How to expand a summation with different indexes

How to expand a summation with different indexes like this?

Any help would be appreciated.

[John D'Errico]

Don't post the same question every 23 minutes.

[SooShiant]

what about 24 or 18?

[Stephen23]

@SooShiant: Please stop posting the same question again and again.

[SooShiant]

@Stephen Cobeldick

That was different. This is numerical but that one you deleted was symbolical. Don't you know the symbolical answer?

Answer 1

[Thorsten]

 sum(diff(f(1:4)).*n(1:3).*arrayfun(@(x) sum(m(x:end)), 3:5))

[SooShiant]

I pasted that code to matlab and it said:

Error using mupadmex
Error in MuPAD command: Index exceeds matrix dimensions.

Error in sym/subsref (line 1580)
        B = mupadmex('symobj::subsref',A.s,inds{:});

[Thorsten]

The code works only if you have vectors f, n and m and numerically evaluate the sum, not symbolically.

[SooShiant]

So is it mean I can't have an algebraic equation at the end? And matlab cant do that?

[Thorsten]

No. It just means that I gave you the wrong, i.e, numerical answer because I overlooked that by asking to "expand" you asked for a symbolical solution. In the future such mistakes could be avoided if you define your variables as sym and ask for a symbolical solution.

[SooShiant]

By the way thanks for your time. It would be the best if you write that code for me, because I am new to matlab and I have to drive a large 28-line equation and don't know how to do it.

[Muthu Annamalai]

@Thorsten : nice solution exploiting fact that each sum is independent of the other index, i and j, we may use dot products to compute the inner loop, and repeat it again for index i. I wonder if there is also a way to do it with mesgrid() and matrix products.

[SooShiant]

@Muthu Annamalai: don't you know the symbolical code?

Answer 2

[Sean de Wolski]

sum(diff(f(1:4)).*n(1:3).*sum(m(3:5)))

[Thorsten]

No. sum over m depends on i in the formula, but is a constant of value sum(m(3:5)) in the code.

[SooShiant]

I pasted this code to matlab and it said:

Error: Expression or statement is incorrect--possibly unbalanced (, {, or
[.

[Sean de Wolski]

Thorsten, i is 1:3 for the example so I could hardwire j.

[Thorsten]

Sean, yes, i is 1:3, so the starting index of j is 3:5, so the sum runs for j = 3:5 for i = 1, j = 4:5 for i = 2, and j = 5 for i = 3, i.e., assumes values sum(m(3:5)), sum(m(4:5)) and sum(m(5)) for i=1,2,3. You forgot to sum over the different m(j), as far as I can see.

[Sean de Wolski]

Ah, so I need to tril() that part.

Answer 3

[SooShiant]

As I said I want a code to expand summation (algebraic) not to get a numerical answer. How bad is it. There is no way. May I need to try Mathematica. Can any one help with Mathematica?

[Thorsten]

Have a look at http://de.mathworks.com/help/symbolic/mupad_ug/compute-symbolic-sums.html

[SooShiant]

I've seen this page before but as I said I'm new to matlab and need an emergency help. May you write down this code for me pleeeeeease??????????

[Thorsten]

Unfortunately I don't have the symbolic toolbox.

Answer 4

[SooShiant]

I need Matlab answer me:

I wonder how you experts can't writes such a simple code. May it relates to Matlab capabilities and should use Mathematica. Can anyone help with Mathematica?