31*x41    
     1  +coeff( 64)        *x32    *x54
     2  +coeff( 65)*x11*x21    *x42    
     3  +coeff( 66)*x11*x22        *x51
     4  +coeff( 67)    *x23*x33    *x51
     5  +coeff( 68)    *x24*x31*x41*x51
     6  +coeff( 69)    *x23    *x44*x51
     7  +coeff( 70)*x11*x23*x31    *x51
     8  +coeff( 71)*x11*x23    *x42*x51
      x_rf_dext   =x_rf_dext           
     9  +coeff( 72)*x11*x24*x33    *x51
     1  +coeff( 73)            *x41    
     2  +coeff( 74)        *x31*x42    
     3  +coeff( 75)            *x43    
     4  +coeff( 76)    *x23    *x41    
     5  +coeff( 77)    *x22    *x42    
     6  +coeff( 78)    *x22    *x41*x51
     7  +coeff( 79)    *x21*x31    *x52
     8  +coeff( 80)    *x24*x31        
      x_rf_dext   =x_rf_dext           
     9  +coeff( 81)        *x33*x42    
     1  +coeff( 82)    *x23*x31    *x51
     2  +coeff( 83)    *x23    *x41*x51
     3  +coeff( 84)    *x22*x31*x41*x51
     4  +coeff( 85)    *x21*x32    *x52
     5  +coeff( 86)        *x32*x41*x52
     6  +coeff( 87)    *x21    *x42*x52
     7  +coeff( 88)    *x21        *x54
     8  +coeff( 89)    *x23*x32    *x51
      x_rf_dext   =x_rf_dext           
     9  +coeff( 90)    *x23    *x42*x51
c                                      
c                                      
c  transform to TRANSPORT x            
c                                      
      x_rf_dext=x_rf_dext*0.866025     
                                       
      return                           
      end                              
      function t_rf_dext   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 27)             
      data ncoeff/ 26/                 
      data avdat/ -0.3936141E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.32788885E-02,-0.74530602E-01, 0.22706429E-01, 0.19594897E-02,
     + -0.13963753E-01,-0.20124144E-02, 0.62948471E-03, 0.31808463E-02,
     + -0.17810537E-02,-0.13042630E-02, 0.62066484E-02, 0.45039733E-02,
     +  0.12206588E-02, 0.44317781E-02,-0.17577202E-03, 0.26748613E-02,
     + -0.88222622E-03, 0.46768168E-03,-0.17325538E-02, 0.10602683E-01,
     +  0.61525963E-02,-0.26084640E-03, 0.16081125E-03,-0.15477963E-03,
     + -0.60062762E-03,-0.64732687E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      t_rf_dext   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x21        *x51
     6  +coeff(  6)    *x22            
     7  +coeff(  7)        *x31*x41    
     8  +coeff(  8)    *x23            
      t_rf_dext   =t_rf_dext           
     9  +coeff(  9)            *x42    
     1  +coeff( 10)                *x52
     2  +coeff( 11)    *x21*x31*x41    
     3  +coeff( 12)    *x21    *x42    
     4  +coeff( 13)    *x21        *x52
     5  +coeff( 14)    *x23*x32        
     6  +coeff( 15)    *x21*x34        
     7  +coeff( 16)    *x21*x32        
     8  +coeff( 17)    *x22        *x51
      t_rf_dext   =t_rf_dext           
     9  +coeff( 18)        *x32    *x51
     1  +coeff( 19)            *x42*x51
     2  +coeff( 20)    *x23*x31*x41    
     3  +coeff( 21)    *x23    *x42    
     4  +coeff( 22)        *x32        
     5  +coeff( 23)*x11*x21            
     6  +coeff( 24)*x11            *x51
     7  +coeff( 25)        *x31*x41*x51
     8  +coeff( 26)    *x23        *x51
c                                      
      return                           
      end                              
      function y_rf_dext   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 37)             
      data ncoeff/ 36/                 
      data avdat/ -0.1194795E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.13662379E-02,-0.20449815E-01, 0.12603922E+00,-0.30821471E-01,
     + -0.50888985E-01, 0.48242345E-01, 0.65199740E-01,-0.25741907E-01,
     + -0.34670826E-01,-0.13960632E-01,-0.15159538E-03,-0.16702002E-01,
     + -0.20735459E-01,-0.87156584E-02,-0.88942330E-02,-0.48480602E-02,
     + -0.51184478E-02,-0.96751722E-02,-0.13276974E-03,-0.32665452E-03,
     +  0.13800710E-02,-0.15497152E-03, 0.52653505E-02,-0.59539201E-02,
     + -0.79062273E-04,-0.44222600E-02, 0.86551352E-03, 0.84262630E-02,
     +  0.35915554E-02, 0.10093978E-02, 0.58290539E-02, 0.34080865E-02,
     +  0.10290309E-02, 0.45611020E-02, 0.88970177E-02, 0.70226765E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x35 = x34*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x45 = x44*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      y_rf_dext   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)    *x21*x31        
     5  +coeff(  5)    *x21    *x41    
     6  +coeff(  6)        *x31    *x51
     7  +coeff(  7)            *x41*x51
     8  +coeff(  8)    *x22*x31        
      y_rf_dext   =y_rf_dext           
     9  +coeff(  9)    *x22    *x41    
     1  +coeff( 10)    *x21    *x41*x51
     2  +coeff( 11)    *x21*x33    *x51
     3  +coeff( 12)        *x32*x41    
     4  +coeff( 13)        *x31*x42    
     5  +coeff( 14)            *x43    
     6  +coeff( 15)    *x21*x31    *x51
     7  +coeff( 16)        *x31    *x52
     8  +coeff( 17)            *x41*x52
      y_rf_dext   =y_rf_dext           
     9  +coeff( 18)    *x22    *x41*x51
     1  +coeff( 19)        *x35        
     2  +coeff( 20)    *x22*x33    *x51
     3  +coeff( 21)*x11        *x41    
     4  +coeff( 22)        *x33    *x51
     5  +coeff( 23)    *x23    *x41    
     6  +coeff( 24)    *x22*x31    *x51
     7  +coeff( 25)*x11    *x33        
     8  +coeff( 26)        *x33        
      y_rf_dext   =y_rf_dext           
     9  +coeff( 27)*x11    *x31        
     1  +coeff( 28)    *x21*x31*x42    
     2  +coeff( 29)    *x23*x31        
     3  +coeff( 30)*x11*x21    *x41    
     4  +coeff( 31)    *x21*x34*x41    
     5  +coeff( 32)    *x21    *x45    
     6  +coeff( 33)*x11*x21*x33        
     7  +coeff( 34)    *x23*x33        
     8  +coeff( 35)    *x23*x32*x41    
      y_rf_dext   =y_rf_dext           
     9  +coeff( 36)    *x23*x35*x42    
c                                      
      return                           
      end                              
      function p_rf_dext   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 45)             
      data ncoeff/ 44/                 
      data avdat/ -0.2151448E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.22827109E-03,-0.15509893E-04,-0.16875243E-01, 0.98668532E-02,
     + -0.12494702E-01, 0.98245647E-02, 0.14473061E-01,-0.81327409E-02,
     + -0.53715468E-02, 0.17357556E-02, 0.69816556E-03, 0.56060657E-04,
     +  0.53716713E-03,-0.42281835E-03,-0.69853985E-02,-0.48250109E-02,
     + -0.24144091E-02,-0.27538901E-02, 0.30446239E-03,-0.42647324E-02,
     + -0.69428980E-03, 0.18131976E-02,-0.15340940E-02,-0.39383920E-03,
     + -0.12127154E-03, 0.31081832E-04,-0.12218836E-03,-0.61113322E-04,
     +  0.21739611E-03, 0.17883396E-03,-0.91723696E-03,-0.31897288E-02,
     + -0.16523219E-02, 0.27202239E-03, 0.14842799E-02,-0.42983590E-03,
     +  0.12040493E-03, 0.19678569E-02,-0.20159058E-03, 0.60695648E-03,
     +  0.20185341E-02, 0.20581519E-02, 0.11452491E-02,-0.26193652E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      p_rf_dext   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)            *x41    
