function vnacs(r,xa)
! This function provides the NaCs X-state potential energy surface 
! according to the parameters provided by Stephane Valladier
! 
! IMPORTANT: From the given parameters, the Ground (X) State is in 
! the units of Inverse Centimeters and Angstroms. The first excited
! state (A) is in atomic units of Hartree and Bohr. 
! This routine accepts arguments only in Bohr. They are converted here
! into the appropriate units if need be. 
!
! 2008-03-21  D. A. Brue
implicit none

integer :: i  !index

double precision, intent(in) :: r  ! r in bohr, INPUT

double precision :: r_ang  ! r in ANGSTROM

! THESE CONVERSIONS PROVIDED BY NIST : 2008-03-21
double precision, parameter :: ang_to_bohr = 1.88972613289d0
double precision, parameter :: cm_to_hartree=4.556335252760d-6

character(len=1), intent(in) :: xa
! if xa = "X" then get ground state
! if xa = "A" then get excited state
! else, return error


double precision :: vnacs
double precision :: temp1, temp2,temp3

! NOTE: X GROUND STATE PARAMETERS IN INVERSE CENTIMETERS AND ANGSTROMS

! X REGION DEFINING PARAMETERS
double precision, parameter  :: X_RLong = 10.20d0  ! In Angstroms
double precision, parameter :: X_RShort = 2.8453d0 ! In Angstroms

! X SHORT RANGE
double precision, parameter :: X_A = -0.121078258d5   ! inverse centimeters
double precision, parameter :: X_B = 0.278126476d6    ! invcm*angstrom^3

! X LONG RANGE
double precision, parameter :: X_C6=1.555214d7   ! invcm*Angstrom^6
double precision, parameter :: X_C8=4.967239d8   ! invcm*Angstrom^8
double precision, parameter :: X_C10=1.971387d10 ! invcm*Angstrom^10

double precision, parameter :: X_Aex=2.549087d4  ! Invcm*Angstrom*{-gamma}
double precision, parameter :: X_gamma = 5.12271 ! unitless
double precision, parameter :: X_beta = 2.17237 ! 1/Angstrom

! X MIDDLE - WELL RANGE POTENTIAL PARAMETERS
double precision, parameter :: X_bm  = -0.400d0
double precision, parameter :: X_Rm  = 3.85062906d0
double precision :: X_am(0:29)

! NOTE: A EXCITED STATE SHORT RANGE PARAMETERS IN ATOMIC UNITS

! A REGION DEFINING PARAMETERS
double precision, parameter :: A_Rshort=3d0   ! Bohr
double precision, parameter :: A_Rlong =22.8d0  ! Bohr

! A SHORT RANGE PARAMETERS 
double precision, parameter :: A_SRA= 195.78215776042984d0
double precision, parameter :: A_SRB = 1.8169218805040748d0
double precision, parameter :: A_A = 0d0
double precision, parameter :: A_B = 0d0
double precision, parameter :: A_N = 0d0
double precision, parameter :: A_Ri = 0d0

! A MIDDLE - WELL RANGE PARAMETERS
double precision :: A_am(0:33)
double precision, parameter :: A_bm=0.6d0
double precision, parameter :: A_Rm=8.575355152471342d0

! A STATE LONG RANGE PARAMETERS
double precision, parameter :: A_De=0.02822916744062809d0 ! HARTREE
double precision, parameter :: A_C6=18353D0  ! HARTREE/a0^6
double precision, parameter :: A_C8=3.7927D6   ! HARTREE/a0^8
double precision, parameter :: A_C10=0D0 ! HARTREE/a0^10
double precision, parameter :: A_SHIFT1=0.05093193928700017134d0 !HARTREE for Cs p1/2 state
double precision, parameter :: A_SHIFT2=0.0534563280810046448d0  !HARTREE for Cs p3/2 state
!NOV-19 version
!double precision, parameter :: A_LRA= 
!double precision, parameter :: A_LRB=
!double precision, parameter :: A_LRC=
!Integer, parameter :: A_LRS=1 ! A_LRS=(-1)^S

LOGICAL Xthcall,Athcall
data Xthcall/.TRUE./
data Athcall/.TRUE./
data A_am(0) / 0/
data A_am(1) / -1.3834268903061839D-6/
data A_am(2) / 0.2528803528761001D0/
data A_am(3) / -0.353368581145282D0/
data A_am(4) / 0.7547780046205766D0/
data A_am(5) / 2.4141259359882796D0/
data A_am(6) / 0.5127394798976013D0/
data A_am(7) / -32.35167227983407D0/
data A_am(8) / -174.17731123350774D0/
data A_am(9) / -25.518173590057728D0/
data A_am(10) / 3918.130731909468D0/
data A_am(11) / 5019.3874587235905D0/
data A_am(12) / -62347.937173925246D0/
data A_am(13) / -64722.86740096807D0/
data A_am(14) / 826057.2806706572D0/
data A_am(15) / 250413.81434859676D0/
data A_am(16) / -8.698685144460078D6/
data A_am(17) / 2.851617831379752D6/
data A_am(18) / 6.949525580735298D7/
data A_am(19) / -5.0144953511870325D7/
data A_am(20) / -4.182425732031162D8/
data A_am(21) / 3.826026759969647D8/
data A_am(22) / 1.9217585925201888D9/
data A_am(23) / -1.7822620553656301D9/
data A_am(24) / -6.797720160796914D9/
data A_am(25) / 5.204740612111462D9/
data A_am(26) / 1.8155849522567413D10/
data A_am(27) / -8.53836798294337D9/
data A_am(28) / -3.4372227955333305D10/
data A_am(29) / 4.0734127113037696D9/
data A_am(30) / 4.056258700150139D10/
data A_am(31) / 8.895490276401073D9/
data A_am(32) / -2.21172670924856D10/
data A_am(33) / -1.1222105600486395D10/
save

if (xa=="X") then
    r_ang=r/Ang_To_Bohr
endif

SELECT CASE (xa)
    CASE ("X")  ! GROUND STATE
        IF(Xthcall)THEN
        xthcall=.false.
        X_am(0 ) = -4954.2371d0
        X_am(1 ) = 0.8986226306643612d0
        X_am(2 ) = 0.1517322178913964d5
        X_am(3 ) = 0.1091020582856565d5
        X_am(4 ) = -0.2458305372316654d4
        X_am(5 ) = -0.1608232170898541d5
        X_am(6 ) = -0.8705012336065982d4
        X_am(7 ) = 0.2188049902097992d5
        X_am(8 ) = -0.3002538575091348d6
        X_am(9 ) = -0.7869349638160045d6
        X_am(10) = 0.3396165699038170d7
        X_am(11) = 0.7358409786704151d7
        X_am(12) = -0.2637478410890963d8
        X_am(13) = -0.4458510225166618d8
        X_am(14) = 0.1351336683376161d9
        X_am(15) = 0.1762627710924772d9
        X_am(16) = -0.4756878196167457d9
        X_am(17) = -0.4474883319488960d9
        X_am(18) = 0.1216000437881570d10
        X_am(19) = 0.7460756868876818d9
        X_am(20) = -0.2291733580271494d10
        X_am(21) = -0.8708937018502138d9
        X_am(22) = 0.3095441526749659d10
        X_am(23) = 0.8199544778493311d9
        X_am(24) = -0.2806754517994001d10
        X_am(25) = -0.6963731313587832d9
        X_am(26) = 0.1516535916964652d10
        X_am(27) = 0.4445582751072266d9
        X_am(28) = -0.3669908996749862d9
        X_am(29) = -0.1352434762493831d9
        ENDIF

        if ( r_ang < X_RShort ) then
            ! SHORT RANGE CASE  
            vnacs=X_A+X_B/r_ang**3
        else if ( r_ang >= X_Rshort .and. r_ang <= X_RLong) then
            ! MIDDLE RANGE WELL CASE
            temp1=X_am(0)
            temp2=(r_ang-X_rm)/(r_ang+X_bm*X_rm)
            temp3=temp2
            do i=1,29
                temp1=temp1+X_am(i)*temp3
                temp3=temp3*temp2
            enddo
            vnacs=temp1
        else if (r_ang > X_Rlong) then
            IF(10.d0*LOG10(R_ang)<308.d0)THEN
               temp1=-X_C6/r_ang**6-X_C8/r_ang**8-X_C10/r_ang**10
            ELSE
               temp1=0.d0
            ENDIF
            temp2=-X_Aex*r_ang**X_gamma*exp(-X_beta*r_ang)
            vnacs=temp1+temp2
        end if 
        ! now change energy to Hartree
        vnacs=vnacs*CM_to_Hartree
    CASE ("A")   ! FIRST EXCITED STATE

