MATLAB function and symbolic function give different answers

Question

James Akula 2022-4-5

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1689225-matlab-function-and-symbolic-function-give-different-answers

编辑： James Akula 2022-4-21

% Some values for the plot
A = 0.5
B = 2
% MATLAB and symbolic functions generated two ways
f = @(a, b, x) (a .* (x - b).^2) .* ((x - b) >= 0)
fsym = sym(f); % Uncommenting this line hangs Live Script
syms a b x
fsym2(a, b, x) = (a * (x - b)^2) * ((x - b) >= 0); % Uncommenting this line hangs Live Script
% Plot both functions
figure
X = (0:0.001:3*B);
subplot(1, 3, 1)
plot(X, f(A, B, X), '-r')
title('MATLAB function')
subplot(1, 3, 2)
plot(X, subs(subs(subs(fsym, sym('a'), A), sym('b'), B), sym('x'), X), '-b')
title('Function from sym')
subplot(1, 3, 3)
plot(X, fsym2(A, B, X), '-b')
title('Declared symbolic function')

I am trying to get better at using symbolic functions. I am struggling to understand why the two symbolic subplots do not appear identical (other than color) to the subplot generated by the MATLAB function. Can someone explain why, and what I would do to create a "working" symbolic version of f?

As an aside, both lines 7 and 9 hangs the Live Editor if uncommented...does that suggest a bug in what I am doing?

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Answer 1

David Hill 2022-4-5

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1689225-matlab-function-and-symbolic-function-give-different-answers#answer_935490

在 MATLAB Online 中打开

A = 0.5;
B = 2;
f = @(a, b, x) (a .* (x - b).^2) .* ((x - b) >= 0);
syms a b x;
fsym1 = piecewise((x-b)>=0,(a * (x - b)^2),(x-b)<0,0); 
figure
X = (0:0.001:3*B);
subplot(1, 3, 1)
plot(X, f(A, B, X), '-r')
title('MATLAB function')
subplot(1, 3, 2)
fsym=subs(fsym1,[a b],[A B]);
fplot(fsym,[0,3*B]);
title('Function from sym')

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Paul 2022-4-6

编辑：Paul 2022-4-6

在 MATLAB Online 中打开

The result from fsym2 can be explained as follows. However, there might be something odd going on because the Live editor can't render the result, so I'll copy/paste from my local installation.

syms a z
fsym2 = a*(z>=0);

On the right hand side, 'a' is symbolic varibale and 'z >= 0' is an equation. So the the multiplication by 'a' distributes across the equation as it would in a standard mathematical sense. Recall that multiplying an inequality by a negative number reverses the direction of the inequality. Also, the sign of 'a' is unknown absent any additional assumptions, so multiplying through by 'a' has to account for the cases of a <= 0 and a > = 0. The result is

fsym2 = piecewise(0 <= a, 0 <= a*z, a <= 0, a*z <= 0)

The bottom line is that in Symbolic math 'z >= 0' is a math equation, whereas in base Matab 'z >= 0' is an expression to be evaluated to T/F and then converted to double.

James Akula 2022-4-20

编辑：James Akula 2022-4-21

I think this explains it. It is weird behavior though...might catagorize it as a bug. Certainly, the fact that piecewise seems to crash the live editor is a problem!

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