     5  +coeff(  5)    *x21    *x41    
     6  +coeff(  6)        *x31    *x51
     7  +coeff(  7)            *x41*x51
     8  +coeff(  8)    *x22    *x41    
      p_rf_dext   =p_rf_dext           
     9  +coeff(  9)    *x21    *x41*x51
     1  +coeff( 10)    *x23*x31        
     2  +coeff( 11)    *x21*x33        
     3  +coeff( 12)    *x24*x31        
     4  +coeff( 13)    *x23*x31    *x51
     5  +coeff( 14)    *x23*x33        
     6  +coeff( 15)    *x21*x31        
     7  +coeff( 16)    *x22*x31        
     8  +coeff( 17)    *x21*x31    *x51
      p_rf_dext   =p_rf_dext           
     9  +coeff( 18)    *x22    *x41*x51
     1  +coeff( 19)*x11        *x41    
     2  +coeff( 20)        *x31*x42    
     3  +coeff( 21)            *x41*x52
     4  +coeff( 22)    *x23    *x41    
     5  +coeff( 23)    *x22*x31    *x51
     6  +coeff( 24)    *x22*x32*x41    
     7  +coeff( 25)        *x34*x41    
     8  +coeff( 26)    *x22    *x43    
      p_rf_dext   =p_rf_dext           
     9  +coeff( 27)    *x22*x31    *x52
     1  +coeff( 28)        *x33    *x52
     2  +coeff( 29)    *x22*x34*x41    
     3  +coeff( 30)*x11    *x31        
     4  +coeff( 31)        *x33        
     5  +coeff( 32)        *x32*x41    
     6  +coeff( 33)            *x43    
     7  +coeff( 34)*x11*x21    *x41    
     8  +coeff( 35)    *x23    *x41*x51
      p_rf_dext   =p_rf_dext           
     9  +coeff( 36)        *x31    *x52
     1  +coeff( 37)*x11*x21*x31        
     2  +coeff( 38)    *x21*x31*x42    
     3  +coeff( 39)    *x21    *x41*x52
     4  +coeff( 40)    *x24    *x41    
     5  +coeff( 41)    *x23*x32*x41    
     6  +coeff( 42)    *x21*x34*x41    
     7  +coeff( 43)    *x23    *x43    
     8  +coeff( 44)    *x23*x34*x41    
c                                      
      return                           
      end                              
      function l_rf_dext   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 13)             
      data ncoeff/ 12/                 
      data avdat/ -0.1085893E-01/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.55757291E-02,-0.43646351E+00,-0.98900631E-01, 0.13182926E-01,
     + -0.29986398E-01,-0.10982285E+00, 0.27551977E-01, 0.69284014E-01,
     +  0.40863913E-01, 0.10210987E-02, 0.30620981E-01,-0.87750936E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
c                                      
c                  function            
c                                      
      l_rf_dext   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)    *x23            
     8  +coeff(  8)    *x21*x31*x41    
      l_rf_dext   =l_rf_dext           
     9  +coeff(  9)    *x21    *x42    
     1  +coeff( 10)    *x23*x32        
     2  +coeff( 11)    *x21*x32        
     3  +coeff( 12)    *x22        *x51
c                                      
      return                           
      end                              
      function x_rf_q3en   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 91)             
      data ncoeff/ 90/                 
      data avdat/ -0.7352035E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.89849522E-02, 0.17638408E+00,-0.17169023E-06, 0.13906473E+00,
     +  0.18306607E-01, 0.63395575E-01,-0.62042656E-02,-0.56876661E-02,
     + -0.80264127E-02,-0.61346684E-02,-0.47286972E-02, 0.73109902E-02,
     + -0.21329794E-01,-0.53941435E-02,-0.39925254E-02,-0.45885411E-02,
     + -0.29507456E-02,-0.24913175E-02,-0.26081791E-04,-0.85977727E-03,
     + -0.49237624E-01,-0.28323799E-01,-0.14239076E-02,-0.30214824E-02,
     + -0.15085790E-02, 0.58494229E-03,-0.33017129E-02, 0.90989437E-04,
     +  0.11778801E-02, 0.15595273E-04,-0.81582123E-03, 0.35649218E-03,
     +  0.24076896E-03,-0.41548457E-01,-0.31191213E-01,-0.83678307E-04,
     + -0.11644674E-02,-0.36315454E-03, 0.11057834E-01, 0.25707098E-01,
     + -0.15326352E-02,-0.55312651E-03,-0.24637231E-02,-0.49733993E-03,
     + -0.23661030E-01,-0.89403382E-02, 0.13466292E-02,-0.28244988E-02,
     +  0.25838401E-04, 0.22424540E-01, 0.66238828E-02, 0.81898941E-03,
     + -0.27948659E-04,-0.10744167E-03,-0.41740542E-03,-0.37335779E-03,
     + -0.12515197E-03,-0.24154446E-03, 0.15926035E-03,-0.29874712E-02,
     + -0.15241938E-03,-0.66284102E-03, 0.39751781E-03, 0.26875616E-02,
     +  0.14908260E-03,-0.13926945E-03,-0.68279664E-03,-0.35274064E-03,
     + -0.13819806E-02,-0.23085201E-03,-0.24511613E-03, 0.17992173E-02,
     + -0.48351465E-03, 0.12330452E-02,-0.52544702E-03, 0.73652680E-03,
     + -0.39020838E-03, 0.16242648E-02, 0.59067080E-03, 0.16013875E-04,
     +  0.17048653E-03,-0.12484023E-03,-0.25022673E-03, 0.14809925E-03,
     +  0.67325185E-04,-0.20608729E-03, 0.19103618E-03,-0.19435186E-03,
     +  0.14452229E-03,-0.22325518E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      x_rf_q3en   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)                *x51
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)*x11                
     8  +coeff(  8)                *x52
      x_rf_q3en   =x_rf_q3en           
     9  +coeff(  9)    *x23            
     1  +coeff( 10)    *x21*x31*x41    
     2  +coeff( 11)    *x21    *x42    
     3  +coeff( 12)    *x22        *x51
     4  +coeff( 13)    *x23*x32        
     5  +coeff( 14)    *x21*x34        
     6  +coeff( 15)        *x31*x41    
     7  +coeff( 16)            *x42    
     8  +coeff( 17)    *x21*x32        
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 18)    *x22*x32        
     1  +coeff( 19)        *x34        
     2  +coeff( 20)*x11*x21            
     3  +coeff( 21)    *x23*x31*x41    
     4  +coeff( 22)    *x23    *x42    
     5  +coeff( 23)        *x32        
     6  +coeff( 24)    *x24            
     7  +coeff( 25)            *x42*x51
     8  +coeff( 26)    *x21        *x52
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 27)    *x22*x31*x41    
     1  +coeff( 28)    *x22    *x42    
     2  +coeff( 29)    *x23        *x51
     3  +coeff( 30)        *x33*x41*x51
     4  +coeff( 31)        *x31*x41*x51
     5  +coeff( 32)                *x53
     6  +coeff( 33)    *x21*x32    *x51
     7  +coeff( 34)    *x21*x32*x42    
     8  +coeff( 35)    *x21*x31*x43    
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 36)*x11            *x51
     1  +coeff( 37)    *x24        *x51
     2  +coeff( 38)*x11*x22            
     3  +coeff( 39)    *x23*x33*x41    
     4  +coeff( 40)    *x23*x32*x42    
     5  +coeff( 41)    *x21*x33*x43    
     6  +coeff( 42)    *x21*x32*x44    
     7  +coeff( 43)    *x23*x34*x42    
     8  +coeff( 44)    *x21    *x42*x51
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 45)    *x21*x33*x41    
     1  +coeff( 46)    *x21    *x44    
     2  +coeff( 47)    *x22    *x42*x51
     3  +coeff( 48)    *x24    *x42    
     4  +coeff( 49)    *x22*x31*x41*x52
     5  +coeff( 50)    *x23*x31*x43    
     6  +coeff( 51)    *x23    *x44    
     7  +coeff( 52)    *x24*x31*x41*x51
     8  +coeff( 53)    *x21    *x41    
