Operations on consecutive elements of a vector

Imagine there is a vector C with n elements, c(i). Without using a loop I would like to a have new vector D whose elements are:

d(i)= c(i) if i=1
d(i)= c(i-1)-c(i) if 1<i<n  
d(i)= -c(i) if i=n

I do not care about the first and last elements which I could add by concatenation, but generally I am looking for a way to perform mathematical operations on consecutive elements of a vector without using a loop. Is this possible?

Answer 1

[dpb]

If'en I interprets your requirements correctly...

d=[c(1) diff(c(1:end-1)) -c(end)];

Example:

>> c=randi(10,1,5)
c =
   9     9     4     7     3
>> d=[c(1) diff(c(1:end-1)) -c(end)]
d =
   9     0    -5     3    -3
>>

[Stephen23]

The question specifies the difference as " c(i-1)-c(i)" rather than the c(i)-c(i-1) that diff supports. A simple minus resolves the problem:

d = [c(1),-diff(c(1:end-1)),-c(end)]

[dpb]

I had it that way first and decided probably was misstated by OP... :)

[Saeid]

Thank you both. Your answers saved me a lot of time again!

[Saeid]

By the way, what if I want to perform some other basic operation on consecutive elements, e.g. adding, multiplication etc.?

[dpb]

All depends on what the operation(s) is(are); sometimes it's easily vectorized, other times "not so much". filter can do many operations but not all. See

help datafun  % for list to give some ideas on what's builtin

After that, it's mostly just thinking about the operations and using "time in grade" to apply Matlab syntax to the particular case.

Oh, and it helps if you're reasonably fluent in matrix algebra and have some knowledge of some of the special properties of matrices so that can recognize when magic occurs...

ADDENDUM

Oh, I am not into image processing so didn't think of it originally, but there's blockproc in that toolbox or, if you don't have access to it a submission in the File Exchange (not tried)... Apply function on subsets of array>

[Saeid]

Thnaks a lot!