rem Data Peak Finder
[loop]
cls
print
print "Data Peak Finder Using Least Squares"
print "     equally spaced points"
print

REM enter data

dim y(100)
dim z(100)

rem data entry
input "Number of points to input? ";n
[dleap]
input "Use keyboard (k) or read from data (d)? ";c$
if c$="k" then
 for i=1 to n
  print "y(";i;")= ";
  input " ";y1
  y(i)=y1
 next i
end if
if c$="d" then
 for i=1 to n
  read y1
  y(i)=y1
 next i
end if
if c$<>"d" and c$<>"k" then [dleap]

rem mode of operation
print "Chose mode:"
print "  1.  Absolute max and min.  "
print "  2.  Calculated max and min."
print "  3.  Quit."
print
[again]
input "(1,2,3) ";q
if q=1 then gosub [absolute]
if q=2 then gosub [relative]
if q=3 then end
gosub [again]
print

rem absolute min and max
[absolute]
a=y(3)
b=y(3)
j=3
k=3
for r=3 to n-2
 if a>y(r) then
  goto [aleap]
 else
  a=y(r)
  j=r
 end if
 goto [bleap]
 [aleap]
 if y(r)>b then
  goto [bleap]
 else
  b=y(r)
  k=r
 end if
 [bleap]
next r
gosub [fit]
gosub [prin]
return

rem find deriative
[relative]
for k=3 to n-2
 z(k)=y(k+1)-y(k-1)+2*(y(k+2)-y(k-2))
 z(k)=z(k)/10
next k
z(1)=z(3)
z(2)=z(3)
z(n)=z(n-2)
z(n-1)=z(n)
rem find zeros
for k=4 to n-2
 t=z(k)*z(k-1)
 if t>=0 then [rleap]
 j=k
 gosub [fit]
 u=x
 j=k-1
 gosub [fit]
 if abs(x)<abs(u) then [sleap]
 j=k
 gosub [fit]
 [sleap]
 gosub [prin]
 [rleap]
next k
return

rem calculate coefficients of parabolic fit
[fit]
c=17*y(j)+12*(y(j-1)+y(j+1))-3*(y(j-2)+y(j+2))
c=c/35
d=y(j+1)-y(j-1)+2*(y(j+2)-y(j-2))
d=d/10
e=2*(y(j-2)-y(j)+y(j+2))-y(j-1)-y(j+1)
e=e/7
if e=0 then goto [mleap]
x=-1*d/e
p=c+(d+e*x/2)*x
b$="Max= "
if e<0 then goto [nleap]
b$="Min= "
goto [nleap]
[mleap]
b$="Indeterminate "
x=0
p=0
[nleap]
return

[prin]
print
print b$;p;" at x= ";j+x
print
return

data 84,85,83,105,108,123,107,96,102,92
data 111,93,102,76,78,64,64,61,54,51

end