        if ( R < A_Rshort ) then
            vnacs=A_SRA*exp(-A_SRB*r)
        else if ( R >= A_Rshort .and. R <= A_Rlong) then
            temp2=A_am(0)
            temp1=((r-A_Rm)/(r+A_bm*A_Rm))
!            print*,'A_abm=',a_am(1),A_bm,A_Rm,temp2
!            stop
            do i=1,33
                temp2=temp2+A_am(i)*temp1**i
            enddo
            vnacs=temp2
!            print*,'temp2=',temp2
!            stop
!            IF(abs(R-22.6).lt.0.01)THEN
!               print*,'vnacs',vnacs,R
!               stop
!            ENDIF
        else if (R >= A_Rlong) then
            temp1=A_De-A_C6/r**6-A_C8/r**8
!            temp2=A_Aex*R**A_gamma*exp(-A_dzeta*r)
             CALL POT_EX(R,temp2)
            vnacs=temp2+temp1
!            print*,'potL=',temp1,temp2,R
!            stop
        endif
            vnacs=vnacs-A_DE+A_shift1
    
    CASE DEFAULT
        PRINT*,"ERROR IN GETTING NaCs POTENTIAL: unknown character"
        STOP "ERROR IN vnacs.f90"

END SELECT


end function vnacs
SUBROUTINE POT_EX(x,V)
IMPLICIT NONE
real*8 tab(3),EP,x,V
INTEGER Istate,ithcall,iop(2),i
INTEGER,parameter:: nr1=1592
Real*8 E(nr1),R(nr1),temp
real*8 aa(nr1),bb(nr1),cc(nr1)
REAL*8 SECOND(nr1),shiftss,shiftsp,shiftpp
data ithcall /0/
!-----------------------------
   data R(   1) / 0.228000000000000D+02/
   data R(   2) / 0.228200000000000D+02/
   data R(   3) / 0.228400000000000D+02/
   data R(   4) / 0.228600000000000D+02/
   data R(   5) / 0.228800000000000D+02/
   data R(   6) / 0.229000000000000D+02/
   data R(   7) / 0.229200000000000D+02/
   data R(   8) / 0.229400000000000D+02/
   data R(   9) / 0.229600000000000D+02/
   data R(  10) / 0.229800000000000D+02/
   data R(  11) / 0.230000000000000D+02/
   data R(  12) / 0.230200000000000D+02/
   data R(  13) / 0.230400000000000D+02/
   data R(  14) / 0.230600000000000D+02/
   data R(  15) / 0.230800000000000D+02/
   data R(  16) / 0.231000000000000D+02/
   data R(  17) / 0.231200000000000D+02/
   data R(  18) / 0.231400000000000D+02/
   data R(  19) / 0.231600000000000D+02/
   data R(  20) / 0.231800000000000D+02/
   data R(  21) / 0.232000000000000D+02/
   data R(  22) / 0.232200000000000D+02/
   data R(  23) / 0.232400000000000D+02/
   data R(  24) / 0.232600000000000D+02/
   data R(  25) / 0.232800000000000D+02/
   data R(  26) / 0.233000000000000D+02/
   data R(  27) / 0.233200000000000D+02/
   data R(  28) / 0.233400000000000D+02/
   data R(  29) / 0.233600000000000D+02/
   data R(  30) / 0.233800000000000D+02/
   data R(  31) / 0.234000000000000D+02/
   data R(  32) / 0.234200000000000D+02/
   data R(  33) / 0.234400000000000D+02/
   data R(  34) / 0.234600000000000D+02/
   data R(  35) / 0.234800000000000D+02/
   data R(  36) / 0.235000000000000D+02/
   data R(  37) / 0.235200000000000D+02/
   data R(  38) / 0.235400000000000D+02/
   data R(  39) / 0.235600000000000D+02/
   data R(  40) / 0.235800000000000D+02/
   data R(  41) / 0.236000000000000D+02/
   data R(  42) / 0.236200000000000D+02/
   data R(  43) / 0.236400000000000D+02/
   data R(  44) / 0.236600000000000D+02/
   data R(  45) / 0.236800000000000D+02/
   data R(  46) / 0.237000000000000D+02/
   data R(  47) / 0.237200000000000D+02/
   data R(  48) / 0.237400000000000D+02/
   data R(  49) / 0.237600000000000D+02/
   data R(  50) / 0.237800000000000D+02/
   data R(  51) / 0.238000000000000D+02/
   data R(  52) / 0.238200000000000D+02/
   data R(  53) / 0.238400000000000D+02/
   data R(  54) / 0.238600000000000D+02/
   data R(  55) / 0.238800000000000D+02/
   data R(  56) / 0.239000000000000D+02/
   data R(  57) / 0.239200000000000D+02/
   data R(  58) / 0.239400000000000D+02/
   data R(  59) / 0.239600000000000D+02/
   data R(  60) / 0.239800000000000D+02/
   data R(  61) / 0.240000000000000D+02/
   data R(  62) / 0.240200000000000D+02/
   data R(  63) / 0.240400000000000D+02/
   data R(  64) / 0.240600000000000D+02/
   data R(  65) / 0.240800000000000D+02/
   data R(  66) / 0.241000000000000D+02/
   data R(  67) / 0.241200000000000D+02/
   data R(  68) / 0.241400000000000D+02/
   data R(  69) / 0.241600000000000D+02/
   data R(  70) / 0.241800000000000D+02/
   data R(  71) / 0.242000000000000D+02/
   data R(  72) / 0.242200000000000D+02/
   data R(  73) / 0.242400000000000D+02/
   data R(  74) / 0.242600000000000D+02/
   data R(  75) / 0.242800000000000D+02/
   data R(  76) / 0.243000000000000D+02/
   data R(  77) / 0.243200000000000D+02/
   data R(  78) / 0.243400000000000D+02/
   data R(  79) / 0.243600000000000D+02/
   data R(  80) / 0.243800000000000D+02/
   data R(  81) / 0.244000000000000D+02/
   data R(  82) / 0.244200000000000D+02/
   data R(  83) / 0.244400000000000D+02/
   data R(  84) / 0.244600000000000D+02/
   data R(  85) / 0.244800000000000D+02/
   data R(  86) / 0.245000000000000D+02/
   data R(  87) / 0.245200000000000D+02/
   data R(  88) / 0.245400000000000D+02/
   data R(  89) / 0.245600000000000D+02/
   data R(  90) / 0.245800000000000D+02/
   data R(  91) / 0.246000000000000D+02/
   data R(  92) / 0.246200000000000D+02/
   data R(  93) / 0.246400000000000D+02/
   data R(  94) / 0.246600000000000D+02/
   data R(  95) / 0.246800000000000D+02/
   data R(  96) / 0.247000000000000D+02/
   data R(  97) / 0.247200000000000D+02/
   data R(  98) / 0.247400000000000D+02/
   data R(  99) / 0.247600000000000D+02/
   data R( 100) / 0.247800000000000D+02/
   data R( 101) / 0.248000000000000D+02/
   data R( 102) / 0.248200000000000D+02/
   data R( 103) / 0.248400000000000D+02/
   data R( 104) / 0.248600000000000D+02/
   data R( 105) / 0.248800000000000D+02/
   data R( 106) / 0.249000000000000D+02/
   data R( 107) / 0.249200000000000D+02/
   data R( 108) / 0.249400000000000D+02/
   data R( 109) / 0.249600000000000D+02/
   data R( 110) / 0.249800000000000D+02/
