Simple Fit

wiki

Download the whole package from:

http://luaforge.net/projects/luamatrix/

The code and method is very simple.

First you get the x values into a table. Then you concatenate it with the y-values. Use the Gauss-Jordan Method to get the results for your variables.

The only thing one had to think about with exponential functions was how to make them linear. That is easy; for example:

y = a * x^b | ln ==> ln(y) = ln( a ) + b * ln( x )

Then one can use fit.linear() again to get the variables a and b.

--///////////////////--

--// Curve Fitting //--

--///////////////////--



-- v 0.2



-- Lua 5.1 compatible



-- little add-on to the matrix module, to show some curve fitting



-- http://luaforge.net/projects/LuaMatrix

-- http://lua-users.org/wiki/SimpleFit



-- Licensed under the same terms as Lua itself.



-- requires matrix module

local matrix = require "matrix"



-- The Fit Table

local fit = {}



-- Note all these Algos use the Gauss-Jordan Method to caculate equation systems



-- function to get the results

local function getresults( mtx )

   assert( #mtx+1 == #mtx[1], "Cannot calculate Results" )

   mtx:dogauss()

   -- tresults

   local cols = #mtx[1]

   local tres = {}

   for i = 1,#mtx do

      tres[i] = mtx[i][cols]

   end

   return unpack( tres )

end



-- fit.linear ( x_values, y_values )

-- fit a straight line

-- model (  y = a + b * x  )

-- returns a, b

function fit.linear( x_values,y_values )

   -- x_values = { x1,x2,x3,...,xn }

   -- y_values = { y1,y2,y3,...,yn }

   

   -- values for A matrix

   local a_vals = {}

   -- values for Y vector

   local y_vals = {}



   for i,v in ipairs( x_values ) do

      a_vals[i] = { 1, v }

      y_vals[i] = { y_values[i] }

   end



   -- create both Matrixes

   local A = matrix:new( a_vals )

   local Y = matrix:new( y_vals )



   local ATA = matrix.mul( matrix.transpose(A), A )

   local ATY = matrix.mul( matrix.transpose(A), Y )



   local ATAATY = matrix.concath(ATA,ATY)



   return getresults( ATAATY )

end



-- fit.parabola ( x_values, y_values )

-- Fit a parabola

-- model (  y = a + b * x + c * x² )

-- returns a, b, c

function fit.parabola( x_values,y_values )

   -- x_values = { x1,x2,x3,...,xn }

   -- y_values = { y1,y2,y3,...,yn }



   -- values for A matrix

   local a_vals = {}

   -- values for Y vector

   local y_vals = {}



   for i,v in ipairs( x_values ) do

      a_vals[i] = { 1, v, v*v }

      y_vals[i] = { y_values[i] }

   end



   -- create both Matrixes

   local A = matrix:new( a_vals )

   local Y = matrix:new( y_vals )



   local ATA = matrix.mul( matrix.transpose(A), A )

   local ATY = matrix.mul( matrix.transpose(A), Y )



   local ATAATY = matrix.concath(ATA,ATY)



   return getresults( ATAATY )

end



-- fit.exponential ( x_values, y_values )

-- Fit exponential

-- model (  y = a * x^b )

-- returns a, b

function fit.exponential( x_values,y_values )

   -- convert to linear problem

   -- ln(y) = ln(a) + b * ln(x)

   for i,v in ipairs( x_values ) do

      x_values[i] = math.log( v )

      y_values[i] = math.log( y_values[i] )

   end



   local a,b = fit.linear( x_values,y_values )



   return math.exp(a), b

end



return fit



--///////////////--

--// chillcode //--

--///////////////--

Testcode:

-- require fit

-- local fit = require "fit"

local fit = dofile( "fit.lua" )



print( "Fit a straight line " )

-- x(i) = 2  | 3  | 4  | 5

-- y(i) = 5  | 9  | 15 | 21

-- model = y = a +  b * x

-- r(i) = y(i) - ( a + b * x(i) )

local a,b = fit.linear(	{ 2,3, 4, 5 },

			{ 5,9,15,21 } )

print( "=>    y = ( "..a.." )  +  ( "..b.." ) * x")



print( "Fit a parabola " )

local a, b, c = fit.parabola(	{ 0,1,2,4,6 },

				{ 3,1,0,1,4 } )

print( "=>    y = ( "..a.." )  +  ( "..b.." ) * x  +  ( "..c.." ) * x²")



print( "Fit exponential" )

local a, b = fit.exponential( {1,  2,  3,  4,   5},

			{1,3.1,5.6,9.1,12.9} )

print( "=>    y = ( "..a.." )  *  x^( "..b.." )")