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 54)    *x23*x31        
     1  +coeff( 55)    *x21*x31*x41*x51
     2  +coeff( 56)        *x31*x41*x52
     3  +coeff( 57)    *x21        *x53
     4  +coeff( 58)                *x54
     5  +coeff( 59)    *x21    *x42*x52
     6  +coeff( 60)    *x24*x31*x41    
     7  +coeff( 61)*x11*x21        *x51
     8  +coeff( 62)        *x32*x42*x52
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 63)    *x22        *x54
     1  +coeff( 64)    *x23*x34        
     2  +coeff( 65)*x11*x21*x31*x41    
     3  +coeff( 66)*x11*x22        *x51
     4  +coeff( 67)    *x24*x34        
     5  +coeff( 68)*x11*x21    *x42*x51
     6  +coeff( 69)    *x23    *x44*x51
     7  +coeff( 70)        *x33*x41*x54
     8  +coeff( 71)*x11*x24*x31    *x51
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 72)*x11*x23    *x42*x51
     1  +coeff( 73)*x11*x23    *x43*x51
     2  +coeff( 74)*x11*x23*x32    *x52
     3  +coeff( 75)*x11*x21*x34    *x52
     4  +coeff( 76)    *x24*x34*x41*x52
     5  +coeff( 77)*x11*x24    *x44    
     6  +coeff( 78)*x11*x23*x31*x43*x51
     7  +coeff( 79)*x11*x22    *x42*x54
     8  +coeff( 80)            *x43    
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 81)    *x21    *x41*x51
     1  +coeff( 82)    *x23    *x41    
     2  +coeff( 83)        *x33*x41    
     3  +coeff( 84)            *x44    
     4  +coeff( 85)    *x22    *x41*x51
     5  +coeff( 86)    *x22        *x52
     6  +coeff( 87)    *x21*x31*x42*x51
     7  +coeff( 88)    *x21    *x43*x51
     8  +coeff( 89)    *x23        *x52
      x_rf_q3en   =x_rf_q3en           
     9  +coeff( 90)    *x21*x32    *x52
c                                      
      return                           
      end                              
      function t_rf_q3en   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 24)             
      data ncoeff/ 23/                 
      data avdat/ -0.3072115E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.24071755E-02,-0.75206608E-01, 0.22674385E-01, 0.19786688E-02,
     + -0.15445093E-01, 0.51282495E-04,-0.13792310E-02, 0.39803758E-02,
     +  0.66898684E-02,-0.29216581E-02,-0.30430648E-03, 0.38019062E-02,
     +  0.30458327E-02,-0.12874693E-02, 0.11447689E-02, 0.71209349E-03,
     +  0.22889717E-03,-0.13514748E-03, 0.65531780E-03, 0.81021655E-02,
     +  0.54085818E-02, 0.70654991E-03, 0.25993073E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      t_rf_q3en   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x21        *x51
     6  +coeff(  6)    *x24            
     7  +coeff(  7)                *x52
     8  +coeff(  8)    *x23            
      t_rf_q3en   =t_rf_q3en           
     9  +coeff(  9)    *x21*x31*x41    
     1  +coeff( 10)    *x22            
     2  +coeff( 11)        *x31*x41    
     3  +coeff( 12)    *x21*x32        
     4  +coeff( 13)    *x21    *x42    
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)    *x21        *x52
     7  +coeff( 16)            *x42    
     8  +coeff( 17)*x11*x21            
      t_rf_q3en   =t_rf_q3en           
     9  +coeff( 18)*x11            *x51
     1  +coeff( 19)            *x42*x51
     2  +coeff( 20)    *x23*x31*x41    
     3  +coeff( 21)    *x23    *x42    
     4  +coeff( 22)        *x33*x41*x51
     5  +coeff( 23)    *x23*x34        
c                                      
      return                           
      end                              
      function y_rf_q3en   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 39)             
      data ncoeff/ 38/                 
      data avdat/ -0.1757677E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.19542342E-02,-0.36080182E-01, 0.13978131E+00,-0.25657333E-04,
     + -0.36342766E-01,-0.65333754E-01, 0.60069215E-01, 0.80039524E-01,
     + -0.30229421E-01,-0.41854866E-01,-0.19541841E-01, 0.63118791E-05,
     + -0.20378631E-01,-0.25442831E-01,-0.10619878E-01,-0.11099190E-01,
     + -0.61239959E-02,-0.69271647E-02,-0.11549613E-01,-0.78107056E-04,
     + -0.12910743E-03, 0.17234741E-02,-0.17478818E-03, 0.78995116E-02,
     + -0.71542319E-02,-0.81565042E-04,-0.54680463E-02, 0.97924203E-03,
     +  0.10754870E-01, 0.49863844E-02, 0.11890383E-02, 0.72487481E-02,
     +  0.30496434E-03, 0.45835380E-02, 0.11925914E-02, 0.56500817E-02,
     +  0.11211697E-01, 0.92316791E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x35 = x34*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x45 = x44*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      y_rf_q3en   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)        *x32        
     5  +coeff(  5)    *x21*x31        
     6  +coeff(  6)    *x21    *x41    
     7  +coeff(  7)        *x31    *x51
     8  +coeff(  8)            *x41*x51
      y_rf_q3en   =y_rf_q3en           
     9  +coeff(  9)    *x22*x31        
     1  +coeff( 10)    *x22    *x41    
     2  +coeff( 11)    *x21    *x41*x51
     3  +coeff( 12)    *x21*x33    *x51
     4  +coeff( 13)        *x32*x41    
     5  +coeff( 14)        *x31*x42    
     6  +coeff( 15)            *x43    
     7  +coeff( 16)    *x21*x31    *x51
     8  +coeff( 17)        *x31    *x52
      y_rf_q3en   =y_rf_q3en           
     9  +coeff( 18)            *x41*x52
     1  +coeff( 19)    *x22    *x41*x51
     2  +coeff( 20)        *x35        
     3  +coeff( 21)    *x22*x33    *x51
     4  +coeff( 22)*x11        *x41    
     5  +coeff( 23)        *x33    *x51
     6  +coeff( 24)    *x23    *x41    
     7  +coeff( 25)    *x22*x31    *x51
     8  +coeff( 26)*x11    *x33        
      y_rf_q3en   =y_rf_q3en           
     9  +coeff( 27)        *x33        
     1  +coeff( 28)*x11    *x31        
     2  +coeff( 29)    *x21*x31*x42    
     3  +coeff( 30)    *x23*x31        
     4  +coeff( 31)*x11*x21    *x41    
     5  +coeff( 32)    *x21*x34*x41    
     6  +coeff( 33)    *x21*x31*x44    
     7  +coeff( 34)    *x21    *x45    
     8  +coeff( 35)*x11*x21*x33        
      y_rf_q3en   =y_rf_q3en           
     9  +coeff( 36)    *x23*x33        
     1  +coeff( 37)    *x23*x32*x41    
     2  +coeff( 38)    *x23*x35*x42    
c                                      
      return                           
      end                              
      function p_rf_q3en   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 39)             
      data ncoeff/ 38/                 
      data avdat/ -0.2960975E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.31568212E-03,-0.15209448E-04,-0.15694993E-01, 0.14788645E-01,
     + -0.78882212E-02,-0.12592305E-01, 0.10953239E-01, 0.16286140E-01,
     + -0.92976652E-02,-0.44108010E-02, 0.15793648E-03, 0.17892904E-03,
     + -0.58981432E-02,-0.23105466E-02,-0.29261447E-02, 0.30950214E-04,
     + -0.37153703E-02,-0.46062199E-02,-0.19619002E-02, 0.18244958E-02,
     + -0.24279077E-05,-0.12030554E-03,-0.67689303E-04, 0.22259339E-03,
     + -0.99065027E-03, 0.31214091E-03,-0.59177488E-03, 0.11863087E-02,
     + -0.20298830E-02, 0.11146666E-02,-0.60009032E-04,-0.46625815E-03,
     +  0.15944362E-03, 0.34011735E-03, 0.75833651E-03, 0.19625768E-03,
