Evaluating a symbolic heaviside function using subs at points where disconuities are located

Question

Aleem Andrew 2020-10-26

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https://ww2.mathworks.cn/matlabcentral/answers/627013-evaluating-a-symbolic-heaviside-function-using-subs-at-points-where-disconuities-are-located

评论： Aleem Andrew 2020-10-30

When trying to evaluate a symbolic function, Matlab outputs 'Nan' when it encounters discontinuities.

syms x 
f = 22*heaviside(x - 5)*(x - 5) - 20*heaviside(x - 2)*(x - 2) - 20*heaviside(x - 3)*(x - 3) - 10*heaviside(x - 1)*(x - 1) + 28*x*heaviside(x)
fplot(diff(f,1),[-2 6])
x = [1 2 3 4] 
subs(diff(f,1))

The output is

ans =
[ NaN, NaN, NaN, -22]

However, I would like to know the value at 1+,2+,3+ and so on so the desired output is [18 -2 -22 -22]. Is there a way to deal with disconituities by outputting the function value as x approaches a particular value from the left or right without typing for example subs(diff(f,1.0001)) or subs(diff(f,1+eps))?

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Answer 1

Shubham Rawat 2020-10-30

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Hi Aleem,

You may use limit function for the discontinuities:

syms x 
f = 22*heaviside(x - 5)*(x - 5) - 20*heaviside(x - 2)*(x - 2) - 20*heaviside(x - 3)*(x - 3) - 10*heaviside(x - 1)*(x - 1) + 28*x*heaviside(x)
g = diff(f,1); % g is differentiation of f
limit(g,x,1,'right') % this gives the right limit of function g at x = 1

You may refer to the limit documentation page for further reference:

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