# error with optimisation

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Villanova on 20 Apr 2012
Hi, I was looking to do optimization for this http://4.bp.blogspot.com/-WSb8BrAmc9w/T5Hy2QaXJqI/AAAAAAAAAac/ZwDB5y19jAs/s1600/toric_optimization.jpg shape. I was wondering if someone could kindly point out my errors in this code:
% objective function for optimization
function F = toric_opt_obj(XX)
global alpha11 alpha12 alpha21 alpha22 alpha0
global icount
alpha11 = XX(1);
alpha12 = XX(2);
alpha21 = XX(3);
alpha22 = XX(4);
alpha0 = XX(5);
icount = icount + 1;
toric_obstacle;
% (x_1^2+x_2^2)^2+alpha12*x_1^2+alpha22*x_2^2+alpha11*x_1+alpha21*x_2+alpha0=0
toric =(z1.^2+z2.^2).^2+alpha12.*z1.^2+alpha22.*z2.^2+alpha11.*z1+alpha21.*z2+alpha0;
L1 = length(z1);
L2 = length(z2);
if z2 == -1*ones(1,L2)
Err_1 = toric - z1;
end
if (z2 == .8*ones(1,L2) && (-1.2*ones(1,L1) <z1< -.5*ones(1,L1)))
Err_2 = toric - z2;
end
if z2 == .5*ones(1,L2)
Err_3 = toric - z1;
end
if (z2 == .8*ones(1,L2) && (.6*ones(1,L1) <z1< 1.2*ones(1,L1)))
Err_4 = toric - z2;
end
Err = Err_1^2 + Err_2^2 + Err_3^2 + Err_4^2;
% Err = (z1.^2+z2.^2).^2+alpha12*z1.^2+alpha22*z2.^2+alpha11*z1+alpha21*z2+alpha0;
F = norm(Err); %error square root of the sum of the error squared
[icount XX F]
this part of code is right which is
% Minimum error - toric section
clear all; clc;
global alpha11 alpha12 alpha21 alpha22 alpha0
alpha11 = 0;
alpha12 = -2;
alpha21 = .2;
alpha22 = -1.5;
alpha0 = .5;
% initial limity cycle shape
ii0 = 0;
for x10=-1.5:.01:1.5
x20 = roots([1 0 (2*x10^2+alpha22) alpha21 (alpha0+alpha11*x10+alpha12*x10^2+x10^4)]);
for ii=1:4
if isreal(x20(ii))
ii0 = ii0 + 1;
x1lci(ii0) = x10;
x2lci(ii0) = x20(ii);
end
end
end
XX0 = [alpha11 alpha12 alpha21 alpha22 alpha0];
lb = [-.1 -3 .01 -2 .3];
ub = [ .1 -1 .40 -1 .7];
optionso = optimset('LargeScale','off','MaxFunEvals',150);
%norm_tol = .01;
%icount = 0;
% [XX,fval,exitflag,output] = fmincon(@objfun,XX0,[],[],[],[],lb,ub,@confun,optionso)
[XX,fval,exitflag,output] = fminsearch(@toric_opt_obj,XX0)
alpha11 = XX(1);
alpha12 = XX(2);
alpha21 = XX(3);
alpha22 = XX(4);
alpha0 = XX(5);
%alpha22=-2.124;
% optimal limity cycle shape
ii0 = 0;
for x10=-1.5:.01:1.5
x20 = roots([1 0 (2*x10^2+alpha22) alpha21 (alpha0+alpha11*x10+alpha12*x10^2+x10^4)]);
for ii=1:4
if isreal(x20(ii))
ii0 = ii0 + 1;
x1lco(ii0) = x10;
x2lco(ii0) = x20(ii);
end
end
end
toric_obstacle;
figure (1)
plot(z1,z2,'k-',x1lci,x2lci,'b*',x1lco,x2lco,'ro','LineWidth',2);
legend('obstacle','initial','optimal');
and this is my obstacle m-file:
% obstacle definition
x0 = -1.2;
y0 = -1;
x1 = -0.6;
y1 = -0.5;
x2 = 0.6;
x3 = 1.2;
y3 = 0.8;
delta = 0.01;
%line 1
i = 0;
for x = x0:delta:x3
i = i + 1;
z1(i) = x;
z2(i) = y0;
end
%line 2
i = i - 1;
for y = y0:delta:y3
i = i + 1;
z1(i) = x3;
z2(i) = y;
end
%line 3
i = i - 1;
for x = x3:-delta:x2
i = i + 1;
z1(i) = x;
z2(i) = y3;
end
%line 4
i = i - 1;
for y = y3:-delta:y1
i = i + 1;
z1(i) = x2;
z2(i) = y;
end
%line 5
i = i - 1;
for x = x2:-delta:x1
i = i + 1;
z1(i) = x;
z2(i) = y1;
end
%line 6
i = i - 1;
for y = y1:delta:y3
i = i + 1;
z1(i) = x1;
z2(i) = y;
end
%line 7
i = i - 1;
for x = x1:-delta:x0
i = i + 1;
z1(i) = x;
z2(i) = y3;
end
%line 8
i = i - 1;
for y = y3:-delta:y0
i = i + 1;
z1(i) = x0;
z2(i) = y;
end
i = i - 1;
z1 = z1(1:i);
z2 = z2(1:i);
Villanova on 24 Apr 2012
I get this error message:
??? Operands to the || and && operators must be convertible to logical
scalar values.
Error in ==> toric_opt_obj at 24
if (z2== .8*ones(1,L2) && (-1.2*ones(1,L1) <z1< -.5*ones(1,L1)))
Error in ==> fminsearch at 205
fv(:,1) = funfcn(x,varargin{:});