   data R( 111) / 0.250000000000000D+02/
   data R( 112) / 0.250200000000000D+02/
   data R( 113) / 0.250400000000000D+02/
   data R( 114) / 0.250600000000000D+02/
   data R( 115) / 0.250800000000000D+02/
   data R( 116) / 0.251000000000000D+02/
   data R( 117) / 0.251200000000000D+02/
   data R( 118) / 0.251400000000000D+02/
   data R( 119) / 0.251600000000000D+02/
   data R( 120) / 0.251800000000000D+02/
   data R( 121) / 0.252000000000000D+02/
   data R( 122) / 0.252200000000000D+02/
   data R( 123) / 0.252400000000000D+02/
   data R( 124) / 0.252600000000000D+02/
   data R( 125) / 0.252800000000000D+02/
   data R( 126) / 0.253000000000000D+02/
   data R( 127) / 0.253200000000000D+02/
   data R( 128) / 0.253400000000000D+02/
   data R( 129) / 0.253600000000000D+02/
   data R( 130) / 0.253800000000000D+02/
   data R( 131) / 0.254000000000000D+02/
   data R( 132) / 0.254200000000000D+02/
   data R( 133) / 0.254400000000000D+02/
   data R( 134) / 0.254600000000000D+02/
   data R( 135) / 0.254800000000000D+02/
   data R( 136) / 0.255000000000000D+02/
   data R( 137) / 0.255200000000000D+02/
   data R( 138) / 0.255400000000000D+02/
   data R( 139) / 0.255600000000000D+02/
   data R( 140) / 0.255800000000000D+02/
   data R( 141) / 0.256000000000000D+02/
   data R( 142) / 0.256200000000000D+02/
   data R( 143) / 0.256400000000000D+02/
   data R( 144) / 0.256600000000000D+02/
   data R( 145) / 0.256800000000000D+02/
   data R( 146) / 0.257000000000000D+02/
   data R( 147) / 0.257200000000000D+02/
   data R( 148) / 0.257400000000000D+02/
   data R( 149) / 0.257600000000000D+02/
   data R( 150) / 0.257800000000000D+02/
   data R( 151) / 0.258000000000000D+02/
   data R( 152) / 0.258200000000000D+02/
   data R( 153) / 0.258400000000000D+02/
   data R( 154) / 0.258600000000000D+02/
   data R( 155) / 0.258800000000000D+02/
   data R( 156) / 0.259000000000000D+02/
   data R( 157) / 0.259200000000000D+02/
   data R( 158) / 0.259400000000000D+02/
   data R( 159) / 0.259600000000000D+02/
   data R( 160) / 0.259800000000000D+02/
   data R( 161) / 0.260000000000000D+02/
   data R( 162) / 0.260200000000000D+02/
   data R( 163) / 0.260400000000000D+02/
   data R( 164) / 0.260600000000000D+02/
   data R( 165) / 0.260800000000000D+02/
   data R( 166) / 0.261000000000000D+02/
   data R( 167) / 0.261200000000000D+02/
   data R( 168) / 0.261400000000000D+02/
   data R( 169) / 0.261600000000000D+02/
   data R( 170) / 0.261800000000000D+02/
   data R( 171) / 0.262000000000000D+02/
   data R( 172) / 0.262200000000000D+02/
   data R( 173) / 0.262400000000000D+02/
   data R( 174) / 0.262600000000000D+02/
   data R( 175) / 0.262800000000000D+02/
   data R( 176) / 0.263000000000000D+02/
   data R( 177) / 0.263200000000000D+02/
   data R( 178) / 0.263400000000000D+02/
   data R( 179) / 0.263600000000000D+02/
   data R( 180) / 0.263800000000000D+02/
   data R( 181) / 0.264000000000000D+02/
   data R( 182) / 0.264200000000000D+02/
   data R( 183) / 0.264400000000000D+02/
   data R( 184) / 0.264600000000000D+02/
   data R( 185) / 0.264800000000000D+02/
   data R( 186) / 0.265000000000000D+02/
   data R( 187) / 0.265200000000000D+02/
   data R( 188) / 0.265400000000000D+02/
   data R( 189) / 0.265600000000000D+02/
   data R( 190) / 0.265800000000000D+02/
   data R( 191) / 0.266000000000000D+02/
   data R( 192) / 0.266200000000000D+02/
   data R( 193) / 0.266400000000000D+02/
   data R( 194) / 0.266600000000000D+02/
   data R( 195) / 0.266800000000000D+02/
   data R( 196) / 0.267000000000000D+02/
   data R( 197) / 0.267200000000000D+02/
   data R( 198) / 0.267400000000000D+02/
   data R( 199) / 0.267600000000000D+02/
   data R( 200) / 0.267800000000000D+02/
   data R( 201) / 0.268000000000000D+02/
   data R( 202) / 0.268200000000000D+02/
   data R( 203) / 0.268400000000000D+02/
   data R( 204) / 0.268600000000000D+02/
   data R( 205) / 0.268800000000000D+02/
   data R( 206) / 0.269000000000000D+02/
   data R( 207) / 0.269200000000000D+02/
   data R( 208) / 0.269400000000000D+02/
   data R( 209) / 0.269600000000000D+02/
   data R( 210) / 0.269800000000000D+02/
   data R( 211) / 0.270000000000000D+02/
   data R( 212) / 0.270200000000000D+02/
   data R( 213) / 0.270400000000000D+02/
   data R( 214) / 0.270600000000000D+02/
   data R( 215) / 0.270800000000000D+02/
   data R( 216) / 0.271000000000000D+02/
   data R( 217) / 0.271200000000000D+02/
   data R( 218) / 0.271400000000000D+02/
   data R( 219) / 0.271600000000000D+02/
   data R( 220) / 0.271800000000000D+02/
   data R( 221) / 0.272000000000000D+02/
   data R( 222) / 0.272200000000000D+02/
   data R( 223) / 0.272400000000000D+02/
   data R( 224) / 0.272600000000000D+02/
   data R( 225) / 0.272800000000000D+02/
   data R( 226) / 0.273000000000000D+02/
   data R( 227) / 0.273200000000000D+02/
   data R( 228) / 0.273400000000000D+02/
   data R( 229) / 0.273600000000000D+02/
   data R( 230) / 0.273800000000000D+02/
   data R( 231) / 0.274000000000000D+02/
   data R( 232) / 0.274200000000000D+02/
   data R( 233) / 0.274400000000000D+02/
   data R( 234) / 0.274600000000000D+02/
   data R( 235) / 0.274800000000000D+02/
   data R( 236) / 0.275000000000000D+02/
   data R( 237) / 0.275200000000000D+02/
   data R( 238) / 0.275400000000000D+02/
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   data R(1102) / 0.448200000000000D+02/
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   data R(1104) / 0.448600000000000D+02/
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   data R(1106) / 0.449000000000000D+02/
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   data R(1113) / 0.450400000000000D+02/
   data R(1114) / 0.450600000000000D+02/
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   data R(1117) / 0.451200000000000D+02/
