I have a function at first defined anonymously inside the same script. After performing optimization through fminunc, it provides acceptable optimized parameter values.
f=@(A)0;
for i=1:1:size(c,1)
disp(i)
v(i,1)=(p2(i,1)-p1(i,1))/(sqrt(((p2(i,1)-p1(i,1)).^2)+((p2(i,2)-p1(i,2)).^2)+((p2(i,3)-p1(i,3)).^2)));
v(i,2)=(p2(i,2)-p1(i,2))/(sqrt(((p2(i,1)-p1(i,1)).^2)+((p2(i,2)-p1(i,2)).^2)+((p2(i,3)-p1(i,3)).^2)));
v(i,3)=(p2(i,3)-p1(i,3))/(sqrt(((p2(i,1)-p1(i,1)).^2)+((p2(i,2)-p1(i,2)).^2)+((p2(i,3)-p1(i,3)).^2)));
x=c(i,24)*((n-k+2)/127.59);
N11=BSpline1(k,t,x,n,periodic);
N22=BSpline2(k,t,x,N11,periodic);
N33=BSpline3(k,t,x,N22,periodic);
fx=@(A)0;fy=@(A)0;fz=@(A)0;
for j=1:1:(n+1)
fx=@(A)(fx(A)+A(j,1)*N33(j,1));
fy=@(A)(fy(A)+A(j,2)*N33(j,1));
fz=@(A)(fz(A)+A(j,3)*N33(j,1));
end
f=@(A)(f(A)+((p1(i,1)-fx(A))^2+(p1(i,2)-fy(A))^2+(p1(i,3)-fz(A))^2-(((p1(i,1)-fx(A))*v(i,1))+((p1(i,2)-fy(A))*v(i,2))+((p1(i,3)-fz(A))*v(i,3)))^2));
end
A0=ones(n+1,3);
[Aopt,fopt]=fminunc(f,A0);
But this implementation is very slow and to make it run faster I have separatly defined the function and also instead of for loops I used vector and matrix definition directly.
for i=1:1:size(c,1)
disp(i)
v(i,1)=(p2(i,1)-p1(i,1))/(sqrt(((p2(i,1)-p1(i,1)).^2)+((p2(i,2)-p1(i,2)).^2)+((p2(i,3)-p1(i,3)).^2)));
v(i,2)=(p2(i,2)-p1(i,2))/(sqrt(((p2(i,1)-p1(i,1)).^2)+((p2(i,2)-p1(i,2)).^2)+((p2(i,3)-p1(i,3)).^2)));
v(i,3)=(p2(i,3)-p1(i,3))/(sqrt(((p2(i,1)-p1(i,1)).^2)+((p2(i,2)-p1(i,2)).^2)+((p2(i,3)-p1(i,3)).^2)));
x=c(i,24)*((n-k+2)/128.689);
N11(:,i)=BSpline1(k,t,x,n,periodic);
N22(:,i)=BSpline2(k,t,x,N11,periodic);
N33(:,i)=BSpline3(k,t,x,N22,periodic);
end
function f=myObjective(A,N33,p1,v)
fxyz=N33.'*A;
D=p1-fxyz;
E1=D.^2;
E2=E1';
E3=sum(E2);
F1=(D.*v);
F2=F1';
F3=sum(F2);
F4=F3.^2;
G=E3-F4;
f=sum(G);
end
A0=ones(n+1,3);
[Aopt,fopt]=fminunc(@(A)myObjective(A,N33,p1,v),A0);
At same initial values in two cases (anonymous function and .m function) the objective function gives same values which means the function definition in two cases are same.
But after performing optimization in last case (.m function case), I get totally wrong values of input matrix.
n=3
Aopt=
-1.53685543885162 6.36319472017170 0.0251668191421513
13.1109550026546 -54.9314786364682 -0.248200752927807
37.2709897604245 49.3077792319788 -0.169381729039393
50.0220902870506 2.38624594683487 0.217368669572959
n=3
Aopt=
0.599435929547115 -26.1229467554614 -0.286717780987037
26.0699535504464 -0.642922198673024 -0.0939110197500202
1.00105690382098 1.00025671501624 0.999976771178033
1 1 1
How do I correct it?
