DEFINITION MODULE LLSs;

   (* EXPORT QUALIFIED LFit, CovSrt, FLeg, FPoly, SVDFit, SVDVar; *)

   FROM NRVect IMPORT Vector;
   FROM NRMatr IMPORT Matrix;
   FROM NRIVect IMPORT IVector;

   TYPE Function = PROCEDURE (REAL, Vector);

   PROCEDURE LFit(    X, Y, SIG, A: Vector; 
                      LISTA: IVector; 
                      mfit:  INTEGER;
                      COVAR: Matrix; 
                      funcs: Function;
                  VAR chisq: REAL); 
   (*
     Given a set of points X[0, ndata-1], Y[0, ndata-1] with individual 
     standard deviations given by SIG[0, ndata-1], use chi^2 minimization to 
     determine mfit of the coefficients A[0, ma-1] of a function that depends 
     linearly on A, [y = (sum(i)) Aii x AFUNCi(x)]. The array LISTA[0, ma-1] 
     renumbers the parameters 
     so that the first mfit elements correspond to the parameters actually 
     being determined; the remaining ma-mfit elements are held fixed at their 
     input values. The program returns values for the ma fit parameters 
     A, chi ^2= chsiq, and the elements [mfit, mfit] of
     the covariance matrix COVAR[ma, ma]. 
     The user supplies a routine FUNCS(x,afunc,ma) that returns 
     the ma basis functions evaluated at x=x in the array AFUNC[0, ma-1].
   *)

   PROCEDURE CovSrt(COVAR: Matrix; ma: INTEGER; LISTA: IVector; mfit: INTEGER); 
   (*
     Given the covariance matrix COVAR[ma, ma] of a fit for mfit of
     ma total parameters, and their ordering LISTA[0, ma-1], repack the
     covariance matrix to the true order of the parameters. Elements
     associated with fixed parameters will be zero.
   *)

   PROCEDURE FLeg(x: REAL; PL: Vector); 
   (*
     Fitting routine for an expansion with NL Legendre polynomials
     PL, evaluated using the recurrence relation as in section 4.5.
   *)

   PROCEDURE FPoly(x: REAL; P: Vector); 
   (*
     Fitting routine for a polynomial of degree NP-1, with
     coefficients in the array P[0, np-1].
   *)

   PROCEDURE SVDFit(    X, Y, SIG, A: Vector; 
                        U, V: Matrix; 
                        W: Vector; 
                        func: Function;
                    VAR chisq: REAL); 
   (*
     Given a set of points X[0, ndata-1], Y[0, ndata-1] with individual 
     standard deviations given by
     SIG[0, ndata-1], use chi ^2 minimization to determine 
     the coefficients A[0, ma-1] of the fitting function 
     y= sumiaiimesAFUNCi(x).
     Here we solve the fitting equations using singular 
     value decomposition of the ndata by ma matrix, as in section 2.9. 
     On input, arrays U[ndata, ma], V[ma, ma], and W[0, ma-1]
     provide workspace;
     on output they define the 
     singular value decomposition, and can be used to obtain the covariance 
     matrix. The 
     program returns values for the ma fit parameters A, and chi ^2, 
     chisq. The user supplies a routine FUNCS(x,AFUNC,MA) that 
     returns the ma basis functions evaluated at x=x in
     the array AFUNC[0, ma-1].
   *)

   PROCEDURE SVDVar(V: Matrix; W: Vector; CVM: Matrix); 
   (*
     To evaluate the covariance matrix CVM[ma, ma] of the fit for ma 
     parameters obtained by SVDFit, call this routine with matrices V[ma, ma],
     W[0, ma-1] 
     as returned from SVDFit.
   *)

END LLSs.