Walter Roberson on 24 Apr 2012
Use & instead of && .
Read the documentation for all() and any()
a < b < c is interpreted as (a < b) < c . The first part produces a logical value, 0 or 1, and it is that logical value that is compared to c. Consider using (a < b & b < c)

Villanova on 26 Apr 2012
I also have this error :(
Undefined function or variable "Err_1".
Error in ==> toric_opt_obj at 36
Err = Err_1^2 + Err_2^2 + Err_3^2 + Err_4^2;
Walter Roberson on 26 Apr 2012
Please show the current code for the "if" lines, including the current version of
if z2 == -1*ones(1,L2)
Please also show L2, and size(z2)

Villanova on 26 Apr 2012
hi the if was ok i believe. the only thing wrong seemed to be &&. So I didn't change much: this is the new one:
function F = toric_opt_obj(XX)
global alpha11 alpha12 alpha21 alpha22 alpha0
global icount
alpha11 = XX(1);
alpha12 = XX(2);
alpha21 = XX(3);
alpha22 = XX(4);
alpha0 = XX(5);
icount = icount + 1;
toric_obstacle;
% (x_1^2+x_2^2)^2+alpha12*x_1^2+alpha22*x_2^2+alpha11*x_1+alpha21*x_2+alpha0=0
toric =(z1.^2+z2.^2).^2+alpha12.*z1.^2+alpha22.*z2.^2+alpha11.*z1+alpha21.*z2+alpha0;
L1 = length(z1);
L2 = length(z2);
if z2 == -1*ones(1,L2)
Err_1 = toric - z1;
end
if (z2 == .8*ones(1,L2) & (-1.2*ones(1,L1) <z1< -.5*ones(1,L1)))
Err_2 = toric - z2;
end
if z2 == .5*ones(1,L2)
Err_3 = toric - z1;
end
if (z2 == .8*ones(1,L2) & (.6*ones(1,L1) <z1< 1.2*ones(1,L1)))
Err_4 = toric - z2;
end
Err = Err_1^2 + Err_2^2 + Err_3^2 + Err_4^2;
% Err = (z1.^2+z2.^2).^2+alpha12*z1.^2+alpha22*z2.^2+alpha11*z1+alpha21*z2+alpha0;
F = norm(Err); %error square root of the sum of the error squared
[icount XX F]

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