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   data R(1122) / 0.452200000000000D+02/
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   data R(1127) / 0.453200000000000D+02/
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   data R(1479) / 0.523600000000000D+02/
   data R(1480) / 0.523800000000000D+02/
   data R(1481) / 0.524000000000000D+02/
   data R(1482) / 0.524200000000000D+02/
   data R(1483) / 0.524400000000000D+02/
   data R(1484) / 0.524600000000000D+02/
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   data R(1486) / 0.525000000000000D+02/
   data R(1487) / 0.525200000000000D+02/
   data R(1488) / 0.525400000000000D+02/
   data R(1489) / 0.525600000000000D+02/
   data R(1490) / 0.525800000000000D+02/
   data R(1491) / 0.526000000000000D+02/
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   data E(1331) /-0.601232759468247D-13/
   data E(1332) /-0.591909077493320D-13/
   data E(1333) /-0.582729597759656D-13/
   data E(1334) /-0.573692096347599D-13/
   data E(1335) /-0.564794383530963D-13/
   data E(1336) /-0.556034303253028D-13/
   data E(1337) /-0.547409732610497D-13/
   data E(1338) /-0.538918581345368D-13/
   data E(1339) /-0.530558791344579D-13/
   data E(1340) /-0.522328336147221D-13/
   data E(1341) /-0.514225220459377D-13/
   data E(1342) /-0.506247479676310D-13/
   data E(1343) /-0.498393179411969D-13/
   data E(1344) /-0.490660415035661D-13/
   data E(1345) /-0.483047311215847D-13/
   data E(1346) /-0.475552021470876D-13/
   data E(1347) /-0.468172727726587D-13/
   data E(1348) /-0.460907639880669D-13/
   data E(1349) /-0.453754995373693D-13/
   data E(1350) /-0.446713058766698D-13/
   data E(1351) /-0.439780121325211D-13/
   data E(1352) /-0.432954500609649D-13/
   data E(1353) /-0.426234540071983D-13/
   data E(1354) /-0.419618608658540D-13/
   data E(1355) /-0.413105100418908D-13/
   data E(1356) /-0.406692434120810D-13/
   data E(1357) /-0.400379052870863D-13/
   data E(1358) /-0.394163423741119D-13/
   data E(1359) /-0.388044037401361D-13/
   data E(1360) /-0.382019407756985D-13/
   data E(1361) /-0.376088071592426D-13/
   data E(1362) /-0.370248588220047D-13/
   data E(1363) /-0.364499539134378D-13/
   data E(1364) /-0.358839527671689D-13/
   data E(1365) /-0.353267178674708D-13/
   data E(1366) /-0.347781138162513D-13/
   data E(1367) /-0.342380073005464D-13/
   data E(1368) /-0.337062670605091D-13/
   data E(1369) /-0.331827638578907D-13/
   data E(1370) /-0.326673704450016D-13/
   data E(1371) /-0.321599615341499D-13/
   data E(1372) /-0.316604137675451D-13/
   data E(1373) /-0.311686056876629D-13/
   data E(1374) /-0.306844177080655D-13/
   data E(1375) /-0.302077320846664D-13/
   data E(1376) /-0.297384328874353D-13/
   data E(1377) /-0.292764059725359D-13/
   data E(1378) /-0.288215389548927D-13/
   data E(1379) /-0.283737211811745D-13/
   data E(1380) /-0.279328437031921D-13/
   data E(1381) /-0.274987992517058D-13/
   data E(1382) /-0.270714822106303D-13/
   data E(1383) /-0.266507885916377D-13/
   data E(1384) /-0.262366160091472D-13/
   data E(1385) /-0.258288636556992D-13/
   data E(1386) /-0.254274322777063D-13/
   data E(1387) /-0.250322241515737D-13/
   data E(1388) /-0.246431430601887D-13/
   data E(1389) /-0.242600942697688D-13/
   data E(1390) /-0.238829845070627D-13/
   data E(1391) /-0.235117219369026D-13/
   data E(1392) /-0.231462161401008D-13/
   data E(1393) /-0.227863780916833D-13/
   data E(1394) /-0.224321201394573D-13/
   data E(1395) /-0.220833559829078D-13/
   data E(1396) /-0.217400006524168D-13/
   data E(1397) /-0.214019704888020D-13/
   data E(1398) /-0.210691831231671D-13/
   data E(1399) /-0.207415574570633D-13/
   data E(1400) /-0.204190136429531D-13/
   data E(1401) /-0.201014730649735D-13/
   data E(1402) /-0.197888583199959D-13/
   data E(1403) /-0.194810931989743D-13/
   data E(1404) /-0.191781026685805D-13/
   data E(1405) /-0.188798128531196D-13/
   data E(1406) /-0.185861510167252D-13/
   data E(1407) /-0.182970455458250D-13/
   data E(1408) /-0.180124259318766D-13/
   data E(1409) /-0.177322227543675D-13/
   data E(1410) /-0.174563676640765D-13/
   data E(1411) /-0.171847933665911D-13/
   data E(1412) /-0.169174336060774D-13/
   data E(1413) /-0.166542231493001D-13/
   data E(1414) /-0.163950977698868D-13/
   data E(1415) /-0.161399942328329D-13/
   data E(1416) /-0.158888502792463D-13/
   data E(1417) /-0.156416046113241D-13/
   data E(1418) /-0.153981968775607D-13/
   data E(1419) /-0.151585676581825D-13/
   data E(1420) /-0.149226584508063D-13/
   data E(1421) /-0.146904116563181D-13/
   data E(1422) /-0.144617705649678D-13/
   data E(1423) /-0.142366793426774D-13/
   data E(1424) /-0.140150830175600D-13/
   data E(1425) /-0.137969274666452D-13/
   data E(1426) /-0.135821594028078D-13/
   data E(1427) /-0.133707263618981D-13/
   data E(1428) /-0.131625766900693D-13/
   data E(1429) /-0.129576595312987D-13/
   data E(1430) /-0.127559248151018D-13/
   data E(1431) /-0.125573232444341D-13/
   data E(1432) /-0.123618062837789D-13/
   data E(1433) /-0.121693261474175D-13/
   data E(1434) /-0.119798357878806D-13/
   data E(1435) /-0.117932888845763D-13/
   data E(1436) /-0.116096398325923D-13/
   data E(1437) /-0.114288437316710D-13/
   data E(1438) /-0.112508563753532D-13/
   data E(1439) /-0.110756342402893D-13/
   data E(1440) /-0.109031344757134D-13/
   data E(1441) /-0.107333148930804D-13/
   data E(1442) /-0.105661339558619D-13/
   data E(1443) /-0.104015507694978D-13/
   data E(1444) /-0.102395250715040D-13/
   data E(1445) /-0.100800172217309D-13/
   data E(1446) /-0.992298819277177D-14/
   data E(1447) /-0.976839956051870D-14/
   data E(1448) /-0.961621349486351D-14/
   data E(1449) /-0.946639275054168D-14/
   data E(1450) /-0.931890065811687D-14/
   data E(1451) /-0.917370111510392D-14/
