MATLAB function and symbolic function give different answers
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James Akula
le 5 Avr 2022
Modifié(e) : James Akula
le 21 Avr 2022
% 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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David Hill
le 5 Avr 2022
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
le 6 Avr 2022
Modifié(e) : Paul
le 6 Avr 2022
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.
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