e04ycf

Purpose

Synopsis

[v,cj,ifail] = e04ycf(m,fsumsq,s,v<,job,ifail>)

Description

 
 E04YCF is intended for use when the nonlinear least-squares 
                 T                                            
 function, F(x)=f (x)f(x), represents the goodness of fit of a 
 nonlinear model to observed data. The routine assumes that the 
 Hessian of F(x), at the solution, can be adequately approximated 
      T                                                       
 by 2J J, where J is the Jacobian of f(x) at the solution. The 
 estimated variance-covariance matrix C is then given by
 
                        2  T  -1    T              
               C=(sigma) (J J)     J J non-singular,
 
              2                                                 
 where (sigma)  is the estimated variance of the residual at the 
           _        
 solution, x, given by
 
                                      _ 
                                 2  F(x)
                          (sigma) = ----,
                                    m-n 
 
 m being the number of observations and n the number of variables.
 
 The diagonal elements of C are estimates of the variances of the 
 estimated regression coefficients. 
 
       T                                 
 When J J is singular then C is taken to be
 
                                  2  T  *
                         C=(sigma) (J J) ,
 
         T  *                           T                       
 where (J J)  is the pseudo-inverse of J J, but in this case the 
 parameter IFAIL is returned as non-zero as a warning to the user 
 that J has linear dependencies in its columns. The assumed rank 
 of J can be obtained from IFAIL.
 
 The routine can be used to find either the diagonal elements of
 C, or the elements of the jth column of C, or the whole of C.
 

Parameters

e04ycf

Required Input Arguments:

m                                     integer
fsumsq                                real
s (:)                                 real
v (:,:)                               real

Optional Input Arguments:                       <Default>

job                                   integer  -1
ifail                                 integer  -1

Output Arguments:

v (:,:)                               real
cj (:)                                real
ifail                                 integer