Differentiate a 5*5 symbolic matrix by a 5*1 symbolic vector

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!

Answer 1

[Walter Roberson]

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

[madhan ravi]

+1 , that makes everything clear

[Tony Cheng]

gradient does not work.

[Walter Roberson]

arrayfun(@(a) gradient(a,v), A, 'uniform', 0)

[Tony Cheng]

Hi Walter,

so you mean

arrayfun(@(dd) gradient(f,dd), A, 'uniform', 0)

specifically to the proposed question?

According to the syntax of arrayfun, I am not sure what does A mean...

[Walter Roberson]

"Here I have a symbolic matrix A with a size of 5*5"

[Tony Cheng]

Hi Walter,

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]

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]);

Answer 2

[madhan ravi]

diff() %?

Answer 3

[Tony Cheng]

diff can be used to differentiate a scalar or vector by a scalar, but not differentiate a matrix by a vector.

[madhan ravi]

can you upload the sample of your vector and matrix ?

[Tony Cheng]

Hi man,

the following is just an example. The true matrix is more complex than the one in the following.

syms a b c  d e 
f = [a   b c d 5*e                   ;
     a+c b+c 2*a a^b  c^e            ;
     3* a+c b+3*c 5*a  e+d+a  a- b-c ;
     b c e d  a ;
     a+c  d+e  c+b  a-c-e  e+f+a ] ; 
 dd = [a;b;c;d;e] ;

[Tony Cheng]

Here I want to compute

[madhan ravi]

Fine ,understood now , what would be your desired result (post the output that you expect from the example above)?

[Tony Cheng]

I have a solution like this.