rem Arbitrary Function Regression
cls
print
print "Arbitrary Function Regression"
print "program will fit data to a general curve supplied in program"
print "an example is: y=a(1)+a(2)*x"
print "place the equation in the subroutine 'function'"
print "you must provide guesses for the coefficients a1...an"
print "you must specify a max error (start with something large like .1)"
print

dim a(5)
dim d(5)
dim x(50)
dim y(50)

rem data entry
input "desired max error? ";r
input "number of coefficients (a1...an)? ";m
print
for i=1 to m
 print "estimate of a(";i;")= ";
 input " ";a1
 a(i)=a1
 d(i)=a(i)/10
next i
print
input "number of points to input? ";n
for i=1 to n
 print "x(";i;")= ";
 input " ";x1
 print "y(";i;")= ";
 input " ";y1
 x(i)=x1
 y(i)=y1
next i
print

[fleap]
for k=1 to m
 [eleap]
 gosub [curve]
 r1=r8
 n7=0
 n8=0
 d=d(k)
 a(k)=a(k)+d
 gosub [curve]
 r2=r8
 if r1>r2 then
  goto [aleap]
 end if
 d=-1*d
 a(k)=a(k)+d
 r9=r1
 r1=r2
 r2=r9
 [aleap]
 n7=n7+1
 n8=n8+1
 a(k)=a(k)+d
 gosub [curve]
 r3=r8
 rem these values can be used for troubleshooting
 rem print
 rem print "R1 = ";r1
 rem print "R2 = ";r2
 rem print "R3 = ";r3
 rem print
 rem for l=1 to m
 rem print "a(";l;" = ";a(l)
 rem next l
 rem print
 if r3>r2 then
  goto [bleap]
 end if
 r1=r2
 r2=r3
 if r1=r2 and r2=r3 then
  goto [cleap]
 end if
 if n8<10 then
  goto [aleap]
 end if
 d(k)=d(k)*10
 goto [eleap]

 [bleap]
 a(k)=a(k)-d*(1/(1+(r1-r2)/(r3-r2))+.5)
 d(k)=d(k)*n7/5
next k

if r8<r then
 goto [cleap]
end if

goto [fleap]

rem results
[cleap]
for k=1 to m
 print "coefficient a(";k;")= ";a(k)
next k
print
print "root mean square error= ";r8

rem estimate y coordinate
[again]
print
print "Interpolation (enter x=q to end program) ";
input "x= ";x$
if x$="q" then
 end
end if
x=val(x$)
x(1)=x
n=1
gosub [curve]
print "y= ";y
goto [again]

[curve]
r8=0
for j=1 to n
 x=x(j)
 rem *********** insert function here *******************
 y=a(1)+a(2)*x
 rem ****************************************************
 r9=y-y(j)
 r8=r8+r9^2
next j
r8=(r8/n)^.5
return