     +  0.67151425E-03, 0.94314601E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      p_rf_q3en   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)            *x41    
     5  +coeff(  5)    *x21*x31        
     6  +coeff(  6)    *x21    *x41    
     7  +coeff(  7)        *x31    *x51
     8  +coeff(  8)            *x41*x51
      p_rf_q3en   =p_rf_q3en           
     9  +coeff(  9)    *x22    *x41    
     1  +coeff( 10)    *x21    *x41*x51
     2  +coeff( 11)    *x24*x31        
     3  +coeff( 12)    *x23*x31    *x51
     4  +coeff( 13)    *x22*x31        
     5  +coeff( 14)    *x21*x31    *x51
     6  +coeff( 15)    *x22    *x41*x51
     7  +coeff( 16)    *x24*x31    *x51
     8  +coeff( 17)        *x32*x41    
      p_rf_q3en   =p_rf_q3en           
     9  +coeff( 18)        *x31*x42    
     1  +coeff( 19)            *x43    
     2  +coeff( 20)    *x23    *x41    
     3  +coeff( 21)    *x22*x33        
     4  +coeff( 22)        *x33    *x52
     5  +coeff( 23)        *x32*x41*x52
     6  +coeff( 24)*x11    *x31        
     7  +coeff( 25)        *x33        
     8  +coeff( 26)*x11        *x41    
      p_rf_q3en   =p_rf_q3en           
     9  +coeff( 27)            *x41*x52
     1  +coeff( 28)    *x23*x31        
     2  +coeff( 29)    *x22*x31    *x51
     3  +coeff( 30)    *x23    *x41*x51
     4  +coeff( 31)*x11*x21    *x43    
     5  +coeff( 32)        *x31    *x52
     6  +coeff( 33)*x11*x21*x31        
     7  +coeff( 34)*x11*x21    *x41    
     8  +coeff( 35)    *x21*x31*x42    
      p_rf_q3en   =p_rf_q3en           
     9  +coeff( 36)    *x21    *x41*x52
     1  +coeff( 37)    *x24    *x41    
     2  +coeff( 38)    *x23*x32*x41    
c                                      
      return                           
      end                              
      function l_rf_q3en   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 18)             
      data ncoeff/ 17/                 
      data avdat/ -0.9411141E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.49918E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12303E+00, 0.49945E-01, 0.33196E-01, 0.49997E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.58224811E-02,-0.29051951E+00,-0.32047410E-01, 0.83557246E-02,
     + -0.28159117E-01,-0.63107155E-01, 0.17750399E-01, 0.42039178E-01,
     +  0.25254605E-01,-0.82762297E-02, 0.71855640E-03,-0.10022246E-01,
     + -0.67466157E-02, 0.18260218E-01, 0.42599281E-02,-0.19981121E-02,
     + -0.48268652E-02,                
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      l_rf_q3en   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)    *x23            
     8  +coeff(  8)    *x21*x31*x41    
      l_rf_q3en   =l_rf_q3en           
     9  +coeff(  9)    *x21    *x42    
     1  +coeff( 10)    *x22        *x51
     2  +coeff( 11)    *x23*x32        
     3  +coeff( 12)        *x31*x41    
     4  +coeff( 13)            *x42    
     5  +coeff( 14)    *x21*x32        
     6  +coeff( 15)    *x21        *x52
     7  +coeff( 16)    *x22*x32        
     8  +coeff( 17)        *x34        
c                                      
      return                           
      end                              
      function x_rf_q3ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 91)             
      data ncoeff/ 90/                 
      data avdat/ -0.3956524E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.47993142E-01,-0.10995745E-04, 0.33247316E+00, 0.24814764E-01,
     +  0.54806750E-01,-0.20103794E-01,-0.40102894E-02,-0.52276249E-02,
     + -0.12312180E-01, 0.55016380E-01,-0.47924491E-02,-0.10479666E-01,
     + -0.67930408E-02,-0.14379786E-01,-0.28766891E-01,-0.14872821E-01,
     + -0.23279451E-02,-0.33437787E-02,-0.11676649E-01, 0.75358027E-02,
     + -0.52185701E-02,-0.97520655E-03,-0.22315931E-04, 0.80106547E-03,
     +  0.27840126E-02, 0.65802148E-03, 0.65920618E-02,-0.30909549E-03,
     + -0.41208849E-02,-0.11419451E-02,-0.44993972E-03,-0.38814645E-02,
     +  0.69140121E-02,-0.30093014E-02, 0.15762354E-02,-0.13019482E-02,
     + -0.76064345E-03,-0.34872943E-02,-0.23515921E-01,-0.32116615E-03,
     + -0.10488973E-02,-0.66355331E-03, 0.81965649E-04,-0.67563262E-03,
     + -0.14081881E-01,-0.15622330E-01,-0.43925131E-02, 0.73834664E-04,
     +  0.23239036E-02,-0.11932952E-02,-0.52212225E-02, 0.41834608E-03,
     + -0.93626144E-03,-0.70997521E-04,-0.79515390E-03,-0.68377156E-03,
     + -0.28999764E-02,-0.45327682E-03,-0.65431988E-03,-0.49075577E-03,
     + -0.52908133E-03,-0.40320149E-02, 0.23479885E-03,-0.17642064E-02,
     + -0.41279863E-03,-0.74418922E-05,-0.25339797E-03,-0.26600328E-02,
     +  0.19110359E-02, 0.42793134E-03,-0.47413701E-04,-0.32845070E-04,
     +  0.11277423E-04,-0.17668547E-03, 0.23004870E-03,-0.50776138E-03,
     +  0.62379702E-04,-0.59789181E-03, 0.78160112E-04,-0.14424828E-02,
     +  0.36975121E-03,-0.35518283E-03,-0.18212516E-03,-0.44548528E-04,
     + -0.14825675E-02,-0.58284606E-03,-0.45596846E-03, 0.48715938E-04,
     + -0.42527530E-03, 0.35154849E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      x_rf_q3ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)                *x51
     4  +coeff(  4)    *x22            
     5  +coeff(  5)    *x21        *x51
     6  +coeff(  6)                *x52
     7  +coeff(  7)    *x23            
     8  +coeff(  8)    *x21*x32        
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff(  9)    *x23*x32        
     1  +coeff( 10)    *x21            
     2  +coeff( 11)*x11                
     3  +coeff( 12)        *x31*x41    
     4  +coeff( 13)            *x42    
     5  +coeff( 14)    *x21    *x42    
     6  +coeff( 15)    *x23*x31*x41    
     7  +coeff( 16)    *x23    *x42    
     8  +coeff( 17)    *x22        *x53
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 18)        *x32        
     1  +coeff( 19)    *x21*x31*x41    
     2  +coeff( 20)    *x22        *x51
     3  +coeff( 21)    *x24            
     4  +coeff( 22)*x11*x21            
     5  +coeff( 23)        *x32    *x51
     6  +coeff( 24)        *x31*x41*x51
     7  +coeff( 25)                *x53
     8  +coeff( 26)    *x22*x31*x41    
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 27)    *x22    *x42    
     1  +coeff( 28)    *x21*x32    *x51
     2  +coeff( 29)    *x21    *x42*x51
     3  +coeff( 30)    *x22        *x52
     4  +coeff( 31)*x11            *x51
     5  +coeff( 32)    *x24        *x51
     6  +coeff( 33)    *x22    *x42*x51
     7  +coeff( 34)    *x23*x31*x41*x51
     8  +coeff( 35)    *x21        *x52
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 36)    *x22*x32        
     1  +coeff( 37)    *x23        *x51
     2  +coeff( 38)    *x21*x31*x41*x51
     3  +coeff( 39)    *x21*x32*x42    
     4  +coeff( 40)*x11*x22            
     5  +coeff( 41)    *x23*x33*x41    
     6  +coeff( 42)            *x42*x51
     7  +coeff( 43)        *x32    *x52
     8  +coeff( 44)                *x54
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 45)    *x21*x33*x41    
     1  +coeff( 46)    *x21*x31*x43    
     2  +coeff( 47)    *x21    *x44    