   data E(1452) /-0.903075857722816D-14/
   data E(1453) /-0.889003804981987D-14/
   data E(1454) /-0.875150507933995D-14/
   data E(1455) /-0.861512574503621D-14/
   data E(1456) /-0.848086665072840D-14/
   data E(1457) /-0.834869491671871D-14/
   data E(1458) /-0.821857817182729D-14/
   data E(1459) /-0.809048454554989D-14/
   data E(1460) /-0.796438266033629D-14/
   data E(1461) /-0.784024162398702D-14/
   data E(1462) /-0.771803102216758D-14/
   data E(1463) /-0.759772091103725D-14/
   data E(1464) /-0.747928180999187D-14/
   data E(1465) /-0.736268469451732D-14/
   data E(1466) /-0.724790098915357D-14/
   data E(1467) /-0.713490256056715D-14/
   data E(1468) /-0.702366171072951D-14/
   data E(1469) /-0.691415117020058D-14/
   data E(1470) /-0.680634409151586D-14/
   data E(1471) /-0.670021404267493D-14/
   data E(1472) /-0.659573500073045D-14/
   data E(1473) /-0.649288134547535D-14/
   data E(1474) /-0.639162785322771D-14/
   data E(1475) /-0.629194969071066D-14/
   data E(1476) /-0.619382240902699D-14/
   data E(1477) /-0.609722193772612D-14/
   data E(1478) /-0.600212457896259D-14/
   data E(1479) /-0.590850700174437D-14/
   data E(1480) /-0.581634623626941D-14/
   data E(1481) /-0.572561966835001D-14/
   data E(1482) /-0.563630503392242D-14/
   data E(1483) /-0.554838041364114D-14/
   data E(1484) /-0.546182422755650D-14/
   data E(1485) /-0.537661522987404D-14/
   data E(1486) /-0.529273250379486D-14/
   data E(1487) /-0.521015545643492D-14/
   data E(1488) /-0.512886381382298D-14/
   data E(1489) /-0.504883761597557D-14/
   data E(1490) /-0.497005721204725D-14/
   data E(1491) /-0.489250325555628D-14/
   data E(1492) /-0.481615669968340D-14/
   data E(1493) /-0.474099879264310D-14/
   data E(1494) /-0.466701107312596D-14/
   data E(1495) /-0.459417536581164D-14/
   data E(1496) /-0.452247377695067D-14/
   data E(1497) /-0.445188869001431D-14/
   data E(1498) /-0.438240276141146D-14/
   data E(1499) /-0.431399891627154D-14/
   data E(1500) /-0.424666034429247D-14/
   data E(1501) /-0.418037049565236D-14/
   data E(1502) /-0.411511307698441D-14/
   data E(1503) /-0.405087204741367D-14/
   data E(1504) /-0.398763161465509D-14/
   data E(1505) /-0.392537623117137D-14/
   data E(1506) /-0.386409059039034D-14/
   data E(1507) /-0.380375962298048D-14/
   data E(1508) /-0.374436849318368D-14/
   data E(1509) /-0.368590259520491D-14/
   data E(1510) /-0.362834754965724D-14/
   data E(1511) /-0.357168920006175D-14/
   data E(1512) /-0.351591360940133D-14/
   data E(1513) /-0.346100705672758D-14/
   data E(1514) /-0.340695603382039D-14/
   data E(1515) /-0.335374724189839D-14/
   data E(1516) /-0.330136758838057D-14/
   data E(1517) /-0.324980418369780D-14/
   data E(1518) /-0.319904433815325D-14/
   data E(1519) /-0.314907555883149D-14/
   data E(1520) /-0.309988554655515D-14/
   data E(1521) /-0.305146219288853D-14/
   data E(1522) /-0.300379357718734D-14/
   data E(1523) /-0.295686796369405D-14/
   data E(1524) /-0.291067379867803D-14/
   data E(1525) /-0.286519970761974D-14/
   data E(1526) /-0.282043449243837D-14/
   data E(1527) /-0.277636712876220D-14/
   data E(1528) /-0.273298676324131D-14/
   data E(1529) /-0.269028271090140D-14/
   data E(1530) /-0.264824445253863D-14/
   data E(1531) /-0.260686163215470D-14/
   data E(1532) /-0.256612405443133D-14/
   data E(1533) /-0.252602168224385D-14/
   data E(1534) /-0.248654463421313D-14/
   data E(1535) /-0.244768318229529D-14/
   data E(1536) /-0.240942774940851D-14/
   data E(1537) /-0.237176890709661D-14/
   data E(1538) /-0.233469737322860D-14/
   data E(1539) /-0.229820400973382D-14/
   data E(1540) /-0.226227982037188D-14/
   data E(1541) /-0.222691594853714D-14/
   data E(1542) /-0.219210367509716D-14/
   data E(1543) /-0.215783441626433D-14/
   data E(1544) /-0.212409972150050D-14/
   data E(1545) /-0.209089127145381D-14/
   data E(1546) /-0.205820087592764D-14/
   data E(1547) /-0.202602047188063D-14/
   data E(1548) /-0.199434212145775D-14/
   data E(1549) /-0.196315801005174D-14/
   data E(1550) /-0.193246044439443D-14/
   data E(1551) /-0.190224185067762D-14/
   data E(1552) /-0.187249477270295D-14/
   data E(1553) /-0.184321187006033D-14/
   data E(1554) /-0.181438591633451D-14/
   data E(1555) /-0.178600979733931D-14/
   data E(1556) /-0.175807650937926D-14/
   data E(1557) /-0.173057915753793D-14/
   data E(1558) /-0.170351095399282D-14/
   data E(1559) /-0.167686521635618D-14/
   data E(1560) /-0.165063536604157D-14/
   data E(1561) /-0.162481492665563D-14/
   data E(1562) /-0.159939752241460D-14/
   data E(1563) /-0.157437687658548D-14/
   data E(1564) /-0.154974680995106D-14/
   data E(1565) /-0.152550123929894D-14/
   data E(1566) /-0.150163417593362D-14/
   data E(1567) /-0.147813972421181D-14/
   data E(1568) /-0.145501208010028D-14/
   data E(1569) /-0.143224552975590D-14/
   data E(1570) /-0.140983444812788D-14/
   data E(1571) /-0.138777329758138D-14/
   data E(1572) /-0.136605662654251D-14/
   data E(1573) /-0.134467906816425D-14/
   data E(1574) /-0.132363533901299D-14/
   data E(1575) /-0.130292023777540D-14/
   data E(1576) /-0.128252864398526D-14/
   data E(1577) /-0.126245551676999D-14/
   data E(1578) /-0.124269589361657D-14/
   data E(1579) /-0.122324488915657D-14/
   data E(1580) /-0.120409769396983D-14/
   data E(1581) /-0.118524957340687D-14/
   data E(1582) /-0.116669586642933D-14/
   data E(1583) /-0.114843198446833D-14/
   data E(1584) /-0.113045341030069D-14/
   data E(1585) /-0.111275569694229D-14/
   data E(1586) /-0.109533446655872D-14/
   data E(1587) /-0.107818540939268D-14/
   data E(1588) /-0.106130428270800D-14/
   data E(1589) /-0.104468690975006D-14/
   data E(1590) /-0.102832917872218D-14/
   data E(1591) /-0.101222704177791D-14/
   data E(1592) /-0.996376514028933D-15/
SAVE

