Newcastle Scientific TM
 Libraries for Numerical Analysis


LeastSqX: LeastSqX provides powerful linear and non-linear least squares algorithms with an easy one-minute learning curve interface. Write your own function for fitting and pass the function name to the control, or simply rely on the default general polynomial function. 

To use LeastSqX, simply make a single call to the FitData method defined by the control. This call includes passing the number of data points, degrees of freedom to fit, array of independent variables (e.g., time), array of dependent variables (e.g., measurements), array of uncertainties of these measurements (may be all set to 0 for non-weighted fitting), function name (or 0 for a general polynomial fit), and initial guess of the coefficients if supplied user fitting function is non-linear. Upon return, the coefficients are replaced by the fit values. Also returned are the one sigma uncertainties of the fit, along with the Chisq value.

Example implementations included with the control demonstrate linear and non-linear fitting, plus a simple demonstration of how to use LeastSqX to perform multidimensional fitting (e.g., z as a function of both x and y).

LeasySqX1.FitData ( numpoints As Long, numco As Long, xd As Double, yd As Double, sigd As Double, userfunc As Long, co As Double, stddev As Double, ChiSquare As Double) As Long
 

A simple least squares example:

Private Sub Perform_Fit()

Static xd(100) As Double, yd(100) As Double, sigd(100) As Double 
Static co(4) As Double, std(4) As Double
Dim ma As Long, npt As Long
Dim chisq as double

npt = 20  ' number of data points
ma = 3     ' degrees of freedom

‘ make up some example data 
For i = 0 To npt - 1
       xd (i) = i
       yd (i) = 3.2 + 2.1 * xd (i)  - 1.7 * xd (i) ^ 2 + 200# * Rnd
 Next i

 'Least Squares Call.
' Upon return the fitted coeffs are returned in co(0), co(1), and co(2), 
' and their uncertainties  are returned in std(0), std(1), and std(2). 
 call  LeastSqX1.FitData(npt, ma, xd(0), yd(0), sigd(0), 0, co(0), std(0), chisq)

End sub

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