function tab,xt,yt,n,k,x
;
; this routine uses aiken's method of interpolation.
; for a given independent variable x, an interpolation
; of order k is performed.
; the calling sequence is y = tab,xt,yt,n,k,x  where:
;   xt = array of independent values in a monotonic sequence.
;   yt = array of dependent values.
;   n  = number of independent values.
;   k  = order of interpolation (must be less than 6).
;   x  = independent value for which interpolation is desired.
;
  x1 = dblarr(6)
  y1 = dblarr(6)

 ; if k ge 6 then k = 5 
 ; if n ge k then k = n - 1

  npts = k + 1
;
; check for asending or descending sequence
;
  if (xt(0) - xt(n-1)) gt 0.0 then begin
;
; sequence is descending, check if extrapolation is needed
;
    if (x - xt(0)) gt 0.0 then goto,skip10
    if (x - xt(n-1)) lt 0.0 then goto,skip30
    for i=1,n do begin
     if (x - xt(i-1)) gt 0.0 then goto,skip50
    endfor
  endif
;
; sequence is ascending, check if extrapolation is needed
;
  if (x - xt(0)) gt 0.0 then goto,skip20
;
  skip10:
  for i=1,npts do begin
    x1(i-1) = xt(i-1)
    y1(i-1) = yt(i-1)
  endfor
  goto,skip100
;
  skip20:
  if (x - xt(n-1)) lt 0.0 then goto,skip40
;
; set up for extrapolation at end of table
;
  skip30:

  for i=1,npts do begin
    nn = n - npts + i
    x1(i-1)=xt(nn-1)
    y1(i-1)=yt(nn-1)
  endfor
  goto,skip100
;
; interpolation needed, find the two table values that the
; independent variable, x, lies between
;
  skip40:
  for i=1,n do begin
    if(x - xt(i-1)) lt 0.0 then goto,skip50
  endfor
  i = n
;
; choose k+1 independent table values closest to x
;
  skip50:
  if (k mod 2) gt 0 then goto,skip60
  if (abs(x-xt(i-1-1))-abs(xt(i-1)-x)) ge 0.0 then goto,skip56
  if (i-2-k/2) lt 0 then goto,skip10
  if (i-1+k/2-n) gt 0 then goto,skip30
  for j=1,npts do begin
    nn=i-2-k/2+j
    x1(j-1)=xt(nn-1)
    y1(j-1)=yt(nn-1)
  endfor
  goto,skip100

  skip56:
  if (i-1-k/2) lt 0 then goto,skip10
  if (i+k/2-n) gt 0 then goto,skip30
  for j=1,npts do begin
    nn=i-k/2+j-1
    x1(j-1)=xt(nn-1)
    y1(j-1)=yt(nn-1)
  endfor
  goto,skip100

  skip60:
  if (i-1+(k+1)/2-n) gt 0 then goto,skip30
  if (i-2-(k-1)/2) lt 0 then goto,skip10
  for j=1,npts do begin
    nn=i-1-(k+1-2*j)/2
    x1(j-1)=xt(nn-1)
    y1(j-1)=yt(nn-1)
  endfor

  skip100:
  for ii=1,k do begin
    savey1=y1(0)
    l=ii+1
    for jj=l,npts do begin
      nn=jj-ii
      ll=nn+1
      y1(nn-1) = (savey1*(x1(jj-1)-x)-y1(ll-1)*(x1(ii-1)-x)) /   $
                  (x1(jj-1)-x1(ii-1))
    endfor
  endfor

  result = y1(0)

  return, result

end

pro reinterp_freq,fixfreq,fmtime,fmfreq,numfm,sltime,slfreq,numsl
;
; user should supply 
; frequenecy of the fixed frequency protion of ionogram (fixfreq),
; the number of freq. markers (numfm),
; the times of the freq. markers (fmtime),
; the frequencies of the freq. markers (fmfreq),
; the number of scan lines in the ionogram (numsl)
; and the times of the scan lines (sltime).
;
; INPUT -
; fixfreq: frequenecy of the fixed frequency protion of ionogram
; fmtime:  times of the freq. markers
; fmfreq:  frequencies of the freq. markers
; numfm:   number of freq. markers
; sltime:  times of the scan lines
; numsl:   number of scan lines in the ionogram
;
; OUTPUT -
; slfreq:  freq of scan lines
;

; delta times between frequency markers from table. (millseconds)
  deltatfmtime = [3309.875d,418.675,696.550,695.575,693.675,       $
                 695.325,693.000,691.125,689.850,965.675,963.625, $
                 971.900,513.200,523.250,536.500,551.025,568.475, $
                 1195.725,1295.450,1433.775,1657.475,2025.425 ]

  deltatfmtime = deltatfmtime * 0.001  ; (seconds)

; Frequency marker times from table
  fm = [0.1d,0.25,0.5,0.75,1.0,1.25,1.5,1.75,2.,3.,4.,5., $
        6.,7.,8.,9.,10.,12.,14.,16.,18.,20. ]

  numfm=22
  maxfm=numfm
  stfmtime = fmtime[0]

; get a count of freq markers up to the point (if it exists) where the 
; default value (-1.0e+31) is used.  This signifies the end of detected 
; freq. markers.
  for ja = 1, numfm do begin
    if fmtime(ja-1) lt 0 then begin
     numfm = ja - 1
     goto, skip721
    endif
  endfor

  skip721: 

  fmerr = 0

; Check to see that valid frequency marker times are increasing.
  for kv = 1, numfm-1 do begin 
    if fmtime(kv+1-1) le fmtime(kv-1) then begin
      print,format='(a,i2,a,f10.3,a,i2,a,f10.3,a)',  $
        ' FM(',kv+1,') Time ',fmtime(kv+1-1),   $
        ' msec is less than FM(',kv,') Time ',fmtime(kv-1),' msec'
      print,' Freq Marker times not increasing. STOP RUN'
      stop
      return
    endif
  endfor