     3  +coeff( 48)    *x22*x32    *x51
     4  +coeff( 49)    *x22*x31*x41*x51
     5  +coeff( 50)    *x23        *x52
     6  +coeff( 51)    *x24    *x42    
     7  +coeff( 52)*x11*x23            
     8  +coeff( 53)    *x23*x34        
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 54)    *x21    *x41    
     1  +coeff( 55)            *x42*x52
     2  +coeff( 56)    *x21        *x53
     3  +coeff( 57)    *x21*x34        
     4  +coeff( 58)        *x32*x42*x51
     5  +coeff( 59)    *x21*x32    *x52
     6  +coeff( 60)        *x32    *x53
     7  +coeff( 61)            *x42*x53
     8  +coeff( 62)    *x24*x31*x41    
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 63)*x11        *x42    
     1  +coeff( 64)    *x23    *x42*x51
     2  +coeff( 65)    *x24        *x52
     3  +coeff( 66)*x11*x21*x31*x41    
     4  +coeff( 67)*x11*x21    *x42    
     5  +coeff( 68)    *x24    *x42*x51
     6  +coeff( 69)    *x24        *x53
     7  +coeff( 70)*x11*x23        *x51
     8  +coeff( 71)    *x21*x31        
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 72)    *x21*x31    *x51
     1  +coeff( 73)        *x33*x41    
     2  +coeff( 74)        *x31*x41*x52
     3  +coeff( 75)        *x31*x43*x51
     4  +coeff( 76)    *x21        *x54
     5  +coeff( 77)*x11    *x32        
     6  +coeff( 78)    *x24*x32        
     7  +coeff( 79)*x11    *x31*x41    
     8  +coeff( 80)    *x22*x31*x43    
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 81)        *x33*x43    
     1  +coeff( 82)    *x22    *x44    
     2  +coeff( 83)*x11*x21        *x51
     3  +coeff( 84)*x11    *x31    *x51
     4  +coeff( 85)    *x23*x32    *x51
     5  +coeff( 86)    *x21*x33*x41*x51
     6  +coeff( 87)    *x21    *x44*x51
     7  +coeff( 88)*x11            *x52
     8  +coeff( 89)    *x22*x32    *x52
      x_rf_q3ex   =x_rf_q3ex           
     9  +coeff( 90)        *x34    *x52
c                                      
      return                           
      end                              
      function t_rf_q3ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 22)             
      data ncoeff/ 21/                 
      data avdat/ -0.2169258E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.20109287E-01,-0.14988198E-01,-0.16363883E-04, 0.13434868E+00,
     +  0.77076405E-02, 0.12853642E-01,-0.11374706E-01,-0.86450134E-03,
     + -0.41511869E-02,-0.20383340E-02,-0.58954773E-02,-0.13267379E-02,
     + -0.57205670E-02, 0.12284288E-02, 0.13624206E-02,-0.57421299E-03,
     +  0.16122493E-03,-0.26994662E-02,-0.38240844E-03, 0.10821311E-02,
     + -0.16459022E-02,                
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
c                                      
c                  function            
c                                      
      t_rf_q3ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)                *x51
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)                *x52
     8  +coeff(  8)*x11                
      t_rf_q3ex   =t_rf_q3ex           
     9  +coeff(  9)        *x31*x41    
     1  +coeff( 10)            *x42    
     2  +coeff( 11)    *x21    *x42    
     3  +coeff( 12)        *x32        
     4  +coeff( 13)    *x21*x31*x41    
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)                *x53
     7  +coeff( 16)    *x23*x32        
     8  +coeff( 17)    *x21*x34        
      t_rf_q3ex   =t_rf_q3ex           
     9  +coeff( 18)    *x21*x32        
     1  +coeff( 19)        *x32    *x51
     2  +coeff( 20)        *x31*x41*x51
     3  +coeff( 21)    *x24            
c                                      
      return                           
      end                              
      function y_rf_q3ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 43)             
      data ncoeff/ 42/                 
      data avdat/ -0.5946762E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.67217270E-03,-0.31193580E-01, 0.53678077E-01, 0.51880426E-04,
     + -0.85663532E-06,-0.19716909E-01,-0.33658016E-01, 0.23472013E-01,
     +  0.40564828E-01,-0.22958715E-01,-0.12525287E-01,-0.80109714E-02,
     +  0.71856473E-03,-0.16497883E-02,-0.56428807E-02,-0.50855107E-02,
     + -0.14901872E-02,-0.76175790E-03, 0.51395316E-03,-0.11042560E-02,
     + -0.11065952E-01,-0.50635710E-02,-0.13476316E-01, 0.81472984E-03,
     + -0.54810545E-02, 0.47674198E-02,-0.46082851E-02,-0.15824453E-04,
     +  0.15418382E-02,-0.97911339E-03,-0.13080974E-02,-0.25195286E-02,
     + -0.90662213E-02, 0.54461852E-03,-0.12760755E-02, 0.26653057E-02,
     +  0.83208398E-03, 0.37113763E-03,-0.10152278E-02,-0.13135995E-02,
     +  0.24468871E-02, 0.20714290E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x35 = x34*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      y_rf_q3ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)                *x51
     5  +coeff(  5)        *x32        
     6  +coeff(  6)    *x21*x31        
     7  +coeff(  7)    *x21    *x41    
     8  +coeff(  8)        *x31    *x51
      y_rf_q3ex   =y_rf_q3ex           
     9  +coeff(  9)            *x41*x51
     1  +coeff( 10)    *x22    *x41    
     2  +coeff( 11)    *x21    *x41*x51
     3  +coeff( 12)    *x22    *x41*x51
     4  +coeff( 13)    *x21*x31    *x52
     5  +coeff( 14)    *x22*x33        
     6  +coeff( 15)    *x22*x32*x41    
     7  +coeff( 16)    *x22*x31*x42    
     8  +coeff( 17)    *x22    *x43    
      y_rf_q3ex   =y_rf_q3ex           
     9  +coeff( 18)    *x21*x33    *x51
     1  +coeff( 19)        *x33    *x52
     2  +coeff( 20)    *x24*x31        
     3  +coeff( 21)        *x31*x42    
     4  +coeff( 22)            *x43    
     5  +coeff( 23)    *x22*x31        
     6  +coeff( 24)*x11        *x41    
     7  +coeff( 25)    *x21*x31    *x51
     8  +coeff( 26)    *x23    *x41    
      y_rf_q3ex   =y_rf_q3ex           
     9  +coeff( 27)    *x22*x31    *x51
     1  +coeff( 28)        *x34*x41    
     2  +coeff( 29)        *x31    *x54
     3  +coeff( 30)        *x35*x42    
     4  +coeff( 31)        *x34*x43    
     5  +coeff( 32)        *x33        
     6  +coeff( 33)        *x32*x41    
     7  +coeff( 34)*x11    *x31        
     8  +coeff( 35)            *x41*x52
      y_rf_q3ex   =y_rf_q3ex           
     9  +coeff( 36)    *x23*x31        
     1  +coeff( 37)*x11*x21    *x41    
     2  +coeff( 38)*x11*x21*x31        
     3  +coeff( 39)        *x31    *x53
     4  +coeff( 40)            *x41*x53
     5  +coeff( 41)    *x23    *x41*x51
     6  +coeff( 42)    *x23*x33    *x51
c                                      
      return                           
      end                              
      function p_rf_q3ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 45)             
      data ncoeff/ 44/                 
      data avdat/  0.8615116E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.96138997E-03, 0.42344836E-04, 0.12959725E-01,-0.76516233E-01,
     +  0.17970137E-01,-0.33480510E-05, 0.32448348E-01,-0.25862841E-01,
     + -0.31182537E-01, 0.21062374E-01, 0.88976213E-03, 0.15027284E-01,
