How to solve n*log2(n)=A in matlab?

Question

n*log2(n) = A, with A a known value. How do I solve for n in Matlab? Note that n isn't necessary an integer.

score 6 · Accepted Answer · answered Sep 21 '12 at 13:20

6

Or solve the equation analytically and use that:

n = A*log(2)/lambertw(A*log(2))

answered Sep 21 '12 at 13:20

Gunther Struyf

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My preference too, but of course this requires the symbolic toolbox. – Sep 21 '12 at 14:02
4

I had to look. There is a lambertw tool on the FEX. http://www.mathworks.com/matlabcentral/fileexchange/3644-real-values-of-the-lambert-w-function – Sep 21 '12 at 14:04

score 2 · Answer 2 · answered Sep 21 '12 at 12:43

2

Not the most elegant solution, but you can use fmincon

n = fmincon(@(N) abs(N*log2(N)-A),10, [],[],[],[],1,Inf)

answered Sep 21 '12 at 12:43

Rasman

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score 2 · Answer 3 · answered Sep 21 '12 at 14:26

2

Just use fzero:

solution = fzero(@(n) n.*log2(n)-A, A/5);

I found the initial guess empirically by examining the solution's behaviour on the interval 0-1000; you might want to adjust it for your use case.

answered Sep 21 '12 at 14:26

Rody Oldenhuis

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that was my first though, but it will fail if A is close to 1 – Rasman Sep 21 '12 at 14:37
@Rasman: not here: `solution = 1.559610469462369e+00` Why do you think it will fail near `A=1`? – Rody Oldenhuis Sep 21 '12 at 14:55

nrz · Answer 4 · 2012-09-21T14:28:52.090

If you have Symbolic Math Toolbox installed, all you need is:

solve('n*log2(n)=A', 'n')

ans =
    (A*log(2))/lambertw(0, A*log(2))

You can also use solve with syms:

syms n A

solve(n*log2(n)==A, n)

After syms n A you can also define the value of A:

A = 0
solve(n*log2(n)==A, n)

ans =
    1

A = 2
solve(n*log2(n)==A, n)

ans =
    2

A = 3
solve(n*log2(n)==A, n)

ans =
    (3*log(2))/lambertw(0, 3*log(2))

How to solve n*log2(n)=A in matlab?

4 Answers4