Why do I receive the error in horzcat?

I'm supposed to solve a convex optimization problem, where I take a specific Newton step and later I use a terminating condition which gives me the solution. However, I receive the horzcat error in the Newton step, even though I believe it is completely correct and it follows exactly the theory. Here's the code:

A = 0.1;
b = 0.5;
x0 = 1;
tol = 1e-3;
[x, xx] = Optimization_Lab1(A, b, x0, tol)

Error using horzcat
Dimensions of arrays being concatenated are not consistent.

Error in solution>Optimization_Lab1 (line 39)
H = [blkdiag(ddf(x), zeros(n)) A' ; A zeros(m)];

function [x, xx] = Optimization_Lab1(A, b, x0, tol)
% [x, xx] = opt(A, b, x0, tol)
%
% Solves 
% min  f(x) = sum(x log(x))
% s.t.    Ax = b
% with Newton method.
%
% Input:
% x0  : feasible startingpoint
% tol : tolerance
%
% Output:
% x  : answer
% xx : solution sequence
%
% Initialize constants
ALPHA = 0.1;
BETA = 0.5;
MAXITER = 100;
% Initialize variables
[m, n] = size(A);
xx = zeros(n,MAXITER);
% Define function, gradient and Hessian
f = @(x) sum(x.*log(x));
df = @(x) log(x)+1;
ddf = @(x) diag(1./(x));
% Main loop
x = x0;
for outer = 1:MAXITER
   % Find search direction
   g = -df(x);
   H = [blkdiag(ddf(x), zeros(n)) A' ; A zeros(m)];
   dxv = H\[g; zeros(n,1); zeros(m,1)];
   dx = dxv(1:m);
   
  xx(:,outer) = x;
   
   % Check terminating condition
   l2 = g'*dx;
   if (l2/2 <= tol)
       xx = xx(:,1:outer);
       x = xx(:,outer);
       return;
   end
   
   % Calculate steplength
   t = 1;
   % Check to see that we are in the domain of f
   while(min((x+t*dx)) <= 0); t = t * BETA; end
   % Calculate steplength
  while(f(x+t*dx) > f(x) + t*ALPHA*df(x)'*dx); t = t*BETA; end
   
   % Take step
   x = x + t*dx;
   
end
end

Input arguments: A=0.1 B=0.5 x0=1 tol=100

The error shows up in the second line under the comment "Search direction".

Answer 1

[Torsten]

blkdiag(ddf(x), zeros(n))

is 2x2,

A'

is 1x1.

Thus it's not possible to concatenate the two horizontally in the command

H = [blkdiag(ddf(x), zeros(n)) A' ; A zeros(m)];

I don't know what the intention of the author of the code was - so I can't help you on how to modify this line.

It will be best to contact the author directly.

[Tilemachos Marmaras]

Thank you!

Answer 2

[Image Analyst]

This happens when you're trying to stitch together, side-by-side, arrays that don't have the same number of rows. For example you can stitch together a 3x2 array with a 3x7 array because they both have 3 rows, but you can't stitch an array with 100 rows next to an array with only 3 rows. You'd have different number of rows in each column and that's not allowed because arrays must be fully rectangular with no "ragged" edges. All elements must be filled with something.

% This will work
m1 = rand(3,2);
m2 = rand(3,7);
m = [m1, m2]

m = 3×9

0.3880 0.2764 0.6785 0.2982 0.6680 0.6617 0.0910 0.0217 0.6808 0.3682 0.4101 0.2743 0.2297 0.1835 0.3036 0.7122 0.3195 0.5432 0.2983 0.6628 0.6712 0.0703 0.2836 0.4501 0.0758 0.1870 0.6469

% This won't work.
m1 = rand(3,7);
m2 = rand(100,7);
m = [m1, m2]

Error using horzcat
Dimensions of arrays being concatenated are not consistent.