Page 185 - Compact Numerical Methods For Computers

174 Compact numerical methods for computers

Algorithm 19. A Nelder-Mead minimisation procedure (cont.)
C : integer; {pointer column in workspace P which stores the
centroid of the polytope. C is set to n+2) here.}
calcvert : boolean; {true if vertices to be calculated, as at start
or after a shrink operation}
convtol : real; {a convergence tolerance based on function
value differences}
f : real; {temporary function value}
funcount : integer; {count of function evaluations}
H : integer; {pointer to highest vertex in polytope}
i,j : integer; {working integers}
L : integer; {pointers to lowest vertex in polytope}
notcomp : boolean; {non-computability flag}
n1 : integer; {n+l}
oldsize : real; {former size measure of polytope}
P : array[l..Prow,1..Pcol] of real; {polytope workspace}
shrinkfail: boolean; {true if shrink has not reduced polytope size}
size : real; {a size measure for the polytope}
step : real; {stepsize used to build polytope}
temp : real; {a temporary variable}
trystep : real; {a trial stepsize}
tstr : string[5]; {storage for function counter in string form
to control display width}
VH,VL,VN : real; {function values of ‘highest’,‘lowest’ and
*next’ vertices}
VR : real; {function value at Reflection}
begin
writeln(‘Nash Algorithm 19 version 2 1988-03-17’);
writeln(‘Nelder Mead polytope direct search function minimiser’);
fail := false; {the method has not yet failed!}
f := fminfn(n,Bvec,Workdata,notcomp); {initial fn calculation -- STEP 1}
if notcomp then
begin
writeln(‘**** Function cannot be evaluated at initial parameters ****‘);
fail := true; {method has failed -- cannot get started}
end
else
begin {proceed with minimisation}
writeln(‘Function value for initial parameters = ‘,f);
if intol<0.0 then intol := Calceps;
funcount := 1; {function count initialized to 1}
convtol := intol*(abs(f)+intol); {ensures small value relative to
function value -- note that we can restart the procedure if
this is too big due to a large initial function value.}
writeln(‘Scaled convergence tolerance is ‘,convtol);
n1 := n+1; C := n+2; P[n1,1] := f; {STEP 2}
for i := 1 to n do P[i,1] := Bvec[i];
{This saves the initial point as vertex 1 of the polytope.}
L := 1; {We indicate that it is the ‘lowest’ vertex at the moment, so
that its funtion value is not recomputed later in STEP 10}
size := 0.0; {STEP 3}
{STEP 4: build the initial polytope using a fixed step size}
step := 0.0;