IF(Ithcall.eq.0)THEN
ithcall=1
CALL spl1d1 (nr1, R(1), E(1), SECOND(1), iop, 1, aa (1), bb (1), cc (1) )
print*,'Initialization DONE'
ENDIF

IF(x.ge.R(1).and.x.le.R(nr1))THEN
CALL spl1d2 (nr1, R(1), E(1), SECOND(1), 1, x, tab)
V=tab(1)
!print*,'tab(1)=',tab(1),tab(2),tab(3)
!print*,'second=',second
!stop
ELSEIF(x.lt.R(1))THEN
V=E(1)
ELSE
V=0d0
ENDIF

return

END
SUBROUTINE ErrWrt (ErrMsg)
!!!USE FileUnits_Module
!
!-------------------------------- ErrWrt -------------------------------
!
! >>> ErrWrt   -- writes a message to the standard error output file
!
! *** Calling Sequence:   CALL ErrWrt ( ErrMsg )
!
! === Latest Revision:    25 May 1988  (typed in)
!
! --- on entry the calling routine supplies --
!
!     ErrMsg   -- character string to be written to standard error
!
! --- on exit the routine returns --
!
!     nothing
!
!----------------------------- local declarations ----------------------
!
!
CHARACTER (len=*) ::    ErrMsg
!
! * * * * *                !  INTEGER globals
CHARACTER (len=8  ) :: IGlobal
! * * * * *              !    output line
CHARACTER (len=80    ) :: Line
! * * * * *               !   output FORMAT
CHARACTER (len=8  ) :: MyForm
!
! * * * * *            !   standard error unit number
INTEGER ::        StdErr
! * * * * *            !   right index function
INTEGER ::        IndexR
! * * * * *           !    # characters to output
INTEGER ::        NCOut
!
!---------------------------- execution begins here --------------------
!
IF(IGlobal ('get', 'StdErr', StdErr) .ne.'OK') RETURN
!
Line   = ErrMsg
NCOut     = max (1, IndexR (Line) )
!
MyForm    = '(a!!)'
WRITE (MyForm (3:4) , '(i2)') NCOut
!
WRITE (StdErr, MyForm) Line (1:NCOut)
!
RETURN
END SUBROUTINE ErrWrt
SUBROUTINE FndInt (n, array, value, start, FindLoc)
USE Numeric_Kinds_Module
!!!USE FileUnits_Module
!
! >>> FndInt -- finds the interval where value lies in the array
!
! --- on entry the calling routine supplies --
!
!     n     -- the number of elements in the array
!     array -- a monotonically nondecreasing array of floating point
!                numbers (i.e., increasing array )
!     value -- test value to find in the array
!     start -- integer initial guess where value is in the array
!
! --- on exit the routine returns --
!
!     FindLoc  -- integer value locating where value is in the array, so
!                that array(FindLoc) .le. value .lt. array(FindLoc+1), and
!                if value .lt. array(1), then FindLoc = 0, and
!                if value .ge. array(n), then FindLoc = n
!
! --- Method:  routine first checks to see if the test value is outside
!                the array bounds (FindLoc=0 or n), then checks
!                the current interval and adjacent intervals,
!                where FindLoc=start, start-1, or start+1.  If correct
!                interval is not located by this point, routine
!                branches into a binary search.  Because of the
!                interval end conditions, it takes
!                   1 test to locate FindLoc=0
!                   2 tests to locate FindLoc=n
!                   4 tests to locate FindLoc=start, or start-1, and
!                   5 tests to locate FindLoc=start+1
INTEGER :: high, low, FindLoc, start, Look, N
REAL*8 :: array (n), value
!
high = n
low = 1
!
!     CHECK SPECIAL CASES
!
!     -- check out of bounds conditions
!
!      ntests = 1
IF(value.lt.array (1) ) THEN
   FindLoc = 0
   RETURN
ELSEIF (value.ge.array (n) ) THEN
   FindLoc = n
!         ntests = 2
   RETURN
ENDIF
!
!    -- check intervals next to the start search
!
look = min0 (n, max0 (1, start) )
!      ntests = 4
IF(value.lt.array (look) ) THEN
   high = look
   IF(value.lt.array (high - 1) ) THEN
      high = high - 1
   ELSE
      FindLoc = high - 1
      RETURN
   ENDIF
ELSE
   low = look
   IF(value.lt.array (low + 1) ) THEN
      FindLoc = low
      RETURN
   ELSE
      low = low + 1
!            ntests = 5
      IF(value.lt.array (low + 1) ) THEN
         FindLoc = low
         RETURN
      ELSE
         low = low + 1
      ENDIF
   ENDIF
ENDIF
!
!     NOT A SIMPLE ANSWER, BEGIN BINARY SEARCH
!
look = (high + low) / 2
look = min0 (high - 1, look)
look = max0 (low + 1, look)
    1 CONTINUE
IF(high - low.eq.1) THEN
   FindLoc = low
   RETURN
ELSE
!         ntests = ntests + 1
   IF(value.lt.array (look) ) THEN
      high = look
   ELSE
      low = look
   ENDIF
!
   look = (high + low) / 2
   look = min0 (high - 1, look)
   look = max0 (low + 1, look)
ENDIF
goto 1
END SUBROUTINE FndInt
FUNCTION IGlobal (Command, Name, Value)
!
!-----------------------------------------------------------------------
!
! >>> IGlobal   -- integer global variable saver routine
!
! *** Calling Sequence:         Result  = IGlobal(Command,Name,Value)
!
! --- on entry the calling routine supplies --
!
!     Command   -- character string indicating whether the indicated glo
!                       variable is to be saved, retrieved, or deleted
!                       Possible Commands are:
!                               Command = 'save'        to save a global
!                               Command = 'get'         to retrieve one
!                               Command = 'delete'      to remove one
!                               Command = 'list'        to write EVERYTH
!               NOTE:  only the first character of Command is significan
!
!     Name      -- character string (8 or fewer characters) indicating t
!                       unique name of the global to be saved/retrieved/
!
!     Value     -- integer which is an input variable if Command='save'
!                       If Command .ne. 'save', Value is not read on inp
!
! --- on exit the routine returns --
!
!     Value     -- is an output integer variable only if Command='get',
!                       which case the remembered value of the Name-d
!                       global variable is returned.
!
!     IGlobal   -- is a character string indicating the success/failure
!                       the operation.  Possible returns are:
!                               IGlobal = 'OK'    if all was OK
!                               IGlobal = 'CANT'  if no internal space l
!                                               a 'save' operation, or i
!                                               Named variable is not he
!                                               a 'delete' or 'get'.
!                               IGlobal = 'WHAT'  if Command unrecognize
!
!-----------------------------------------------------------------------
!
!
CHARACTER (len=4) :: IGlobal
CHARACTER (len=*) :: Command
CHARACTER (len=*) :: Name
INTEGER :: Value
!
INTEGER :: MAXSave
PARAMETER (MAXSave = 100)
!
INTEGER :: NSaved
! * * * * *                             !       loop index
INTEGER :: i
! * * * * *                             !       new value of NSaved
INTEGER :: new
! * * * * *                             !       value of output unit if
INTEGER :: iout
!
INTEGER :: Save (MAXSave)
CHARACTER (len=8) :: VNames (MAXSave)
!
save
!
DATA NSaved / 5 /
!
DATA VNames (1) / 'StdIn' /
DATA Save (1) / 9 /
!
DATA VNames (2) / 'StdOut' /
DATA Save (2) / 9 /
!
DATA VNames (3) / 'StdErr' /
DATA Save (3) / 9 /
!
DATA VNames (4) / 'StdDbg' /
DATA Save (4) / 9 /
!
DATA VNames (5) / 'StdWrt' /
DATA Save (5) / 9 /
!
!
!---------------------------- execution begins here --------------------
!
!
!                        --- blank Names NOT allowed ---
!
IF(Name.eq.' ') THEN
   IGlobal = 'CANT'
