726824314 04/10/20
Smoothing values have been established for each parameter k as described in Smvals.doc. FUNCTION
ROBMFU(CHI,AJP,PC,PPCC,SM,B,NCON,FR,

)calls SUBROUTINE
GSOLVE(CHI,PC,PPCC,SM,ALAMDA,NCON,

,B).
In GSOLVE the diagonal values of the second derivative matrix are changed in according to
 2

2
 c
2 k

 2

2
 c k
2
 exp

( )
  
Then the matrix is inverted and used to find
ROBMFU(

) =
 2
(

) /CHI-FR where CHI is the measured value with the current set of parameters.
The subroutine Brack attempts to find values of

1
,

2
such that
 2
(

1
) is less than Fr × CHI and
 is greater than Fr ×  2
. The exact method for accomplishing this has varied over the years.

2
(

2
)
SUBROUTINE
BRACK(BEG,ENDC,X1,X2,F1,F2,SUCCES,CHI,AJP,
2 PC,PPCC,SM,ALAMDA,NCON,FR,B)
C brack makes alamda larger until romnfu, ajp/chi-fr, is >0.
C This alamda becomes X2 and the value F2.
C Then brack makes alamda smaller until robmfu is < 0. This alamda, robmfu is
C returned as X1,F1
C If these cannot be found, it decides whether to search more and finally
C returns X2,F2 as the best value found with Succes='N'}
1
The function
 2 (

) is not well defined when
GSOLVE cannot invert the matrix, but it should be on the left. This means that if the matrix is not inverted, the value should be taken to be –FR.
Figure 1 Expected values of ROBMFU as a function of λ for invertible matrices.