     +  0.63444045E-02, 0.44453978E-02,-0.18827870E-03,-0.88425243E-03,
     +  0.13105115E-01, 0.44039562E-02, 0.17319884E-02, 0.23659146E-02,
     +  0.71673849E-05,-0.22902146E-03,-0.83794887E-03, 0.74647658E-03,
     + -0.48239197E-03, 0.30146528E-02, 0.53276918E-02,-0.26016994E-02,
     +  0.35933850E-02,-0.16659648E-03, 0.10019364E-01,-0.31505162E-02,
     + -0.53465710E-03,-0.42723627E-02, 0.28145339E-02, 0.58300316E-03,
     + -0.13646682E-02,-0.10768924E-02, 0.18405751E-02,-0.52574172E-03,
     + -0.92284642E-02,-0.32278069E-02,-0.15261959E-01,-0.70022307E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
c                                      
c                  function            
c                                      
      p_rf_q3ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)            *x41    
     5  +coeff(  5)    *x21*x31        
     6  +coeff(  6)        *x32        
     7  +coeff(  7)    *x21    *x41    
     8  +coeff(  8)        *x31    *x51
      p_rf_q3ex   =p_rf_q3ex           
     9  +coeff(  9)            *x41*x51
     1  +coeff( 10)    *x22    *x41    
     2  +coeff( 11)    *x24*x31        
     3  +coeff( 12)    *x22*x31        
     4  +coeff( 13)    *x21    *x41*x51
     5  +coeff( 14)        *x31    *x52
     6  +coeff( 15)    *x23*x31    *x51
     7  +coeff( 16)*x11        *x41    
     8  +coeff( 17)        *x31*x42    
      p_rf_q3ex   =p_rf_q3ex           
     9  +coeff( 18)    *x21*x31    *x51
     1  +coeff( 19)            *x41*x52
     2  +coeff( 20)    *x22*x32*x41    
     3  +coeff( 21)        *x34*x41    
     4  +coeff( 22)        *x32*x43    
     5  +coeff( 23)    *x22*x34*x41    
     6  +coeff( 24)        *x34*x43    
     7  +coeff( 25)*x11    *x31        
     8  +coeff( 26)        *x33        
      p_rf_q3ex   =p_rf_q3ex           
     9  +coeff( 27)            *x43    
     1  +coeff( 28)    *x23    *x41    
     2  +coeff( 29)    *x22    *x41*x51
     3  +coeff( 30)    *x24*x31    *x51
     4  +coeff( 31)        *x32*x41    
     5  +coeff( 32)    *x23*x31        
     6  +coeff( 33)*x11*x21    *x41    
     7  +coeff( 34)    *x21*x31*x42    
     8  +coeff( 35)    *x22*x31    *x51
      p_rf_q3ex   =p_rf_q3ex           
     9  +coeff( 36)    *x21*x31    *x52
     1  +coeff( 37)        *x31    *x53
     2  +coeff( 38)            *x41*x53
     3  +coeff( 39)    *x22*x31*x42    
     4  +coeff( 40)*x11*x23*x31        
     5  +coeff( 41)    *x23*x32*x41    
     6  +coeff( 42)    *x23    *x43    
     7  +coeff( 43)    *x23*x33*x42    
     8  +coeff( 44)    *x21*x34*x43    
c                                      
      return                           
      end                              
      function l_rf_q3ex   (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 18)             
      data ncoeff/ 17/                 
      data avdat/ -0.1074684E-01/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.60187825E-02,-0.29188818E+00,-0.29154586E-01, 0.84272660E-02,
     + -0.32120012E-01,-0.46527565E-01,-0.95864013E-02, 0.16493596E-01,
     +  0.40675618E-01, 0.26516093E-01,-0.68920752E-04,-0.85965060E-02,
     +  0.16896024E-01,-0.79913875E-02,-0.62756832E-02,-0.99819787E-02,
     + -0.10389735E-01,                
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x51 = x5                         
      x52 = x51*x5                     
c                                      
c                  function            
c                                      
      l_rf_q3ex   =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)                *x52
     8  +coeff(  8)    *x23            
      l_rf_q3ex   =l_rf_q3ex           
     9  +coeff(  9)    *x21*x31*x41    
     1  +coeff( 10)    *x21    *x42    
     2  +coeff( 11)    *x23*x32        
     3  +coeff( 12)            *x42    
     4  +coeff( 13)    *x21*x32        
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)        *x31*x43    
     7  +coeff( 16)        *x32    *x52
     8  +coeff( 17)        *x31*x41*x52
c                                      
      return                           
      end                              
      function x_rf_fp     (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 91)             
      data ncoeff/ 90/                 
      data avdat/ -0.1019981E-01/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.10574530E+00, 0.12525082E-01,-0.11930539E-04, 0.71929336E+00,
     +  0.47612417E-01, 0.93105428E-01,-0.51332809E-01,-0.73544853E-02,
     + -0.22303548E-01,-0.12694317E-01,-0.30871974E-01,-0.69691502E-02,
     + -0.22086358E-01, 0.11318222E-01,-0.19400783E-01,-0.54812622E-02,
     + -0.88601252E-02, 0.12998686E-03, 0.25697551E-02, 0.64881165E-02,
     + -0.11131279E-01,-0.17991443E-02,-0.43492867E-02, 0.25020079E-02,
     +  0.13853105E-01,-0.85386559E-02,-0.98965066E-02,-0.41098174E-01,
     + -0.19161507E-01,-0.86935458E-03, 0.17331207E-01,-0.28871768E-02,
     + -0.46106465E-02, 0.23923985E-03,-0.64348145E-02,-0.13552669E-02,
     +  0.93526312E-03,-0.28911368E-02,-0.14653612E-02,-0.44870186E-02,
     + -0.34739364E-01,-0.20939323E-03, 0.68397960E-02,-0.11307469E-02,
     + -0.32174066E-02, 0.58529573E-03,-0.56540238E-03,-0.10543000E-01,
     + -0.35501674E-02,-0.12094502E-02, 0.60768094E-03, 0.16410384E-03,
     + -0.26386711E-02,-0.74911531E-03,-0.18728803E-02,-0.21397866E-01,
     + -0.21131575E-01,-0.56219366E-02, 0.14935684E-02,-0.10467446E-02,
     + -0.31046441E-02,-0.87832874E-02, 0.40580691E-02, 0.11452141E-02,
     +  0.92896633E-03,-0.57867081E-02, 0.35966553E-02,-0.11933749E-02,
     + -0.69379125E-03, 0.87720115E-03, 0.60661654E-02,-0.30519308E-02,
     + -0.89479458E-04,-0.64890349E-03,-0.60912204E-03,-0.45980260E-03,
     + -0.13431343E-02, 0.11781032E-03,-0.21338423E-02,-0.18216856E-02,
     + -0.96523669E-03, 0.91571914E-04,-0.59817663E-04, 0.37334772E-03,
     + -0.27058243E-02,-0.26894134E-03, 0.10089426E-03,-0.32620460E-02,
     + -0.20830552E-02, 0.11119268E-03,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      x_rf_fp     =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)                *x51
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)                *x52
     8  +coeff(  8)*x11                
      x_rf_fp     =x_rf_fp             
     9  +coeff(  9)        *x31*x41    
     1  +coeff( 10)            *x42    
     2  +coeff( 11)    *x21    *x42    
     3  +coeff( 12)        *x32        
     4  +coeff( 13)    *x21*x31*x41    
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)    *x23*x32        
     7  +coeff( 16)    *x21*x34        
     8  +coeff( 17)    *x21*x32        
      x_rf_fp     =x_rf_fp             
     9  +coeff( 18)        *x32    *x51
     1  +coeff( 19)        *x31*x41*x51
     2  +coeff( 20)                *x53
     3  +coeff( 21)    *x24            
     4  +coeff( 22)*x11*x21            
     5  +coeff( 23)    *x23            
     6  +coeff( 24)    *x22*x31*x41    
     7  +coeff( 25)    *x22    *x42    
     8  +coeff( 26)    *x21*x31*x41*x51
      x_rf_fp     =x_rf_fp             
     9  +coeff( 27)    *x21    *x42*x51
