Beginner's question - why doesn't a variable overwrite when vectorizing a loop?

I am learning using the book "Matlab for Engineers and Scientists." Unfortunately this book does not provide answers to the exercises.

I've never been good at writing for loops, or really understanding how to index well, so I am running into problems.

Here's the one at hand. I need to convert a for loop into a vectorization. For simplicity I've written a short example:

s=0;
for n=1:10;
    s=s+n
end

This gives the answers 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. When I try to vectorize it like this, s does not overwrite itself after each iteration, but stays at zero:

s=0;
n=1:10;
s=s+n

This gives s=1:10.

Now if s is a simple variable to explain I could just make it a vector as well, but when I don't know what its values will be I can't specify it beforehand. Any help would be appreciated. I know this is simple, but going through this book, the earlier examples aren't relevant to this type of problem.

EDIT: Here is the actual question:

====================

Work out by hand the output of the following script for n = 4:

n = input( ’Number of terms? ’ );

s = 0;

for k = 1:n

s = s + 1 / (k ˆ 2);

end;

disp(sqrt(6 * s))

If you run this script for larger and larger values of n, you will find that the output approaches a well-known limit. Can you figure out what it is? Now rewrite the script using vectors and array operations. ====================

The limit is pi. When I try to do this with vectors I am entering the following:

====================

s=0;

n=4; (just to start)

k=1:1:n;

s=s+1./k.^2;

a=[sqrt(6.*s)];

====================

Of course, this doesn't work. What am I not getting? (Other that you can't overwrite variables if you aren't doing a for loop...but the exercise asks specifically to do this not using a for loop)

Answer 1

[Walter Roberson]

cumsum(1:10)

[Walter Roberson]

Vectorization is all about doing the same thing to every value. You are not doing the same thing to every value. Letting f(x,y) represent the operation that is being done to any one specific (x,y) then vectorization would do

[f(x(1),0), f(x(2),0), f(x(3),0), ... f(x(n),0)]

whereas what you are asking for is

[f(x(1)), f(x(2),f(x(1),0)), f(x(3),f(x(2),f(x(1),0))), f(x(4),f(x(2),f(x(1),0)))) ...]

There is no built-in operation to do that, other than cumsum() and cumprod()

[Matt J]

Vectorization is all about doing the same thing to every value

@Walter

Actually the way I've seen "vectorization" used, it just means "feeding vector/matrix arguments to optimized MATLAB functions" instead of working on their indiviudal elements manually. Your use of CUMSUM qualifies perfectly as an example of vectorization, even though its not doing the same thing to every value.

[B.M.]

Ok, I think I get what you're saying, thanks. I'm just going to post the actual question (to the original post) so you can see what the exercise asks.

Answer 2

[B.M.]

The above was just an example. I just need to know how to get a variable to overwrite itself outside of a for loop.

[Matt J]

There is no such thing as variables overwriting themselves when you don't use loops. That's a concept you seem to have invented yourself.

In vectorized operations, recursively changing variables, if there are any, are always hidden from you inside black-box MATLAB functions. But even in those functions, a loop is being done to perform the recursive updates. In Walter's answer, for example, the CUMSUM function is internally running a loop very much like the one you posted, except that it is hidden from you in compiled C/C++ code.

[Patrik Ek]

I would say sum(1:10) is fair enough since the output is only a single double

[B.M.]

Thanks. I don't understand how to complete the exercise as written. I've appended it in the original post.

[Matt J]

HINT. You should study the documentation for the SUM command and understand what it does. In particular, notice how it allows you to sum up many numbers without using a loop!

Another piece of advice is to study the output of some of the code you've already written and understand what it has done, e.g.

>> n=4;   k=1:n;  s=1./k.^2

s =

      1.0000    0.2500    0.1111    0.0625

[B.M.]

The SUM commend is what is used in my book when first learning about for loops, but I'm not trying to sum anything in the actual problem (see "EDIT" in original post). The initial s=s+n post was just a simpler example.

[Matt J]

I have seen your EDIT and fail to see how it is not a sum. The only difference I see relative to your original example is that the formula for the terms in the series being summed is different 1./k.^2

[B.M.]

Ah, you're right. Sorry. I've been doing other exercises since I posted this and didn't remember accurately what the issue was here. I'll go back and look again at the earlier examples.

EDIT: I got it. Jeez. I think I was fatigued or something after doing all those exercises, now it seems very clear. Thanks to all of you.