plot using matlab(parabolic)

Question

Carc 2023-1-25

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编辑： John D'Errico 2023-1-25

This is watt sepctrum equation, but i don't know why my plot is weired. The plot might be parabolic shape, but mine is not. Could you let me know what's the problem?

x = linspace(10,10^7);

y = 0.453 .* exp(-1.036 .* x) .* sinh((2.29.* x).^0.5);

plot(x,y);

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Answer 1

John D'Errico 2023-1-25

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It IS curved, though not truly parabolic. A parabola means something specific about the shape, as a polynomial curve. But you just need to look carefully at what you have done. I'll do this for fewer points.

x = linspace(10,10^7,20)
x = 1×20
1.0e+07 *

    0.0000    0.0526    0.1053    0.1579    0.2105    0.2632    0.3158    0.3684    0.4211    0.4737    0.5263    0.5789    0.6316    0.6842    0.7368    0.7895    0.8421    0.8947    0.9474    1.0000
y = 0.453 .* exp(-1.036 .* x) .* sinh((2.29.* x).^0.5)
y = 1×20
1.0e-03 *

    0.8590       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN

So what happened? you had numerical problems. Do you see the NaNs there?

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Walter Roberson 2023-1-25

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Note the exp(negative of large large number)

format long g
-1317311753049245359/134217728000
ans = 
         -9814737.38736842

exp() of negative 10 million is going to be tiny.

John D'Errico 2023-1-25

编辑：John D'Errico 2023-1-25

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Sorry. I had to end that answer before I was really finished writing. The point is, you are going out as far as 1e7 in x. What happens when x is REALLY REALLY large?

x = 1e7;
exp(-1.036 .* x)
ans = 0

So that subexpression underflows. But what is

sinh((2.29.* x).^0.5)
ans = Inf

And that term overflows. What is the product of 0*inf? That is an indeterminate expression. We could come up with entirely valid arguments that result should be 0, inf, or any finite number. Therefore MATLAb is forced to call it a NaN,

0*inf
ans = NaN

Thus an indeterminate result. It has no value you can assign to it.

In fact, this happens even for relatively small values of x in that interval. Even 1e5 is far too large to let you see anything. I'm not sure whay you are starting at x==10, but you can see stuff happening out there.

x = linspace(10,30);

y = 0.453 .* exp(-1.036 .* x) .* sinh((2.29.* x).^0.5);

plot(x,y)

As I said, this is not at all parabolic.

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