     1  +coeff( 28)    *x23*x31*x41    
     2  +coeff( 29)    *x23    *x42    
     3  +coeff( 30)*x11            *x51
     4  +coeff( 31)    *x22    *x42*x51
     5  +coeff( 32)    *x22*x32        
     6  +coeff( 33)    *x22        *x52
     7  +coeff( 34)        *x32    *x52
     8  +coeff( 35)    *x24        *x51
      x_rf_fp     =x_rf_fp             
     9  +coeff( 36)            *x42*x51
     1  +coeff( 37)    *x21        *x52
     2  +coeff( 38)    *x23        *x51
     3  +coeff( 39)    *x21*x32    *x51
     4  +coeff( 40)            *x42*x52
     5  +coeff( 41)    *x21*x32*x42    
     6  +coeff( 42)    *x22*x32    *x51
     7  +coeff( 43)    *x22*x31*x41*x51
     8  +coeff( 44)        *x32*x42*x51
      x_rf_fp     =x_rf_fp             
     9  +coeff( 45)    *x23        *x52
     1  +coeff( 46)        *x31*x41*x53
     2  +coeff( 47)*x11*x22            
     3  +coeff( 48)    *x24    *x42    
     4  +coeff( 49)    *x23*x33*x41    
     5  +coeff( 50)    *x21*x33*x43    
     6  +coeff( 51)    *x21*x34    *x52
     7  +coeff( 52)*x11        *x44    
     8  +coeff( 53)    *x23*x34*x42    
      x_rf_fp     =x_rf_fp             
     9  +coeff( 54)*x11*x21    *x44    
     1  +coeff( 55)                *x54
     2  +coeff( 56)    *x21*x33*x41    
     3  +coeff( 57)    *x21*x31*x43    
     4  +coeff( 58)    *x21    *x44    
     5  +coeff( 59)        *x31*x43*x51
     6  +coeff( 60)        *x32    *x53
     7  +coeff( 61)            *x42*x53
     8  +coeff( 62)    *x24*x31*x41    
      x_rf_fp     =x_rf_fp             
     9  +coeff( 63)    *x22    *x42*x52
     1  +coeff( 64)        *x32    *x54
     2  +coeff( 65)*x11*x23            
     3  +coeff( 66)    *x24    *x42*x51
     4  +coeff( 67)    *x21*x33*x41*x52
     5  +coeff( 68)        *x34    *x53
     6  +coeff( 69)    *x24*x34        
     7  +coeff( 70)*x11*x23        *x51
     8  +coeff( 71)    *x24*x31*x41*x52
      x_rf_fp     =x_rf_fp             
     9  +coeff( 72)    *x23*x32    *x53
     1  +coeff( 73)    *x21    *x41    
     2  +coeff( 74)        *x32*x42    
     3  +coeff( 75)            *x44    
     4  +coeff( 76)        *x31*x41*x52
     5  +coeff( 77)    *x21        *x53
     6  +coeff( 78)    *x22    *x43    
     7  +coeff( 79)    *x21*x32    *x52
     8  +coeff( 80)    *x22        *x53
      x_rf_fp     =x_rf_fp             
     9  +coeff( 81)    *x21        *x54
     1  +coeff( 82)*x11    *x32        
     2  +coeff( 83)*x11*x21    *x41    
     3  +coeff( 84)*x11        *x42    
     4  +coeff( 85)    *x22*x31*x43    
     5  +coeff( 86)*x11*x21        *x51
     6  +coeff( 87)*x11        *x41*x51
     7  +coeff( 88)    *x23*x31*x41*x51
     8  +coeff( 89)    *x23    *x42*x51
      x_rf_fp     =x_rf_fp             
     9  +coeff( 90)*x11            *x52
c                                      
      return                           
      end                              
      function t_rf_fp     (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 22)             
      data ncoeff/ 21/                 
      data avdat/ -0.2169220E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.20109184E-01,-0.14988630E-01,-0.16384643E-04, 0.13434954E+00,
     +  0.77081122E-02, 0.12852818E-01,-0.11376053E-01,-0.86447183E-03,
     + -0.41505401E-02,-0.20389550E-02,-0.58952286E-02,-0.13263058E-02,
     + -0.57186438E-02, 0.12295106E-02, 0.13569648E-02,-0.57314028E-03,
     +  0.16027471E-03,-0.26991589E-02,-0.38327926E-03, 0.10882306E-02,
     + -0.16463447E-02,                
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
c                                      
c                  function            
c                                      
      t_rf_fp     =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)                *x51
     5  +coeff(  5)    *x22            
     6  +coeff(  6)    *x21        *x51
     7  +coeff(  7)                *x52
     8  +coeff(  8)*x11                
      t_rf_fp     =t_rf_fp             
     9  +coeff(  9)        *x31*x41    
     1  +coeff( 10)            *x42    
     2  +coeff( 11)    *x21    *x42    
     3  +coeff( 12)        *x32        
     4  +coeff( 13)    *x21*x31*x41    
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)                *x53
     7  +coeff( 16)    *x23*x32        
     8  +coeff( 17)    *x21*x34        
      t_rf_fp     =t_rf_fp             
     9  +coeff( 18)    *x21*x32        
     1  +coeff( 19)        *x32    *x51
     2  +coeff( 20)        *x31*x41*x51
     3  +coeff( 21)    *x24            
c                                      
      return                           
      end                              
      function y_rf_fp     (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 39)             
      data ncoeff/ 38/                 
      data avdat/  0.1886036E-02/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.21162033E-02, 0.62739532E-02,-0.16608748E+00, 0.37333498E-05,
     +  0.31302989E-01, 0.61261833E-01,-0.51010024E-01,-0.48981316E-01,
     +  0.30059239E-01, 0.36648657E-01, 0.11222418E-01, 0.26951568E-01,
     + -0.17204538E-02, 0.68799276E-02, 0.59368950E-02, 0.30949188E-02,
     + -0.25813195E-02,-0.19573700E-02, 0.18205157E-02,-0.40356870E-04,
     + -0.39539183E-02, 0.60010948E-02, 0.21489097E-01, 0.84372545E-02,
     + -0.77701511E-03,-0.83589545E-02,-0.47366079E-02,-0.50928132E-02,
     + -0.94796149E-02,-0.35199705E-02, 0.29384471E-02, 0.19437850E-02,
     +  0.21516955E-02,-0.18193024E-02, 0.38015544E-02,-0.83449082E-02,
     + -0.34418337E-02,-0.33173247E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x35 = x34*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x44 = x43*x4                     
      x45 = x44*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
      x54 = x53*x5                     
c                                      
c                  function            
c                                      
      y_rf_fp     =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)        *x31        
     3  +coeff(  3)            *x41    
     4  +coeff(  4)        *x32        
     5  +coeff(  5)    *x21*x31        
     6  +coeff(  6)    *x21    *x41    
     7  +coeff(  7)        *x31    *x51
     8  +coeff(  8)            *x41*x51
      y_rf_fp     =y_rf_fp             
     9  +coeff(  9)    *x22*x31        
     1  +coeff( 10)    *x22    *x41    
     2  +coeff( 11)        *x31    *x52
     3  +coeff( 12)        *x31*x42    
     4  +coeff( 13)*x11        *x41    
     5  +coeff( 14)    *x21*x31    *x51
     6  +coeff( 15)    *x21    *x41*x51
     7  +coeff( 16)            *x41*x52
     8  +coeff( 17)        *x34*x41    
      y_rf_fp     =y_rf_fp             
     9  +coeff( 18)        *x32*x43    
     1  +coeff( 19)            *x45    
     2  +coeff( 20)    *x22*x33        
     3  +coeff( 21)        *x35*x42    
     4  +coeff( 22)        *x33        
     5  +coeff( 23)        *x32*x41    
     6  +coeff( 24)            *x43    
     7  +coeff( 25)*x11    *x31        
     8  +coeff( 26)    *x23    *x41    
      y_rf_fp     =y_rf_fp             
