Why is cumsum not working with symbolic vectors?

user_4027729 0
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I wrote a small Octave script involving cumsum on symbolic vectors, which I expected to work but unfortunately, it does not. Here's the code:

pkg load symbolic
n = 3;
syms q x
q = sym('q', [n 1]);
x = sym('x', [n 1]);
cumsum(q - x)

Instead of the expected result, I get:

error: cumsum: wrong type argument 'class'

Why does this happen? Would it work with Matlab Symbolic Toolbox? (I don't have it so I cannot test, unfortunately.)

cumsum symbolic-math octave
2 Answers

That's just because cumsum written in Octave is not supported for symbolic elements as indicated by the error message. Your code gives the following in MATLAB:

ans =
                     q1 - x1
           q1 + q2 - x1 - x2
 q1 + q2 + q3 - x1 - x2 - x3

You can do something like this:

t1 = q-x;
t2 = triu(ones(numel(t1)));
sum(repmat(t1,1,3).*t2).'
% repmat is necessary here because implicit expansion is also not 
% supported for matrices of class sym in Octave

Above code in Octave and MATLAB gives the following respectively:

ans = (sym 3×1 matrix)

  ⎡            q₁₁ - x₁₁            ⎤
  ⎢                                 ⎥
  ⎢      q₁₁ + q₂₁ - x₁₁ - x₂₁      ⎥
  ⎢                                 ⎥
  ⎣q₁₁ + q₂₁ + q₃₁ - x₁₁ - x₂₁ - x₃₁⎦

ans =
                     q1 - x1
           q1 + q2 - x1 - x2
 q1 + q2 + q3 - x1 - x2 - x3
user_56986720

At the risk of stating the obvious, this can be impemented as a for loop.
Here is one implementation.

function Y = cumsum( X, N )
    if nargin < 2, N = 1; end
    YDims = size( X );  NDim = YDims(N); Y = sym( zeros( YDims ) );
    XIdx = substruct( '()', repmat( {':'}, 1, ndims( X ) ) );
    YIdx = substruct( '()', repmat( {':'}, 1, ndims( Y ) ) );
    for i = 1 : NDim
        XIdx.subs{N} = 1 : i;
        YIdx.subs{N} = i;
        Y = subsasgn( Y,
                      YIdx,
                      sum( subsref( X, XIdx ), N )
                    );
    end
end

Copy this in your symbolic installation folder1 as cumsum.m and your above script will work as in matlab.

1: (in my case this was ~/.octave/symbolic-2.9.0/@sym/cumsum.m because I have set my pkg prefix as ~/.octave )

user_41831910
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