Livescript results in incorrect Math output

When using a LiveScript for symbolic math, I noticed a presumed bug in which the script outputs the incorrect value for an evaluation. When running the same equation(s) in the command window, the correct value is calculated. I tried restarting MATLAB but no change. It is concerning to me that the LiveScript is somehow providing erroneous calculations. What causes this?

Offending line of code is at the bottom; the rest is just in case you want to run it as a script yourself.

clear all
sympref('AbbreviateOutput',false); sympref('MatrixWithSquareBrackets',true);
syms x1 x2

f = -x1*x2 %objective function
g1 = (1/9)*x1^2 + (1/4)*x2^2 - 1 %given inequality constraint
g2 = -x1 %bounds set as inequality constraints
g3 = x1 - 3
g4 = -x2
g5 = x2 - 2

lambda_j = 1     %initialize inequality lagrange parameter
rp = 1          %initialize penalty parameter
b = 20          %initialize penalty adjustment parameter 'beta'
k = 1; %first ALM iteration
x = [2.5; 1.6] %initial design point

psi_j = max(subs(g1,[x1;x2],x), -lambda_j/(2*rp))
if subs(g1,[x1;x2],x) > 0 %if inequality is violated
    A = f + lambda_j*psi_j + rp*psi_j^2
else %if no constraints are violated
    A = f
end
c = subs(gradient(A),[x1;x2],x) %gradient of objective function at current point
d = -c
% Analytically solve for astar
syms alpha_star
xnew = x + alpha_star*d %update design point with alpha_star
% Solve for alpha using necessary condition df/da = 0
fa = subs(A,[x1;x2],xnew) %create alpha function
df_da = diff(fa)
astar = solve(df_da,alpha_star);
displaySymSolution(astar);
s = astar*d %calclulate the change in design
xnew = x + astar*d %update design point numerically
x = xnew;

%lambda_j + 2*rp*max(subs(g1,[x1;x2],x), -lambda_j/(2*rp)) some issue with
%the live script here makes the lambda_j update incorrect. Must manually
%update.
lambda_j = 1.6689

Lambda_j should == 1.6689; however, the LiveScript outputs '0' while the command window will output '1.6689' for the same code.

[Cris LaPierre]

What code are you running in the command window vs the live script? I get the same result running the following code in both places:

clear all
sympref('AbbreviateOutput',false); sympref('MatrixWithSquareBrackets',true);
syms x1 x2

f = -x1*x2 %objective function

f = 

g1 = (1/9)*x1^2 + (1/4)*x2^2 - 1 %given inequality constraint

g1 = 

g2 = -x1 %bounds set as inequality constraints

g2 = 

g3 = x1 - 3

g3 = 

g4 = -x2

g4 = 

g5 = x2 - 2

g5 = 

lambda_j = 1     %initialize inequality lagrange parameter

lambda_j = 1

rp = 1          %initialize penalty parameter

rp = 1

b = 20          %initialize penalty adjustment parameter 'beta'

b = 20

k = 1; %first ALM iteration
x = [2.5; 1.6] %initial design point

x = 2×1

2.5000 1.6000

psi_j = max(subs(g1,[x1;x2],x), -lambda_j/(2*rp))

psi_j = 

if subs(g1,[x1;x2],x) > 0 %if inequality is violated
    A = f + lambda_j*psi_j + rp*psi_j^2
else %if no constraints are violated
    A = f
end

A = 

c = subs(gradient(A),[x1;x2],x) %gradient of objective function at current point

c = 

d = -c

d = 

% Analytically solve for astar
syms alpha_star
xnew = x + alpha_star*d %update design point with alpha_star

xnew = 

% Solve for alpha using necessary condition df/da = 0
fa = subs(A,[x1;x2],xnew) %create alpha function

fa = 

df_da = diff(fa)

df_da = 

astar = solve(df_da,alpha_star);
displaySymSolution(astar);

astar = 

s = astar*d %calclulate the change in design

s = 

xnew = x + astar*d %update design point numerically

xnew = 

x = xnew;

lambda_j + 2*rp*max(subs(g1,[x1;x2],x), -lambda_j/(2*rp))

ans = 

0

[Colton Campbell]

Ah yes I see... I was not updating the x-value when executing in the command window. Thank you!

Answer 1

[Chris]

The commented-out line is:

lambda_j + 2*rp*max(subs(g1,[x1;x2],x), -lambda_j/(2*rp))

lambda_j is 1. The second term (which uses the second argument to max(), containing lambda_j) is -1. The sum of the two is zero.

[Colton Campbell]

Ah yes I see... I was not updating the x-value when executing in the command window. Thank you!