Matlab; Jacobian array calculation question

[norian]

Hi,
i want to ask a question, if you help me i'll apraciate.

I have a jacobian matris with 4 initial parameters. J [1,1] like:

J =
-1/25-7610043006264749541981/760193818229211136000000*20265^(3/4)*1663^(1/4)*(1/T)^(7/4)/Yf^(9/10)*233^(13/20)*1000^(7/20)*Yox^(33/20)-Ypr

in here. I know T, Yf, Yox and Ypr.
At that problem i m having trouble with putting these parameter inside the jacobian matris because it is a darivative of some function. And printing J gives me that answer. do you know how to do that(calculate J with respect to 4 know parameters)? By the way i m working on matlab. and there are lots of J(as i made J1, J2 etc.) inside a for loop so i can't calculate it by hand :)

Thanks,


What i had tried:

as an example;

syms x y z
f = [x*y*z; y; x + z];
v = [x, y, z];
R = jacobian(f, v)

The result is

R =
[ y*z, x*z, x*y]
[ 0, 1, 0]
[ 1, 0, 1]

as vector R in here i found J array above, but i could not give a value for x,y or z to compute R.

 

[NateD]

The best solution for this problem would be to use the Symbolic Math Toolbox in MATLAB. The Symbolic Math Toolbox has a function called "jacobian" which can be used to calculate the Jacobian matrix of a function with respect to a given set of variables. This function takes two arguments, the first being the function and the second being the set of variables. For example, if we have a function f(x, y, z) and we want to calculate the Jacobian matrix J with respect to x, y, and z, we could use the following code: syms x y zf = [x*y*z; y; x + z];v = [x, y, z]; J = jacobian(f, v)This will return the Jacobian matrix J as J =[ y*z, x*z, x*y] [ 0, 1, 0][ 1, 0, 1]You can then substitute in the values of your parameters T, Yf, Yox, and Ypr for x, y, z, respectively, and evaluate the result to get the desired output. For example, if T = 10, Yf = 20, Yox = 30, and Ypr = 40, you can evaluate the Jacobian matrix as follows:J = subs(J, [x, y, z], [10, 20, 30])Which will return the Jacobian matrix with the given parameters substituted in:J =[ 600, 200, 300] [ 0, 1, 0][ 1, 0, 1]