; calculate delta times between detected freq markers.
  deltafmtime = dblarr(numfm)
  deltafmtime(0) = fmtime(0)
  for k = 2, numfm do begin
    deltafmtime(k-1) = fmtime(k-1) - fmtime(k-1-1)
  endfor

;for now for only isis-1
   if fmerr eq 0 then goto,skip81

; compare table and detected FM deltimes and see if detected are within 
; +- X % (perc) of table. Do not compare first delta time (0.1mhz). For 
; 0.25mhz delta time double the % when comparing.
  perc = 10.0d
  for k = 2, numfm do begin
    percent = perc/100.0d
    if k eq 2 then percent = 2.0d * percent
    pmv = percent * deltatfmtime(k-1)
    rminfm = deltatfmtime(k-1) - pmv
    rmaxfm = deltatfmtime(k-1) + pmv
; if the detected FM delta time are not within +- "perc" percent of
; table delta times then set maximum freq marker limit for performing
; frequency interpolation.  All beyond this point will be set to
; default.
    if deltafmtime(k-1) lt rminfm or  $
       deltafmtime(k-1) gt rmaxfm then begin
       fmerr=k
      goto,skip81
    endif
  endfor

  skip81:

; FILL FREQUENCIES FOR ALL SCAN LINES WITH DEFAULT OF -1.0e+31.
  slfreq=dblarr(numsl)
 ; for jh = 1, numsl do begin
 ;   slfreq(jh-1) = -1.0d+31
 ; endfor
  slfreq[*] = -1.0d+31

; do not interpolate if less than 3 good detected freq markers.

  if (fmerr eq 1 or fmerr eq 2) or $
     (numfm eq 1 or numfm eq 2) then begin
    print,'Do not interpolate if less than 3 good detected freq markers.'
    numsl1 = 0
    for m = 1,numsl do begin
     if sltime(m-1) lt stfmtime then begin
      slfreq(m-1) = fixfreq
      numsl1=numsl1+1
     endif
    endfor
    return
  endif
;
  kk = numfm
  if fmerr ne 0 then begin
    kk=fmerr-1
  endif
;
; assign first freq. marker frequency and time to variables.
;
  stfm = fmfreq(0)
  endfm = fmfreq(kk-1)
  stfmtime = fmtime(0)
  endfmtime = fmtime(kk-1)
;
; get the freq. marker frequencies and times
; within each sweep rate group (.1-2, 2-5, 5-20 MHZ).
; interpolation will be performed within each sweep rate group.
; do not want interpolation that spans more than one sweep rate group.
;
  i1 = 0
  i2 = 0
  i3 = 0
  fmtm1 = dblarr(15)
  fmtm2 = dblarr(15)
  fmtm3 = dblarr(15)
  fmfr1 = dblarr(15)
  fmfr2 = dblarr(15)
  fmfr3 = dblarr(15)

  for k=1,kk do begin
    if fmfreq(k-1) ge 0.0 and fmfreq(k-1) le 2.0 then begin
      i1=i1+1
      fmtm1(i1-1) = fmtime(k-1)
      fmfr1(i1-1) = fmfreq(k-1)
    endif
    if fmfreq(k-1) ge 2.0 and fmfreq(k-1) le 5.0 then begin
      i2=i2+1
      fmtm2(i2-1) = fmtime(k-1)
      fmfr2(i2-1) = fmfreq(k-1)
    endif
    if fmfreq(k-1) ge 5.0 and fmfreq(k-1) le 20.0 then begin
      i3=i3+1
      fmtm3(i3-1) = fmtime(k-1)
      fmfr3(i3-1) = fmfreq(k-1)
    endif
  endfor

;
; determine if interpolation will be 2nd or 3rd degree based on
; the number of freq. markers in that group.
;
  ideg1 = 3
  if i1 le 2 then ideg1 = 2
  ideg2 = 3
  if i2 le 2 then ideg2 = 2
  ideg3 = 3
  if i3 le 2 then ideg3 = 2
;
; set freq = fix freq for fixed freq portion of iono then
; determine freq of each scan line in the swept freq portion.
; interpolation or extrapolation will be used.
;
  numsl1=0

  for k=1,numsl do begin
    stime=sltime(k-1)
    if stime lt stfmtime then begin
      slfreq(k-1) = fixfreq
      numsl1=numsl1+1
    endif else if kk ne maxfm and $
                  sltime(k-1) gt endfmtime then begin
      return
    endif else if stime ge fmtm1(0) and stime le fmtm1(i1-1) then begin
      slfreq(k-1) = tab(fmtm1,fmfr1,i1,ideg1,stime)
    endif else if stime gt fmtm1(i1-1) and fmtm2(0) eq 0 then begin
      slfreq(k-1) = tab(fmtm1,fmfr1,i1,ideg1,stime) 
    endif else if stime ge fmtm2(0) and stime le fmtm2(i2-1) then begin
      slfreq(k-1) = tab(fmtm2,fmfr2,i2,ideg2,stime)
    endif else if stime gt fmtm2(i2-1) and fmtm3(0) eq 0 then begin
      slfreq(k-1) = tab(fmtm2,fmfr2,i2,ideg2,stime)
    endif else if stime ge fmtm3(0) and stime le fmtm3(i3-1) then begin
      slfreq(k-1) = tab(fmtm3,fmfr3,i3,ideg3,stime)
    endif else if stime gt fmtm3(i3-1) then begin
      slfreq(k-1) = tab(fmtm3,fmfr3,i3,ideg3,stime)
    endif 
  endfor

  return
  end