leastsqu.h

eC++编译器源码

/*NRY 1/90 -  The following procedures are interfaces to curve fitting 
   	algorithms which use the Least Square Method.  Given a set of data 
        points and an uncertainty factor for each point, the equation of 
	a line or curve is returned depending on which function is used.  
	This line or curve is chosen such that the square of the distance 
	from any datapoint to a point on the curve is minimized.  More detailed
	descriptions follow after definitions. 
*/
/*POLYFIT NOT TESTED YET*/
#pragma LeastSquare
#include <GaussJ.h>
  typedef
    struct {  /* see UNIT Putpoint */
                   int noNums;
                   double X[MAX+1], Y[MAX+1];
                   double sigma[MAX+1];
           } DataPoints;
  typedef struct {
                  double A, B;        /* A = y-int.  B = slope */
                  double sigA, sigB;  /* A & B's uncertainty factors */
                  double chi2, Q;     /* chi-square and goodness-of-fit */
          } LineReturn;

  void LineFit(DataPoints &ptRec, double weighting, LineReturn &retVal);
  void PolyFit(DataPoints &ptRec, PolyReturn &retVal);

/*
  LineFit 
  -------
	This procedure returns a linear solution using the method stated above.
	LineFit accepts an argument of the type DataPoints which 
	includes:  noNums   - the number of data points to be analyzed.
		   X[], Y[] - the actual coordinates of each point.
		   sigma[]  - the uncertainty factor of each point.
	LineFit also accepts a weighting term which is a flag (zero or nonzero)
	indicating whether or not to use the values in the sigma array for
	weights.  If weighting = 0.0 the all sigmas are uniform and assumed
	to be 1.  In other words sigma[i] = 1 for all points X[i],Y[i].
	LineFit also accepts an argument of the type LineReturn, this is what 
	the resultant linear equation is returned in.  LineReturn 
	includes:  A - the Y-intercept of the line.
		   B - the slope of the line.
		   sigA,sigB - these are the uncertainty factors for A and B.
		   chi2 - chi squared or the "goodness-of-fit" term.
		   Q - the probability of the "goodness-of-fit".
	If Q > .1 the goodness-of-fit is believable;;
	If Q > .001 the goodness-of-fit may be acceptable if errors are
	   nonnormal or have been moderately underestimated.
	If Q < .001 the model and/or estimation can be called into question.

Note:  This function has not been fully implemented to handle a nonzero 
weighting factor.  There is a HALT statement in the function GammaQ.

PolyFit
-------
	This function returns a nonlinear solution using the least square 
	method.  PolyFit takes an argument of the type DataPoints
	just as above.  It also takes an argument of the type PolyReturn which
	is defined in the module GaussJ.  PolyReturn includes:
	    coeff[] - this holds the coefficients of the polynomial equation.
	    noTerms - the number of coefficients.
	    listA[] - this array keeps track of the coefficients to be fitted.
	    minFit  - the number of elements to be fitted from listA[].
	    covarMatrix - the covariance matrix.
	    subI,subJ   - the size of the covariance matrix.
	    chi2    - chi squared, the goodness-of-fit.

   	This procedure returns it's information in the type
	PolyReturn. Several elements of PolyReturn must be filled in before
	the call though.  An initial guess of the coefficients must be made.
	The noTerms must be set.  The coefficients  which are to be fitted 
	must be entered in listA, the others are held constant.  MinFit is set
	to the number of terms to be fitted.  The rest is filled in by PolyFit.

Note: A more detailed description of the process and equations can be found
      in Numerical Recipes by Press, Flannery, Teukolsky, and Vetterling.
         -----------------
*/