     9  +coeff( 27)        *x31    *x53
     1  +coeff( 28)            *x41*x53
     2  +coeff( 29)    *x21*x31*x42    
     3  +coeff( 30)    *x23*x31        
     4  +coeff( 31)    *x22*x31    *x51
     5  +coeff( 32)    *x22    *x41*x51
     6  +coeff( 33)    *x21*x31    *x52
     7  +coeff( 34)    *x21    *x41*x52
     8  +coeff( 35)        *x31    *x54
      y_rf_fp     =y_rf_fp             
     9  +coeff( 36)    *x21*x34*x41    
     1  +coeff( 37)    *x21    *x45    
     2  +coeff( 38)    *x23*x33        
c                                      
      return                           
      end                              
      function p_rf_fp     (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 40)             
      data ncoeff/ 39/                 
      data avdat/  0.8617227E-03/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     + -0.96012477E-03, 0.44766773E-04, 0.12982827E-01,-0.76496154E-01,
     +  0.17974891E-01,-0.19913066E-05, 0.34217685E-01,-0.25838995E-01,
     + -0.31154461E-01, 0.21074381E-01, 0.74273994E-03, 0.15157186E-01,
     +  0.62076431E-02, 0.44507147E-02,-0.18540400E-03,-0.87665068E-03,
     +  0.10313769E-01, 0.13256218E-01, 0.52398588E-02, 0.44200798E-02,
     +  0.17368766E-02,-0.82937157E-04,-0.46277978E-03, 0.29485011E-02,
     + -0.51422347E-02, 0.36600977E-02,-0.58647839E-03,-0.29958481E-04,
     + -0.23041894E-02,-0.51807967E-03,-0.51820814E-02,-0.66618677E-02,
     + -0.28789602E-02, 0.27872550E-02, 0.71432238E-03,-0.13972881E-02,
     + -0.11501752E-02,-0.58113359E-03,-0.18308559E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x24 = x23*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x43 = x42*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
c                                      
c                  function            
c                                      
      p_rf_fp     =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)        *x31        
     4  +coeff(  4)            *x41    
     5  +coeff(  5)    *x21*x31        
     6  +coeff(  6)        *x32        
     7  +coeff(  7)    *x21    *x41    
     8  +coeff(  8)        *x31    *x51
      p_rf_fp     =p_rf_fp             
     9  +coeff(  9)            *x41*x51
     1  +coeff( 10)    *x22    *x41    
     2  +coeff( 11)    *x24*x31        
     3  +coeff( 12)    *x22*x31        
     4  +coeff( 13)    *x21    *x41*x51
     5  +coeff( 14)        *x31    *x52
     6  +coeff( 15)    *x23*x31    *x51
     7  +coeff( 16)*x11        *x41    
     8  +coeff( 17)        *x32*x41    
      p_rf_fp     =p_rf_fp             
     9  +coeff( 18)        *x31*x42    
     1  +coeff( 19)            *x43    
     2  +coeff( 20)    *x21*x31    *x51
     3  +coeff( 21)            *x41*x52
     4  +coeff( 22)    *x22*x33        
     5  +coeff( 23)*x11    *x31        
     6  +coeff( 24)        *x33        
     7  +coeff( 25)    *x23    *x41    
     8  +coeff( 26)    *x22    *x41*x51
      p_rf_fp     =p_rf_fp             
     9  +coeff( 27)    *x23*x31*x42    
     1  +coeff( 28)    *x24*x31    *x51
     2  +coeff( 29)    *x23*x31        
     3  +coeff( 30)*x11*x21    *x41    
     4  +coeff( 31)    *x21*x32*x41    
     5  +coeff( 32)    *x21*x31*x42    
     6  +coeff( 33)    *x21    *x43    
     7  +coeff( 34)    *x22*x31    *x51
     8  +coeff( 35)    *x21*x31    *x52
      p_rf_fp     =p_rf_fp             
     9  +coeff( 36)        *x31    *x53
     1  +coeff( 37)            *x41*x53
     2  +coeff( 38)*x11*x21*x33        
     3  +coeff( 39)    *x23*x33        
c                                      
      return                           
      end                              
      function l_rf_fp     (x,m)       
      dimension x(m)                   
      dimension xmin(10),xmax(10),scale(10),xmean(10)
      dimension coeff( 21)             
      data ncoeff/ 20/                 
      data avdat/ -0.2029912E-01/      
      data xmin/                       
     1 -0.99929E-03,-0.12092E+00,-0.49962E-01,-0.33099E-01,-0.37163E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data xmax/                       
     1  0.99947E-03, 0.12032E+00, 0.49945E-01, 0.33196E-01, 0.48438E-01,
     2  0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00, 0.00000E+00/
      data scale /10*0./               
      data coeff/                      
     +  0.16468860E-01,-0.28878596E+00,-0.37217401E-01, 0.82934005E-02,
     + -0.33415060E-01,-0.17289860E-01,-0.39428461E-01,-0.36975827E-01,
     + -0.60759783E-02, 0.14691332E-01,-0.58957371E-02, 0.38977977E-01,
     +  0.30292448E-01,-0.92726015E-02,-0.61210552E-02,-0.42987890E-02,
     +  0.64414050E-02, 0.81325909E-02, 0.13193375E-01, 0.55314926E-02,
     +      0.      /                  
      data ientry/0/                   
c                                      
      if (ientry.ne.0) go to 10        
      ientry=1                         
      do 5 i=1,m                       
      if (xmin(i).eq.xmax(i)) go to 5  
      scale(i)=2./(xmax(i)-xmin(i))    
   5  continue                         
c                                      
  10  continue                         
c      normalize variables between -1 and +1
      x1 =1.+(x(  1)-xmax(  1))*scale(  1)
      x2 =1.+(x(  2)-xmax(  2))*scale(  2)
      x3 =1.+(x(  3)-xmax(  3))*scale(  3)
      x4 =1.+(x(  4)-xmax(  4))*scale(  4)
      x5 =1.+(x(  5)-xmax(  5))*scale(  5)
c          set up monomials   functions
      x11 = x1                         
      x21 = x2                         
      x22 = x21*x2                     
      x23 = x22*x2                     
      x31 = x3                         
      x32 = x31*x3                     
      x33 = x32*x3                     
      x34 = x33*x3                     
      x41 = x4                         
      x42 = x41*x4                     
      x51 = x5                         
      x52 = x51*x5                     
      x53 = x52*x5                     
c                                      
c                  function            
c                                      
      l_rf_fp     =avdat               
     1  +coeff(  1)                    
     2  +coeff(  2)    *x21            
     3  +coeff(  3)                *x51
     4  +coeff(  4)*x11                
     5  +coeff(  5)    *x22            
     6  +coeff(  6)            *x42    
     7  +coeff(  7)    *x21        *x51
     8  +coeff(  8)                *x52
      l_rf_fp     =l_rf_fp             
     9  +coeff(  9)        *x32        
     1  +coeff( 10)    *x23            
     2  +coeff( 11)        *x31*x41    
     3  +coeff( 12)    *x21*x31*x41    
     4  +coeff( 13)    *x21    *x42    
     5  +coeff( 14)    *x22        *x51
     6  +coeff( 15)            *x42*x51
     7  +coeff( 16)    *x21        *x52
     8  +coeff( 17)                *x53
      l_rf_fp     =l_rf_fp             
     9  +coeff( 18)    *x23*x32        
     1  +coeff( 19)    *x21*x34        
     2  +coeff( 20)        *x34    *x51
c                                      
      return                           
      end