   RETURN
ENDIF
!
!                    --- special case if Command = 'list' ---
!
IF(Command (1:1) .eq.'l') THEN
   DO 100 i = 1, NSaved
      IF(Name.eq.VNames (i) ) THEN
         iout = Save (i)
         goto 101
      ENDIF
  100    END DO
   iout = 0
   IGlobal = 'CANT'
  101    CONTINUE
   IF(iout.eq.0) RETURN
!
WRITE (iout,  * ) '   === INTEGER Globals ==='
   DO 200 i = 1, NSaved
      IF(VNames (i) .ne.' ') THEN
         WRITE (iout, '(5x,a8,'' = '',i10)') VNames (i) , Save (i)
      ENDIF
  200    END DO
   IGlobal = 'OK'
   RETURN
ENDIF
!
!                     --- has Name already been defined? ---
!
DO 1 i = 1, NSaved
   IF(Name.eq.VNames (i) ) goto 2
    1 END DO
i = 0
    2 CONTINUE
!
!---------------------------- saving a value ---------------------------
!
IF(Command (1:1) .eq.'s') THEN
!
   IF(i.eq.0) THEN
      new = NSaved+1
      IF(new.gt.MAXSave) THEN
!
!               --- arrays full, look for a blank entry ---
!
         DO 10 i = 1, NSaved
            IF(VNames (i) .eq.' ') goto 11
   10          END DO
         i = 0
   11          CONTINUE
         IF(i.eq.0) THEN
            IGlobal = 'CANT'
            RETURN
         ELSE
            new = NSaved
         ENDIF
      ENDIF
!
!                --- save value for the newly defined global ---
!
      NSaved = new
      VNames (NSaved) = Name
      Save (NSaved) = Value
      IGlobal = 'OK'
!
!           --- save a new value for a previously defined global ---
!
   ELSE
      Save (i) = Value
      IGlobal = 'OK'
   ENDIF
!
!----------------------------- retrieving a value ----------------------
!
ELSEIF (Command (1:1) .eq.'g') THEN
!
   IF(i.eq.0) THEN
      IGlobal = 'CANT'
   ELSE
      IGlobal = 'OK'
      Value = Save (i)
   ENDIF
!
!----------------------------- deleting a global -----------------------
!
ELSEIF (Command (1:1) .eq.'d') THEN
!
   IF(i.eq.0) THEN
      IGlobal = 'CANT'
   ELSE
      IGlobal = 'OK'
      VNames (i) = ' '
   ENDIF
!
!---------------------------- unrecognized command ---------------------
!
ELSE
   IGlobal = 'WHAT'
ENDIF
!
RETURN
END FUNCTION IGlobal
FUNCTION IndexR (String)
!
!-----------------------------------------------------------------------
!
! >>> IndexR -- returns the index of the last non-blank character, or a
! >>>             if the entire string is blank
!
! *** Calling Sequence:         IPos    = IndexR ( String )
!
!-----------------------------------------------------------------------
!
!
INTEGER :: IndexR
CHARACTER (len=*) :: String
!
! * * * * *                             !       loop index
INTEGER :: i
!
!----------------------- execution begins here -------------------------
!
DO 1 i = len (String), 1, - 1
   IF(String (i:i) .ne.' ') THEN
      IndexR = i
      RETURN
   ENDIF
    1 END DO
!
IndexR = 0
!
RETURN
END FUNCTION IndexR
SUBROUTINE SPL1D1 (N, X, F, W, IOP, IJ, A, B, C)
USE Numeric_Kinds_Module
SAVE
!***BEGIN PROLOGUE  SPL1D1
!***DATE WRITTEN   790301   (YYMMDD)
!***REVISION DATE  831207   (YYMMDD)
!***CATEGORY NO.  E1A
!***KEYWORDS  SPLINES,CUBIC SPLINES,COEFFICIENTS
!***AUTHOR  JORDAN, TOM, LOS ALAMOS NATIONAL LABORATORY
!***PURPOSE  Finds coefficients of cubic for spline interpolation.
!***DESCRIPTION
!
!     SPL1D1 computes the coefficients of a sequence of cubics for
!     spline interpolation.  This subroutine will normally be used in
!     conjunction with SPL1D2.
!
!     -ARGUMENTS-
!
!      N = integer specifying the number of points.
!      X = origin of the table of floating point values of independent
!          variable.  This table must be in ascending order.
!      F = origin of the table of floating point values of the dependent
!          variable.
!      W = origin of the table of floating point values of the second
!          derivatives of the spline at each knot.  The W's and F's
!          define the cubic over each interval.
!    IOP = an array of dimension 2 containing combinations of the
!          integers 1 through 5 for specifying the boundary conditions
!          (see Boundary Conditions).
!     IJ = integer specifying spacing in tables F and W.  Normally,
!          IJ = 1.
!  A,B,C = arrays of dimension N used for temporary storage.  These
!          arrays may be used by the calling program at any other
!          time.
!
!     The second derivatives are computed and stored in W, length N.
!
!     ERROR CONDITIONS:
!
!        If option 5 is specified with N < 4, this routine uses XERROR
!     to print the following error message:  "SPL1D1 N LESS THAN 4.
!     RESULTS INCORRECT."
!
!     BOUNDARY CONDITIONS:
!
!        IOP(1) and IOP(2) are integers = 1,2,3,4 or 5.  By proper
!     combinations of these parameters, the user has a variety of
!     allowable end conditions.  The information associated with the end
!     conditions must be stored in W(1) and W(K) where K = (N-1)*IJ+1.
!
!        If IOP(1) = 1, then W(1) is the value of the second derivative
!     at X .  If IOP(1) = 2, then W(1) determines F''(X ) by the
!         1                                            1
!     relation F''(X ) = W(1) * F''(X ).  If IOP(1) = 3, then W(1) is
!                   1                2
!     the value of the first derivative at X .  IOP(1) = 4 allows
!                                           1
!     periodic boundary conditions, i.e., F'' = F'', F  = F .  If
!                                          1     N    1    N
!     IOP(1) = 5, the first derivative at X, is calculated by using a
!     differentiated four-point Lagrangian interpolation formula
!     evaluated at X .  For this case, W(1) need not be specified.
!                   1
!
!     The paragraph above describes the possibilities at the left
!     boundary.  The same holds at the right boundary, i.e., at X ,
!                                                                N
!     with the necessary boundary information stored at W(K). For
!     example, if IOP(2) = 2 then W(K) determines F''(X ) by the
!                                                      N
!     relation F''(X ) = W(K) * F''(X   ).
!                   N                N-1
!
!         Also, any combination of the above boundary conditions with
!     the exception of the periodic case may be used.  If the user
!     knows the second derivative at the left boundary and the first
!     derivative at the right boundary then IOP=(1) = 1, IOP(2) = 3,
!     W(1) = y'', W(K) = y'.  For LOGICAL results, the user must have
!             1           N
!     IOP(1) = 4 and IOP(2) = 4 for the periodic boundary conditions.
!
!     CAUTION:
!
!        In options 2 and 3, the input data in W(1) and W(K) is
!     destroyed by SPL1D1.  These boundary conditions must be reset if
!     SPL1D1 is to be used again.  For option 5, the user must have
!     N >= 4.
!
!
!     METHOD:
!
!        Given N knots a = X  < X  < X  ... X  = b on the interval
!                           1    2    3      N
!     [a,b] and prescribed function values at the knots, say
!     F(X ) = F , k = 1, 2, ..., N, cubics are joined between the points
!        k     k
!     (X ,F ) with the requirement that first and second derivatives
!       k  k
!     be continuous at these points.  This requirement yields N-2
!     equations in the N unknowns F'', F'', ..., F'' which when coupled
!                                  1    2         N
!     with two boundary conditions yields a system of equations solvable
!     for the quantities F''.  A complete discussion of the method may
