Differentiate a 55 symbolic matrix by a 51 symbolic vector

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Tony Cheng 2018-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/435665-differentiate-a-5-5-symbolic-matrix-by-a-5-1-symbolic-vector

评论： Walter Roberson 2018-12-20

Hi there,

Here I have a symbolic matrix A with a size of 5*5. The elements inside is composed of 5 symbolic variables , i.e., a,b,c,d,e. These 5 varibales together make a 5*1 vector q =[a;b;c;d;e].

During the computation in the project, I need to compute the differentation of A by q, i.e.,

Is there any command can be used to realize that?

Thanks very much!

回答（3 个）

Walter Roberson 2018-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/435665-differentiate-a-5-5-symbolic-matrix-by-a-5-1-symbolic-vector#answer_352300

https://www.mathworks.com/help/symbolic/gradient.html

These days I hv tried to use arrayfun to make the codes more compact than those with for loop and diff code as shown in the figure. However, according to the syntax of arrayfun, I really do not know how to make it.

Could you pls write a command using arrayfun based on its syntax?

Here I hv a 5*5 matrix A, a 5*1 vector dd, and I want to derive

A and dd are both symbolic. and elements in A are composed of the five elements in dd.

Thank you very much for your great help!

Walter Roberson 2018-12-20

在 MATLAB Online 中打开

dd = sym('d', [1 5]);
rng(0); P1 = randi([-2 2],5,5); P2 = randi([-2 2],5,5); P3 = randi([-2 2],5,5); P4 = randi([-2 2],5,5); P5 = randi([-2 2], 5,5);
A = dd(1).^P1 .* dd(2).^P2 .* dd(3).^P3 .* dd(4).^P4 .* dd(5).^P5;
%A is now 5 x 5 involving the 5 different varialbes that are stored in dd
G = arrayfun(@(f) gradient(f, dd), A, 'uniform', 0);
%G is now a 5 x 5 cell array, each entry of which is the gradient of
%the corresponding entry of A with respect to the 5 different variables in dd
%if you want five panes of 5 x 5, one plane for each variable in dd, then
planes = permute(reshape(cat(3,G{:}),5,5,5),[2 3 1]);