Symbol matrix function differentiation

1.The function 'diff' seems could only work with one-element variable 'v',

diff(f,v); % f(v), v is a one-lelement variable

while I would like do differentiation on a symbol matrix

diff(F, V); % F(V), V is a symbol matrix variable

2.If I make differentiation to each element of the symbol matrix, and obtain the result of diff(F, V), while the result is in element by element format,

[g1(v_i), g2(v_i), ..., gn(v_i)]

so I want to know are there some methods to make the result in symbol matrix variable format like this?

g(V)

3.for example

diff(x^T*A*x, x) = A^T*x + A*x; % A is a constant matrix, x is a vector

Answer 1

[Walter Roberson]

If you want the result to be like in your (2) above, then use a "for" loop, or use

g = feval(symengine, 'zip', F, V, 'diff');

or use

g = cell2mat(arrayfun(@diff, F, V, 'Uniform', 0));

You might be able to just use

g = arrayfun(@diff, F, V);

but I think I recall seeing that have problems with arrayfun expecting numeric results.

[Youssef Khmou]

hi Walter, the first & last options :

 g=arrayfun(@diff, F, 2)  % or V generally
 g = cell2mat(arrayfun(@diff, f, 1, 'Uniform', 0))

do not work :

 ??? Error using ==> arrayfun
Unsupported ARRAYFUN input type: sym

[Walter Roberson]

Ah. Well there are always the syntax-disguised for loops:

g = reshape( cell2mat( arrayfun(@(K) diff(F(K), V(K)), 1:numel(F), 'Uniform', 0) ), size(F))

[chen xy]

Hi Walter, thx for answering. I already could obtain the result liked in (2) by using 'for' loop, what I want to do is like this: 1.type the command

diff(x.'*A*x, x)

2.the output is better as the follow

ans = 

    A.'*x + A*x

It seems be a very difficult work for implementation, I'd better deduce the formula on the paper as assistance.

[Walter Roberson]

If the .' represents transpose, then how could that be the correct output if A is not square?

[chen xy]

If A isn't square, "x.'*A*x" will be wrong for matrix dimensions.

[Walter Roberson]

True.