Page 186 - Compact Numerical Methods For Computers

Direct search methods 175
Algorithm 19. A Nelder-Mead minimisation procedure (cont.)

for i := 1 to n do if 0.1*abs(Bvec[i])>step then step := 0.1*abs(Bvec[i]);
writeln(‘Stepsize computed as ‘,step);
for j := 2 to n1 do {main loop to build polytope} {STEP 5}
begin {STEP 6}
action := ‘BUILD‘;
for i := 1 to n do P[i,j] := Bvec[i]; {set the parameters}
{alternative strategy -- variable step size -- in the build phase}
{ step := 0.1*abs(Bvec[j-l])+0.001; }
{Note the scaling and avoidance of zero stepsize.}
trystep := step; {trial step -- STEP 7}
while P[j-1,j]=Bvecu[j-1] do
begin
P[j-1,j] := Bvec[j-1]+trystep; trystep := trystep*10;
end; (while]
size := size+trystep; {to compute a size measure for polytope -- STEP 8}
end; {loop on j for parameters}
oldsize := size; {to save the size measure -- STEP 9}
calcvert := true; {must calculate vertices when polytope is new}
shrinkfail := false; {initialize shrink failure flag so we don’t have
false convergence}
repeat {main loop for Nelder-Mead operations -- STEP 10}
if calcvert then
begin
for j := 1 to nl do {compute the function at each vertex}
begin
if j<>L then {We already have function value for L(owest) vertex.}
begin
for i := 1 to n do Bvec[i] := P[i,j]; {get the parameter values}
f := fininfn(n,Bvec,Workdata,notcomp); {function calculation}
if notcomp then f := big; funcount := funcount+1; P[nl,j] := f;
end; {if j<>L clause}
end; {loop on j to compute polytope vertices}
calcvert := false; {remember to reset flag so we don’t calculate
vertices every cycle of algorithm}
end; {calculation of vertices}
{STEP 11: find the highest and lowest vertices in current polytope}
VL := P[nl,L]; {supposedly lowest value}
VH := VL; {highest value must hopefully be higher}
H := L; {pointer to highest vertex initialized to L}
{Now perform the search}
for j := 1 to nl do
begin
if j<>L then
begin
f := P[nl,j]; {function value at vertex j}
if f<VL then
begin
L := j; VL := f; {save new ‘low’}
end;
if f>VH then
begin