How can i take the Jacobian of a function

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Martijn Mouw
Martijn Mouw 2018-6-25
评论： Martijn Mouw 2018-6-26
Hi there, I have a problem that I need to be solved quickly. I need the Jacobian of a function with respect to one of its input values and afterwards to fill in the values of the input. These are the input values and jacobian function:
if true
x = [5 7]
b = [2 3]
h = jacobian(qn(x,b),x)
end
This is the function itself:
if true
function demand = qn(x,b)
z1=b(1)-b(2)*x(1)+b(1)*x(2);
z2=b(1)-b(2)*x(2)+b(1)*x(1);
demand = [z1;z2];
end
However, I receive an error message saying:
"Undefined function 'jacobian' for input arguments of type 'double'.
Error in Algorithm3 (line 21) h = jacobian(qn(x,b),x);"
To recap, I need the Jacobian of the function qn with respect to x(1) and x(2), so that it gives a 2 by 2 matrix back and then I want to 'input' the vectors x & b. Thanks in advance!
  2 个评论
Adam
Adam 2018-6-25
Are you expecting it to find a function called jacobian? There is one in the symbolic Toolbox, but otherwise unless you have a 3rd party one or one you have written yourself the error is understandable.
Martijn Mouw
Martijn Mouw 2018-6-25
Well I have the symbolic Toolbox and for other problems the command 'jacobian' works fine, however when I try to find the jacobian matrix of a function specified with input variables ('qn' in this case) I don't know how to tell MATLAB that I want the jacobian matrix of the output of this function with respect to x(1) and x(2)

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采纳的回答

Torsten
Torsten 2018-6-25
function main
x = [5 7]
b = [2 3]
h = numerical_jacobian(@qn,x,b)
end
function df=numerical_jacobian(f,x,b)
n=length(x);
E=speye(n);
e=eps^(1/3);
for i=1:n
df(:,i)=(f(x+e*E(:,i),b)-f(x-e*E(:,i),b))/(2*e); % zentraler Differenzenquotient
end
end
function demand = qn(x,b)
z1=b(1)-b(2)*x(1)+b(1)*x(2);
z2=b(1)-b(2)*x(2)+b(1)*x(1);
demand = [z1;z2];
end
  4 个评论
显示 2更早的评论
Torsten
Torsten 2018-6-26
编辑：Torsten 2018-6-26
1. As far as I know, "jacobian" only works with symbolic variables.
2. Everybody uses other values as optimal h for numerical differentiation. Just test for your case which order of magnitude fits your needs.
Here is a link that derives h ~ eps^(1/3) for the central difference quotient:
https://math.stackexchange.com/questions/815113/is-there-a-general-formula-for-estimating-the-step-size-h-in-numerical-different
Best wishes
Torsten.

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