Why the seond arugment in the command jacobian is not a vector of variables?
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Hi guys, I am using the code Jacobian in Matlab to symbolically compute the Jacobian matrix for two vectors-A and B.
These two vectors are defined by some symbolic variables and they are all functions of the variable t as follows:
syms t a1(t) a2(t) a3(t) b1(t) b2(t) b3(t)
A = [a1(t) ; a2(t) ; a3(t) ] ;
B = [b1(t) ; b2(t) ; b3(t) ] ;
What I did is C = jacobian(A , B ) .
However, Matlab gives an error to me and says the second argument must be a vector of variables.
I am very confused: the second argument B is obviously 3 times 1 symbolic vector. Why the code is not write?
Can anyone offer me some solutions?
Many thanks!
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Stephan
2019-4-9
编辑:Stephan
2019-4-9
Hi,
you declare b1...b3 as symbolic functions of t - not as symbolic variables. Thats why it doesnt work.
Here is an example:
syms a1(t) a2(t) a3(t) b1 b2 b3
a1(t) = b1*sin(t)/(b2+b3);
a2(t) = 3*t + 5/b2+b3;
a3(t) = 4/t^b3-b1;
A = [a1 a2 a3] ;
B = [b1; b2; b3];
C = jacobian(A ,B)
results in:
C(t) =
[ sin(t)/(b2 + b3), -(b1*sin(t))/(b2 + b3)^2, -(b1*sin(t))/(b2 + b3)^2]
[ 0, -5/b2^2, 1]
[ -1, 0, -(4*log(t))/t^b3]
See the different symbolic types in this simple example:
>> syms a(t) b
>> whos
Name Size Bytes Class Attributes
a 1x1 8 symfun
b 1x1 8 sym
t 1x1 8 sym
Best regards
Stephan
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Stephan
2019-4-9
编辑:Walter Roberson
2023-4-11
Why do you want to do this? Can you explain the context?
Here is a little dirty workaround, that lets you have all the b's as functions of t:
syms a1(t) a2(t) a3(t) b1(t) b2(t) b3(t)
a1(t) = b1(t)*sin(t) + b2 - b3;
a2(t) = b2(t)*cos(t) + 2*b3*b1;
a3(t) = b3(t)*3*t^2 - b2^2;
A(1:3) = [a1 a2 a3]
B(1:3) = [b1 b2 b3]
C_help = sym(zeros(3));
for ii = 1:3
C_help(ii,:) = functionalDerivative(A(ii),B);
end
C(t) = C_help
gives:
A =
[ b2(t) - b3(t) + b1(t)*sin(t), 2*b1(t)*b3(t) + b2(t)*cos(t), 3*t^2*b3(t) - b2(t)^2]
B =
[ b1(t), b2(t), b3(t)]
C(t) =
[ sin(t), 1, -1]
[ 2*b3(t), cos(t), 2*b1(t)]
[ 0, -2*b2(t), 3*t^2]
To check the results we use jacobian - where b1...b3 can not be functions of t, but variables:
syms a11(t) a22(t) a33(t) b11 b22 b33
a11(t) = b11*sin(t) + b22 - b33;
a22(t) = b22*cos(t) + 2*b33*b11;
a33(t) = b33*3*t^2 - b22^2;
AA = [a11 a22 a33]
BB = [b11 b22 b33]
CC = jacobian(AA,BB)
which is:
AA(t) =
[ b22 - b33 + b11*sin(t), 2*b11*b33 + b22*cos(t), - b22^2 + 3*b33*t^2]
BB =
[ b11, b22, b33]
CC(t) =
[ sin(t), 1, -1]
[ 2*b33, cos(t), 2*b11]
[ 0, -2*b22, 3*t^2]
So the given workaround appears to give correct results, including b1...b3 to be functions of t.
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