MatLab function for correcting errors in input matrices using Hopfield Networks

hopfield.m

# hopfield(input, patterns)
#
# Usage Example: 
#   hopfield([0 0 0;0 0 0;1 1 1], {[1 1 1;0 0 0;0 0 0],[0 0 1;0 0 1; 1 1 1]})
#   ans =
#     0   0   1
#     0   0   1
#     1   1   1
#
# Arguments:
#   input:    square matrix of 0s and 1s
#   patterns: cell-array of square matrices with patterns to learn
#
function s = hopfield(input, patterns)
  threshold = 1;
  p = length(patterns); # The number of patterns

  # Preprocess the patterns
  for k = 1:p
    pattern = patterns{k};
    pattern(pattern==0)=-1; # Replace 0 with -1
    patterns{k} = pattern(:);   # Turn matrix into bit vector
    clear pattern
  end

  n = length(patterns{1}); # The number of bits (same for all patterns)
  w = zeros(n);      # Weights: n-by-n matrix filled by zeroes

  # The diagonal is always zero, so nothing to do.

  # The upper half triangle is computes using Hebb's Rule.
  for i = 1:n
    if i < n
      for j = i+1:n
        for k = 1:p
          w(i,j) += patterns{k}(i)*patterns{k}(j);
        end
        w(i,j) /= p;
      end
    end
  end
      
  # The bottom half triangle is copied from the upper half.
  for i = 1:n
    for j = 1:i
      w(i,j) = w(j,i);
    end
  end

  # Run updates
  s = input;
  for t = 1:10
    s2 = s;
    for i = 1:n
      sum = 0;
      for j = 1:n
        sum += w(i,j)*s(j);
      end
      if sum >= threshold
        s2(i) = 1;
      else
        s2(i) = -1;
      end
    end
    s = s2;
  end

  # Replace -1 with 0
  s(s==-1)=0;
  s = reshape(s, [sqrt(n),sqrt(n)]);
end