rem Data Bounding, Smoothing, and Differentiation
[loop]
cls
print
print "Data Bounding, Smoothing, and Differentiation"
print

dim y(100)
dim x(100)

rem data entry
input "Number of points to input? ";n
[gleap]
input "Use keyboard (k) or read from data (d)? ";c$
if c$="k" then
 for i=1 to n
  print "x(";i;")= ";
  input " ";x1
  x(i)=x1
 next i
end if
if c$="d" then
rem 105 data points are used in convolution data
rem we want to skip past them and restore pointers
  for i=1 to 105
    read x1
  next i
  for i=1 to n
  read x1
  x(i)=x1
 next i
restore
end if
if c$<>"d" and c$<>"k" then [gleap]
[again]
print
rem choose process
print "Chose process:"
print "  1.  Data Bounding  "
print "  2.  Data Smoothing "
print "  3.  First Derivative"
print "  4.  Second Derivative"
print "  5.  Quit"
print
input "(1,2,3,4,5) ";q2
q=0
q1=0
if q2=1 then
 q=-1
 gosub [bound]
end if
if q2=2 then
 q=0
 gosub [smooth]
end if
if q2=3 then
 q=1
 q1=3
 gosub [smooth]
end if
if q2=4 then
 q=2
 q1=4
 gosub [smooth]
end if
if q2=5 then end
gosub [again]

rem bounding routine
[bound]
print
print "data bounding"
a$="Data bounded"
input "How many standard deviations? ";s
y(1)=x(1)
for k=2 to n-1
 a=(x(k-1)+x(k+1))/2
 d=x(k)-a
 m=s*(x(k))^.5
 if abs(d)<abs(m) then [aleap]
 if d>0 then [bleap]
 y(k)=x(k)+m
 goto [cleap]
 [bleap]
 y(k)=x(k)-m
 goto [cleap]
 [aleap]
 y(k)=x(k)
 [cleap]
next k
y(n)=x(n)
gosub [prin]
return

[smooth]
rem least squares smoothing and derivative routines
print
[fleap]
input "Degree of smoothing desired (2-4, 1 return to main menu): ";s
if s=1 then [eleap]
if s<2 then [fleap]
if s>4 then [fleap]
restore
t=36*q+(s-2)*(s+3)
for k=1 to t+1
 read b
next k
m=2*s+1
for k=1 to m
 read c1
 c(k)=c1
next k
m1=m
rem smooth each data point
var2=n-1*s
for k=s+1 to n-s
 d=0
 l=m1
 rem compute convolution
 for j=1 to m
  d=d+x(l)*c(j)
  l=l-1
 next j
 y(k)=d/8
 m1=m1+1
next k
rem convolution array coefficients
rem compute end points and 2nd derivative
for k=1 to s
 y(k)=y(s+1)
next k
var1=n-s+1
for k=var1 to n
 y(k)=y(n-s)
next k
a$= "2nd derivative"
if q1=4 then [dleap]
rem first derivative
t=35-2*s
rem read new set of coefficients
for k=1 to t
 read b
next k
for k=1 to m
 read c1
 c(k)=c1
next k
d=0
l=n
r=m
e=0
rem compute convolution
for j=1 to m
 e=e+x(l)*c(j)
 d=d+x(r)*c(j)
 r=r-1
 l=l-1
next j
d=d/b
e=e/b
l=n-s+1
for k=1 to s
 y(k)=y(k)+d*(k-1*s-1)
 y(l)=y(l)+e*k
 l=l+1
next k
a$="1st derivative "
if q1=3 then [dleap]
rem smoothed values
rem read new coeffcients
for k=1 to t
 read b
next k
for k=1 to m
 read c1
 c(k)=c1
next k
d=0
e=0
r=m
l=n
rem compute convolution
for j=1 to m
 d=d+x(r)*c(j)
 e=e+x(l)*c(j)
 r=r-1
 l=l-1
next j
d=d/b
e=e/b
l=n-s+1
for k=1 to s
 y(k)=y(k)+d*(k-1*s-1)*(k-1*s-1)/2
 y(l)=y(l)+e*k*k/2
 l=l+1
next k
a$="smoothed data"
[dleap]
gosub [prin]
[eleap]
return

rem ****************** convolution array data ****************
rem ****************** do not change          ****************
data 35,-3,12,17,12,-3
data 21,-2,3,6,7,6,3,-2
data 231,-21,14,39,54,59,54,39,14,-21
data 429,-36,9,44,69,84,89,84,69,44,9,-36
data 10,2,1,0,-1,-2
data 28,3,2,1,0,-1,-2,-3
data 60,4,3,2,1,0,-1,-2,-3,-4
data 110,5,4,3,2,1,0,-1,-2,-3,-4,-5
data 7,2,-1,-2,-1,2
data 42,5,0,-3,-4,-3,0,5
data 462,28,7,-8,-17,-8,7,28
data 429,15,6,-1,-9,-10,-9,-6,-1,6,15

[prin]
print
print "Result: ";a$
print
for k=1 to n
 print "X(";k;")= ";x(k)
 print "Y(";k;")= ";y(k)
 print
next k
return

rem ****************** insert your data below ****************
rem ****************** if you are using this  ****************
rem ****************** input method           ****************
data 84,85,83,105,108,123,107,96,102,92
data 111,93,102,76,78,64,64,61,54,51

end