Why doesn't matlabFunction properly vectorize the state of an ode system?

Question

Matthias Prechtl 2020-9-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/594886-why-doesn-t-matlabfunction-properly-vectorize-the-state-of-an-ode-system

评论： Matthias Prechtl 2020-9-27

Hey all,

i have reduced my problem to this simple demo case, where i define some ode, reduce its order with odeToVectorField and convert it to a matlab function.

t = sym('t');
c = sym('c');
d = sym('d');
x = str2sym('x(t)');
V = odeToVectorField(diff(diff(x)) == c + d);
matlabFunction(V, 'vars', {t, 'Y', [c; d]})

Outputs:

@(t,Y,in3)[Y(2);in3(1,:)+in3(2,:)]

With the parameters, it correctly vectorizes the parameter access, e.g. in3(2,:) instead of in3(2).

How can i get matlabFunction to vectorize the state as well, e.g. Y(2,:) instead of Y(2)?

Desired output:

@(t,Y,in3)[Y(2,:);in3(1,:)+in3(2,:)]

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Answer 1

Divija Aleti 2020-9-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/594886-why-doesn-t-matlabfunction-properly-vectorize-the-state-of-an-ode-system#answer_500377

The symbols 'c' and 'd' can either be scalars or vectors.The vectorization for 'in3' is done as 'in3(1,:)' and 'in3(2,:)' so that they access the entire first and second rows of the matrix '[c; d]' respectively. However, the function 'odeToVectorField' returns a symbolic vector. Hence, the output shows 'Y(2)' and not 'Y(2,:)'.

Have a look at the following link to understand the algorithm used and what the symbol 'Y' means. A few examples are given too.

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

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Matthias Prechtl 2020-9-27

The underlying algorithm is clear based on engineering classes, 'Y' represents the system as a set of differential equations reduced to first order.

What's not clear to me is what changes i have to take to vectorize the outcoming equations automatically for more efficient solving. I can't find any hints in the document you linked.

I can manually modify the output of matlabFunction, but for sake of clarity and flexibility in my implementation, i'd like to automate that part.

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