MATLAB: N as the natural numbers

\nnatural numbers

What command is used to enter that n is element of the natural numbers?

Best Answer

You might try something like this (if n is a scalar):

if n > 0 && floor(n) == n
    % n is a natural number
else
    % n is not a natural number
end

Or if n is a vector or matrix of numbers, you can see which ones are natural numbers like this:

is_natural = n > 0 & floor(n) == n;

And get just those elements of n that are natural numbers like this:

natural_n = n(is_natural);

Related Solutions

MATLAB: Natural number determination

A == round(A)

That will give a 1 for integers. You can add a test for positiveness if you want it.

MATLAB: Plot Natural Cubic Spline

You were close, in that csape can do it. (My SLM toolbox also has a natural cubic as an option, but there is no need to go that far.) The proper choice in csape is:

pp = csape(x,y,'variational');

The flag 'variational' comes from the calculus of variations, I assume. The calculus of variations can also be seen to call those corresponding end conditions the "natural" boundary conditions.

   'variational' : set end second derivatives equal to zero
                    (ignoring given end condition values if any)

A natural cubic spline is the one that has zero second derivatives at the ends.

As a check, does it produce what I expect? So here a function that has decidedly NON-zero second derivatives at the ends.

x = linspace(0,2*pi,10);
y = cos(x);
pp = csape(x,y,'variational');
pp2 = fnder(pp,2);
fnplt(pp2)
grid on

Yet as you see, the second derivatives at the ends are forced to zero. This is the classic example that I always used when teaching about splines, as to why a natural cubic spline might often be a poor choice.

So if we look at the fit that arises, compare the natural cubic to that produced by spline.

fnplt(pp,[0 1])
hold on
pps = spline(x,y);
fnplt(pps,[0 1])

In blue is the natural cubic, whereas the green curve is the result of spline, which uses not-a-knot end conditions, generally a safer choice. If we remember these curves are an approximation to cos(x), the green curve is clearly much better.

So while you can find a natural cubic in MATLAB, you need to look deeply enough, and know what you should be looking for. That is in general a good thing in this regard.

Best Answer

Related Solutions

MATLAB: Natural number determination

MATLAB: Plot Natural Cubic Spline

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