.-
help for ^amoeba^, ^quasi^                                     (STB-38: sg71) 
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Maximization of Function 
------------------------


Syntax
------

   ^amoeba^ [ obj xin yout xout [stepsize itmax toler ] ]

   ^quasi^  [ obj xin yout xout [g h stepsize itmax toler ^bhhh^] ]


where obj is the name of a program written by the user to evaluate the 
objective function to be maximized, xin is a row vector containing starting 
values, yout is a scalar to receive the maximum value of the objective 
function, and xout is a row vector to receive the value of the vector that 
maximizes the objective function.

Unless using the ^bhhh^ option under ^quasi^, a call to obj must be of the 
form ^obj x y^ where ^x^ is a row vector at which the function is to be 
evaluated, and ^y^ is a scalar to receive the value of the function. When using
the ^bhhh^ option the call to the user-written objective function must take the
form ^obj x y objvar^, ^objvar^ is a variable name (see above).


Options
-------

Under ^amoeba^, stepsize is the percentage change in each parameter used to set
up a simplex in the parameter space.  Under ^quasi^, it is the percentage step 
taken to compute the numerical gradient.  

itmax is the maximum number of iterative steps that should be done.  


toler is how "tight" the simplex (^amoeba^) or how small the gradients (^quasi^)
must be before the algorithm quits.

g is a row vector to receive the final gradient in ^quasi^.

h is a matrix to receive final inverse of hessian in ^quasi^.

^bhhh^ tells ^quasi^ to use the BHHH algorithm rather than BFGS in ^quasi^.

Note that options are ordered and a period can be used to skip optional 
arguments. In addition, invoking ^amoeba^ or ^quasi^ with no arguments will 
display information about them, a la Unix.


Examples
--------

  . ^amoeba obj x f z^
  . ^aomeba obj x f z 0.1^
  . ^aomeba tsls bols sse bhat . . 1E-6^ 
  . ^quasi ols bstart yout bfinal^
  . ^quasi ols bstart yout bfinal . h^
  . ^quasi mylk b0 fout b1 . . . . bhhh^  


Author
------

     Christopher Ferrall
     Queen's University
     Kingston, Ontario
     FAX 613-545-6668
     email: ferrallc@@post.queensu.ca


Also See
--------

    STB:  sg71 (STB-38)
