Extract operations from symbolic expression

Question

Cedric Kotitschke 2023-1-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1902120-extract-operations-from-symbolic-expression

编辑： Paul 2023-2-11

Hello,

given a symbolic expression, I want to extract the fundamental operations that take place in this symbolic expression. In the end, I want to create a Simulink model that does the same as the symbolic expression but without a simple matlab function block but with basic simulink blocks. For that, I need to know what happens to the inputs and in what order.

For example:

I have the symbolic expression z = cos(x)*y + y^2.

How exactly do I get the necessary information from the sym object? I want to extract that the cosine of x is computed which is then multiplied with y and then this product is added to the square of y.

Are there any built-in function that can help me with this? So far, the only solution I could think of was to parse the string generated by "simscapeEquation(z)"

Thanks so much!

2 个评论
显示无隐藏无

Walter Roberson 2023-1-28

在 MATLAB Online 中打开

If you have

z = cos(x)*y + y^2/cos(x)

then what would the desired output look like? For example are you hoping for a stream of RPN operations such as might be used for an HP29c calculator, with code like

x COS DUP y DUP SWAP2 * SWAP DUP * SWAP2 / +

? This specifies the stream of operations (and is at least partially optimized... I would have to think about whether you could do better by entering y first)

Cedric Kotitschke 2023-1-28

I'm not yet sure how the output should look like. I discovered that the Shunting yard algorithm at least brings the operation in the right order so that you can read it from left to right. But yes, a stream of RPN operations would be a good starting point

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Paul 2023-1-28

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1902120-extract-operations-from-symbolic-expression#answer_1158205

Hi Cedric

What's the objection to using a Matlab Function block? If that wasn't a constraint, you could use matlabFunctionBlock

Even if you break down the expression, what would be the next step for implementing all of the individual Simulink blocks to rebuild the expression in Simulink?

5 个评论
显示 3更早的评论隐藏 3更早的评论

Walter Roberson 2023-1-28

在 MATLAB Online 中打开

children does not give priority to anything in particular; it has access to the internal parse tree and just returns the child nodes of the given expression.

The representation of symbolic expressions is as a list. The list starts with a type tag; in a few cases the type tag is enough to fully determine the value of the object. If not, then the next item in the list may be a value (for example for an integer object. In the case of operations or function calls, the second value in the list (after the tag) is the link to the function name node, and values after that are the operands.

For example, cos(x) + y^2 could coded as the tree _plus(cos(x), _power(y,2)) and that can lead to OBJECT1: [EXPRESSION, cos, x], OBJECT2: [EXPRESSION, _power, y, 2], OBJECT3: [EXPRESSION, _plus, OBJECT1, OBJECT2]

and when you do children() on object3 it just throws away the EXPRESSION and function name, and returns a list of the remaining operands. children(OBJECT3) --> [LIST, OBJECT1, OBJECT2], and children(OBJECT2) -> [LIST, y, 2]

The MATLAB level gets returned back the LIST and converts it to a cell array.

Anyhow:

Instead of hasSymType you would probably want symFunType()

syms y f(x)

z = cos(x) + f(y^2)

z =

symFunType(z)

ans = "plus"

cellfun(@symFunType, children(z), 'uniform', 0)

ans = 1×2 cell array

{["f"]} {["cos"]}

Notice how the unknown function f got returned as the "type" of the expression f(y^2)

Paul 2023-1-29

编辑：Paul 2023-2-11

Yes, symFunType is what would be needed. Don't know how I didn't see that.

Assuming the original expression can be implemented in Simulink in the first place ....

One feasible apprroach may be to use symvar to find out the inputs to the epxression and create inport blocks for those, and create an outport block for the output

Then recurse as follows:

Check the symFunType of the expression.

Map the result to the a Simulink library block and add it to the model.

Determine if the expression has additional children that need to processed.

All while keeping track of the parent block to to which the children blocks need to be connected.

Don't know if that will really work, but it seems like it might.