=====Sandbox=====

 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----------------------------------------------------------------------------