Page 161 - Compact Numerical Methods For Computers

150 Compact numerical methods for computers
Algorithm 16. Grid search along a line (cont.)
var
j : integer;
h, p, t : real;
notcomp : boolean;
begin
writeln(‘alg16.pas-- one-dimensional grid search’);
{STEP 0 via the procedure call}
writeln(‘In gridsrch 1bound=‘,lbound,’ubound=‘,ubound);
notcomp:=false; {function must be called with notcomp false or
root will be displayed -- STEP 1}
t:=fnld(lbound, notcomp); {compute function at lower bound and set
pointer k to lowest function value found so far i.e. the 0’th}
writeln(’lbf(‘,lbound,‘)=‘,t);
if notcomp then halt;
fmin:=t; {to save the function value}
minarg:=0; {so far this is the lowest value found}
changarg:=0; {as a safety setting of this value}
h:=(ubound-lbound)/nint;
for j:=l to nint do {STEP 2}
{Note: we increase the number of steps so that the upper bound ubound is
now a function argument. Warning: because the argument is now
calculated, we may get a value slightly different from ubound in
forming (lbound+nint*h). }
begin
p:=fn1d(lbound+j*h, notcomp); {STEP 3}
write(’f(‘,lbound+j*h,‘)=‘,p);
if notcomp then halt;
if p<fmin then {STEP 4}
begin {STEP 5}
fmin:=p; minarg:=j;
end; {if p<fmin}
if p*t<=0 then
begin
writeln(‘ *** sign change ***‘);
changarg:=j; {to save change point argument}
end
else
begin
writeln; {no action since sign change}
end;
t:=p; {to save latest function value} {STEP 6}
end; {loop on j}
writeln( ‘Minimum so far is f( ‘,lbound+minarg*h,‘)=‘,fmin);
if changarg>0 then
begin
writehr(‘Sign change observed last in interval ‘);
writeln(‘[‘,lbound+(changarg-l)*h,‘,‘,lbound+changarg*h,‘]‘);
end
else
writeln(‘Apparently no sign change in [ ‘,lbound,‘,‘,ubound,‘]‘);
end; {alg16.pas == gridsrch}