How to take gradient of matrix(21X21 dimension) with respect to a vector of(1X8) dimensions?

Hello all,

I have a function which is represented in matrix format with 21X21 components. It depends on 8 design variables and I want to calculate the gradient of this function with respect to these 8 design variables. So can somebody guide on how to calculate gradient of 21X21 matrix with respect to 1X8 dimension vector in Matlab? The expected answer is 21X21X8 dimension matrix. Any help in this matter would be appreciated, Thank you in advance,

Sincerely, Nikhil

Answer 1

[Walter Roberson]

vars = symvar(YourMatrix);
for K = length(vars) : -1 : 1
  MatrixGradient(:,:,K) = gradient(YourMatrix, vars(K));
end

[Nikhil]

Hey, Thank you for your answer! But I tried this approach on simple example. It is giving me an error as follows:

clear all;
vars=symvar('x1 2*(x2)+2;(x1)^2 (x2)^3');
syms x1 x2
M=[x1 2*(x2)+2;(x1)^2 (x2)^3];
for K=length(vars):-1:1
    MatrixGrad(:,:,K)=gradient(M,vars(K));
end

The error that I got is as follows: ??? Undefined function or method 'mtimes' for input arguments of type 'cell'.

Error in ==> gradient>parse_inputs at 130 loc(k) = {h*(1:indx(k))};

Error in ==> gradient at 49 [msg,f,ndim,loc,rflag] = parse_inputs(f,varargin);

Looking forward to your assistance in debugging this error, Thank you again,

Sincerely, Nikhil

[Walter Roberson]

syms x1 x2
M = [x1 2*(x2)+2;(x1)^2 (x2)^3];
vars = [x1 x2];
for K = length(vars):-1:1
    MatrixGrad(:,:,K) = diff(M,vars(K));
end

Answer 2

[Nikhil]

even following code is giving an error message

vars=symvar([x1 2*(x2)+2;(x1)^2 (x2)^3]);
for K=length(vars):-1:1
    MatrixGrad(:,:,K)=gradient([x1 2*(x2)+2;(x1)^2 (x2)^3],vars(K));
end

error:

??? Error using ==> zeros
Trailing string input must be a valid numeric class name.

Error in ==> gradient at 64
   g  = zeros(size(f),class(f)); % case of singleton dimension

Is it because I am using older version of matlab (r2011) ??