rem
rem least squares polynomial fitting:-
def fn_polyfit(Order,Npoints,z())


local i
local o% : o%=Order
if o<1 or o>6 then print "cannot have polynomial order of ";o : end




local N% : N%=Npoints
local x(), y(), xn(), xny() : dim x(N%), y(N%), xn(N%), xny(N%)


local m() : dim m(o%,o%) : rem matrix
local v() : dim v(o%) : rem vector


for i=1 to N%
x(i-1)=z(i,0) : y(i-1)=z(i,1)
next


rem all constants, for order 1 to 6, shown here for clarity:-
xny() = y() : _y1 = sum(xny())
xn() = x() : _x1 = sum(xn())


xny() = xn() * y() : _x1y = sum(xny())
xn() = xn() * x() : _x2 = sum(xn())


xny() = xn() * y() : _x2y = sum(xny())
xn() = xn() * x() : _x3 = sum(xn())


xny() = xn() * y() : _x3y = sum(xny())
xn() = xn() * x() : _x4 = sum(xn())


xny() = xn() * y() : _x4y = sum(xny())
xn() = xn() * x() : _x5 = sum(xn())


xny() = xn() * y() : _x5y = sum(xny())
xn() = xn() * x() : _x6 = sum(xn())


xny() = xn() * y() : _x6y = sum(xny())
xn() = xn() * x() : _x7 = sum(xn())


xn() = xn() * x() : _x8 = sum(xn())
xn() = xn() * x() : _x9 = sum(xn())
xn() = xn() * x() : _x10 = sum(xn())
xn() = xn() * x() : _x11 = sum(xn())
xn() = xn() * x() : _x12 = sum(xn())






rem 1st order is straight line fit

if o%=1 then
m() = \
\ N%, _x1, \
\ _x1, _x2


v() = _y1, _x1y


endif




rem 2nd order is quadratic fit

if o%=2 then
m() = \
\ N%, _x1, _x2, \
\ _x1, _x2, _x3, \
\ _x2, _x3, _x4


v() = _y1, _x1y, _x2y


endif


rem 3rd order is cubic fit

if o%=3 then
m() = \
\ N%, _x1, _x2, _x3, \
\ _x1, _x2, _x3, _x4, \
\ _x2, _x3, _x4, _x5, \
\ _x3, _x4, _x5, _x6


v() = _y1, _x1y, _x2y, _x3y


endif


rem 4th order

if o%=4 then
m() = \
\ N%, _x1, _x2, _x3, _x4, \
\ _x1, _x2, _x3, _x4, _x5, \
\ _x2, _x3, _x4, _x5, _x6, \
\ _x3, _x4, _x5, _x6, _x7, \
\ _x4, _x5, _x6, _x7, _x8


v()=_y1, _x1y, _x2y, _x3y, _x4y


endif


rem 5th order
if o%=5 then
m() = \
\ N%, _x1, _x2, _x3, _x4, _x5, \
\ _x1, _x2, _x3, _x4, _x5, _x6, \
\ _x2, _x3, _x4, _x5, _x6, _x7, \
\ _x3, _x4, _x5, _x6, _x7, _x8, \
\ _x4, _x5, _x6, _x7, _x8, _x9, \
\ _x5, _x6, _x7, _x8, _x9, _x10


v()= _y1, _x1y, _x2y, _x3y, _x4y, _x5y


endif


rem 6th order

if o%=6 then
m() = \
\ N%, _x1, _x2, _x3, _x4, _x5, _x6, \
\ _x1, _x2, _x3, _x4, _x5, _x6, _x7, \
\ _x2, _x3, _x4, _x5, _x6, _x7, _x8, \
\ _x3, _x4, _x5, _x6, _x7, _x8, _x9, \
\ _x4, _x5, _x6, _x7, _x8, _x9, _x10, \
\ _x5, _x6, _x7, _x8, _x9, _x10, _x11, \
\ _x6, _x7, _x8, _x9, _x10, _x11, _x12


v()= _y1, _x1y, _x2y, _x3y, _x4y, _x5y, _x6y


endif


rem solve the set of simultaneous equations:-
proc_invert(m())
v()=m().v()

!^v() rem return pointer to vector. (v() is array containing coefficents. eg y

v(0)*x^0 + v(1)*x^1 + .... etc







rem----------------------------------------------------------------------------