Page 204 - Compact Numerical Methods For Computers

Descent to a minimum I: variable metric algorithms 193
Algorithm 21. Variable metric minimiser (cont.)

acctol = 0.0001; {acceptable point tolerance -- see STEP 11}
reltest = 10.0; {to check equality of parameters -- see STEP 8}
var
accpoint : boolean, {to indicate an acceptable point}
B : array[1..Maxparm, 1..Maxparm] of real;
{approximation to inverse Hessian}
c : rvector; {to store last gradient}
count : integer; {to check for parameter equality}
D1, D2 : real; {temporary working storage}
f : real; {temporary function value}
funcount : integer; {count of function evaluations}
g : r-vector; {to hold gradient}
gradcount : integer; {count of gradient evaluations}
gradproj : real; {gradient projection on search vector}
i, j : integer; {working integers}
ilast : integer; {records last step at which B was
initialized to a unit matrix}
notcomp : boolean; {non-computability flag}
s : real; {inner product accumulator}
steplength: real; {linear search steplength}
t : rvector; {to store working vector for line search}
begin
writeln(‘alg21.pas -- version 2 1988-03-24’);
writeln(‘Variable metric function minimiser’);
fail:=false; {method has yet to fail}
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}
end
else {proceed with minimisation}
begin
Fmin:=f;{save the best value so far}
funcount:=l; {function count initialized to 1}
gradcount:=l; {initialize gradient count to 1}
fmingr(n, Bvec, Workdata, g); {STEP 2}
ilast:=gradcount; {set count to force initialization of B}
{STEP 3 -- set B to unit matrix -- top of major cycle}
repeat {iteration for method -- terminates when no progress can be
made, and B is a unit matrix so that search is a steepest
descent direction.}
if ilast=gradcount then
begin
for i:=1 to n do
begin
for j:=1 to n do B[i, j]:=0.0; B[i, i]:=1.0;
end; {loop on i}
end; {initialize B}
writeln(gradcount,’ ‘, funcount,’ ’, Fmin); {STEP 4}
write(‘parameters ’);
for i:=1 to n do write(Bvec[i]:10:5,’ ’);