!                         k
!     be found in the reference listed below.
!
!***REFERENCES  Walsh, Ahlberg, and Nilson, Journal of Mathematics and
!                 Mechanics, Vol. II, No. 2, 1962.
!***ROUTINES CALLED  XERROR
!***END PROLOGUE  SPL1D1
SAVE
INTEGER IOP(2), N, K, M, j1, j2, k2, k3, ij, i, k1, k4, j, l1, l2, l3, mk, ml
REAL*8 con, don, e, c1, c2, a1, a2, a3, a4, a5, a6
REAL*8 b1, b2, b3, b4, b5, b6, bob, bill, d1, d2
REAL*8 X (N), F (N), W (N), A (N), B (N), C (N)
!***FIRST EXECUTABLE STATEMENT  SPL1D1
K = N - 1
A (2) = - (X (2) - X (1) ) / 6.d0
B (2) = (X (3) - X (1) ) / 3.d0
W (IJ + 1) = (F (2 * IJ + 1) - F (IJ + 1) ) / (X (3) - X (2) ) - (F (IJ + 1) - F (1) ) / (X (2) - X (1) )
IF(N.eq.3)GOTO 4
   DO I = 3, K
      M = (I - 1) * IJ + 1
      J1 = M + IJ
      J2 = M - IJ
      CON = (X (I + 1) - X (I - 1) ) / 3.d0
      DON = (X (I) - X (I - 1) ) / 6.d0
      B (I) = CON - (DON**2) / B (I - 1)
      E = (F (J1) - F (M) ) / (X (I + 1) - X (I) ) - (F (M) - F (J2)) / (X (I) - X (I - 1) )
      W (M) = E- (DON * W (J2) ) / B (I - 1)
      A (I) = - (DON * A (I - 1) ) / B (I - 1)
   ENDDO
4  K1 = (N - 2) * IJ + 1
   C (N - 1) = - ( (X (N) - X (N - 1) ) / 6.d0) / B (N - 1)
   W (K1) = W (K1) / B (N - 1)
   A (N - 1) = A (N - 1) / B (N - 1)
   K2 = K - 1
IF(N.eq.3)GOTO 8
   DO I = 2, K2
      J = N - I
      CON = (X (J + 1) - X (J) ) / 6.d0
      A (J) = (A (J) - CON * A (J + 1) ) / B (J)
      C (J) = - (CON * C (J + 1) ) / B (J)
      K3 = (J - 1) * IJ + 1
      M = K3 + IJ
      W (K3) = (W (K3) - CON * W (M) ) / B (J)
   ENDDO
8  K4 = (N - 1) * IJ + 1
IF(IOP (1).eq.5)GOTO 200
  201 C1 = W (1)
IF(IOP (2).eq.5)GOTO 202
  203 C2 = W (K4)
GOTO 205
  200 IF(N.lt.4)GOTO 300
  302 A1 = X (1) - X (2)
A2 = X (1) - X (3)
A3 = X (1) - X (4)
A4 = X (2) - X (3)
A5 = X (2) - X (4)
A6 = X (3) - X (4)
W (1) = F (1) * (1.d0 / A1 + 1. / A2 + 1.d0 / A3) - A2 * A3 * F (IJ + &
 1) / (A1 * A4 * A5) + A1 * A3 * F (2 * IJ + 1) / (A2 * A4 * A6) &
 - A1 * A2 * F (3 * IJ + 1) / (A3 * A5 * A6)
GOTO 201
  202 IF(N.lt.4)GOTO 300
  303 B1 = X (N) - X (N - 3)
B2 = X (N) - X (N - 2)
B3 = X (N) - X (N - 1)
B4 = X (N - 1) - X (N - 3)
B5 = X (N - 1) - X (N - 2)
B6 = X (N - 2) - X (N - 3)
L1 = K4 - IJ
L2 = L1 - IJ
L3 = L2 - IJ
W (K4) = - B2 * B3 * F (L3) / (B6 * B4 * B1) + B1 * B3 * F (L2) &
 / (B6 * B5 * B2) - B1 * B2 * F (L1) / (B4 * B5 * B3) + F (K4) &
 * (1.d0 / B1 + 1.d0 / B2 + 1.d0 / B3)
GOTO 203
  205 CONTINUE
I = 0
   50 CONTINUE
I = I + 1
IF(I.gt.K) goto 100
!
M = (I - 1) * IJ + 1
GOTO 60
   70 IF(I.eq.1)GOTO 50
   80 W (1) = W (1) - BOB * W (M)
W (K4) = W (K4) - BILL * W (M)
A (1) = A (1) - BOB * A (I)
A (N) = A (N) - BILL * A (I)
C (1) = C (1) - BOB * C (I)
C (N) = C (N) - BILL * C (I)
goto 50
!
   60 MK = IOP (1)
IF(MK.eq.1)GOTO 62
IF(MK.eq.2)GOTO 64
IF(MK.eq.3)GOTO 66
IF(MK.eq.4)GOTO 68
IF(MK.eq.5)GOTO 66
   62 IF(I.ne.1)GOTO 71
   63 A (1) = - 1.d0
C (1) = 0.
GOTO 500
   71 BOB = 0.d0
GOTO 500
   64 IF(I.ne.1)GOTO 73
   76 A (1) = - 1.d0
C (1) = 0.
W (1) = 0.
GOTO 500
   73 IF(I.gt.2)GOTO 82
   81 BOB = - C1
GOTO 500
   82 BOB = 0.d0
GOTO 500
   66 IF(I.ne.1)GOTO 83
   84 A (1) = - (X (2) - X (1) ) / 3.d0
C (1) = 0.d0
W (1) = - C1 + (F (IJ + 1) - F (1) ) / (X (2) - X (1) )
GOTO 500
   83 IF(I.gt.2)GOTO 86
   85 BOB = (X (2) - X (1) ) / 6.d0
GOTO 500
   86 BOB = 0.d0
GOTO 500
   68 IF(I.ne.1)GOTO 87
   88 A (1) = - 1.d0
C (1) = 1.d0
W (1) = 0.d0
GOTO 500
   87 BOB = 0.d0
  500 ML = IOP (2)
IF(ML.eq.1)GOTO 120
IF(ML.eq.2)GOTO 130
IF(ML.eq.3)GOTO 140
IF(ML.eq.4)GOTO 150
IF(ML.eq.5)GOTO 140
  120 IF(I.ne.1)GOTO 121
  122 A (N) = 0.d0
C (N) = - 1.d0
GOTO 70
  121 BILL = 0.d0
GOTO 70
  130 IF(I.ne.1)GOTO 131
  132 A (N) = 0.d0
C (N) = - 1.d0
W (K4) = 0.
GOTO 70
  131 IF(I.ne.K)GOTO 134
  133 BILL = - C2
GOTO 70
  134 BILL = 0.d0
GOTO 70
  140 IF(I.ne.1)GOTO 141
  142 A (N) = 0.d0
C (N) = (X (N - 1) - X (N) ) / 3.d0
W (K4) = C2 - (F (K4) - F (K1) ) / (X (N) - X (N - 1) )
GOTO 70
  141 IF(I.ne.K)GOTO 143
  144 BILL = (X (N) - X (N - 1) ) / 6.d0
GOTO 70
  143 BILL = 0.d0
GOTO 70
  150 IF(I.ne.1)GOTO 151
  152 A (N) = 0.
C (N) = (X (N - 1) + X (1) - X (N) - X (2) ) / 3.d0
W (K4) = (F (IJ + 1) - F (1) ) / (X (2) - X (1) ) - (F (K4) &
 - F (K1) ) / (X (N) - X (N - 1) )
GOTO 70
  151 IF(I.ne.2)GOTO 153
  154 BILL = (X (2) - X (1) ) / 6.d0
GOTO 70
  153 IF(I.ne.K)GOTO 155
  156 BILL = (X (N) - X (N - 1) ) / 6.d0
GOTO 70
  155 BILL = 0.
GOTO 70
  100 CON = A (1) * C (N) - C (1) * A (N)
D1 = - W (1)
D2 = - W (K4)
W (1) = (D1 * C (N) - C (1) * D2) / CON
W (K4) = (A (1) * D2 - D1 * A (N) ) / CON
DO I = 2, K
   M = (I - 1) * IJ + 1
   W (M) = W (M) + A (I) * W (1) + C (I) * W (K4)
ENDDO
GOTO 305
  300 CALL ErrWrt (' SPL1D1,  N.LT.4 RESULTS INCORRECT')
  305 RETURN
END SUBROUTINE SPL1D1
SUBROUTINE SPL1D2 (N, X, F, W, IJ, Y, TAB)
USE Numeric_Kinds_Module
!***BEGIN PROLOGUE  SPL1D2
!***DATE WRITTEN   790301   (YYMMDD)
!***REVISION DATE  831207   (YYMMDD)
!***CATEGORY NO.  E1A
!***KEYWORDS  SPLINES,CUBIC SPLINES,INTERPOLATION,DERIVATIVES
!***AUTHOR  JORDAN, TOM, LOS ALAMOS NATIONAL LABORATORY
!***PURPOSE  Interpolates values of a function and its first and
!            second derivatives.
!***DESCRIPTION
!
!     SPL1D2 interpolates in a table, returning values of the function
!     and its first and second derivatives.  This is normally used
!     in conjunction with SPL1D1 which will supply second derivatives.
!
!     -ARGUMENTS-
!
!      N = integer specifying the number of points.
!      X = origin of the table of floating point values of independent
!          variable.  This table must be in ascending order.
!      F = origin of the table of floating point values of the dependent
!          variable.
!      W = origin of the table of floating point values of the second
!          derivative.  (Normally supplied through use of SPL1D1.)
!     IJ = integer specifying spacing in tables F and W.
!      Y = floating point value at which interpolation is desired.
!    TAB = array of dimension >= 3 which contains the results of the
!          interpolation.
!
!     Upon return from SPL1D2, TAB(1) contains F(Y), TAB(2) contains
!     F'(Y), and TAB(3) contains F''(Y).  There are no error messages
!     in SPL1D2.
!
!     NOTE: If Y is outside the range of the X table, extrapolation
!     occurs.
!
!     METHOD:
!
!     A complete discussion of the method may be found in the reference
!     listed below.
!
!***REFERENCES  Walsh, Ahlberg, and Nilson, Journal of Mathematics and
!                 Mechanics, Vol. II, No. 2, 1962.
!***ROUTINES CALLED  (NONE)
!***END PROLOGUE  SPL1D2
IMPLICIT NONE
INTEGER I, IJ, K1, MI, N, ilo
REAL*8 A, B, C, FLK, Y
REAL*8 X (N), F (N), W (N), TAB (3)
save ilo
!***FIRST EXECUTABLE STATEMENT  SPL1D2
!
!     LOCATE Y IN THE X TABLE
!
DATA ilo / 1 /
!
CALL FndInt (N - 1, X, Y, ilo, I)
I = MAX0 (I, 1)
MI = (I - 1) * IJ + 1
K1 = MI + IJ
FLK = X (I + 1) - X (I)
!
!     CALCULATE F(Y)
!
A = (W (MI) * (X (I + 1) - Y) **3 + W (K1) * (Y - X (I) ) **3) &
 / (6. * FLK)
B = (F (K1) / FLK - W (K1) * FLK / 6.) * (Y - X (I) )
C = (F (MI) / FLK - FLK * W (MI) / 6.) * (X (I + 1) - Y)
TAB (1) = A + B + C
!
!     CALCULATE THE FIRST DERIVATIVE AT Y
!
A = (W (K1) * (Y - X (I) ) **2 - W (MI) * (X (I + 1) - Y) **2) &
 / (2. * FLK)
B = (F (K1) - F (MI) ) / FLK
C = FLK * (W (MI) - W (K1) ) / 6.
TAB (2) = A + B + C
!
!     CALCULATE THE SECOND DERIVATIVE AT Y
!
TAB (3) = (W (MI) * (X (I + 1) - Y) + W (K1) * (Y - X (I) ) ) &
 / FLK
RETURN
END SUBROUTINE SPL1D2