How can I find the sum of the perimeter of a matrix?

Hi, I am wondering if I had a matrix [1,2,3;1,2,3;1,2,3] how I could find the sum of the perimeter. Thanks an advance.

Answer 1

[dpb]

One way amongst any number...

>> M=[1,2,3;1,2,3;1,2,3];
>> I=ones(size(M)); I(2:end-1,2:end-1)=0;
>> S=sum(reshape(M.*I,1,[]))
S =
  16
>>

Answer 2

[Stephen23]

In one line is easy and very fast:

>> M = [1,2,3;1,2,3;1,2,3];
>> sum(sum([M([1,end],2:end-1),M(1:end,[1,end]).']))
ans =  16

[dpb]

Nicely done, Stephen...was thinking more trouble writing the outer boundary indices than the inner despite two steps. At least one more one-liner:

>> sum(M(:))-sum(sum(M(2:end-1,2:end-1)))
ans = 16
>>

How many ways to skin this particular cat? :)

[Stephen23]

@dpb: yes, I also considered the difference approach... it could have interesting side effects if the values have quite different magnitudes.

[dpb]

Yes, it isn't nearly as good numerically, agreed...

[dpb]

[ ... Ricardo Florez Answer moved to comment since was a follow-up question on earlier Answer syntax ... dpb]

Hi. Why is it necessary to write two "sum" in the code: sum(sum(M(...)? Please see below:

the sum(M(:))-sum(sum(M(2:end-1,2:end-1)))

Thank you.

[dpb]

Because sum(M(2:end-1,2:end-1)) is a row vector of the sums of the columns in the submatrix; to get the total have to then add those values. This is taken care of in the first sum by the use of the special syntax (:) that returns all elements of an array/matrix in a column so sum only needs to add the one column vector. There is no syntax in Matlab to apply the secondary indexing operation to the result of the first function call return; there've been many suggest the enhancement.

Answer 3

[Sanjay Zamindar]

function final_sum = peri_sum(A)
size_row = size(A,1)
size_col=size(A,2)
Sum_of_first_row = sum (A(1, [1:1:end])); %base 
Sum_of_first_Colmn = sum(A([2:1:size_row],1))
%sum_col= sum(A([2:1:size_col], [1:size_col:size_col]));
Sum_of_last_column= sum(A([2:1:size_row],size_col))
sum_of_last_row = sum(A(size_row,[2:1:size_col-1]))
final_sum = sum_of_last_row+ Sum_of_last_column+Sum_of_first_Colmn+Sum_of_first_row
end

Answer 4

[Ibrahim Abouemira]

Hello,

Here's a function that performs your task.

https://www.mathworks.com/matlabcentral/fileexchange/71595-sum-of-values-on-the-perimeter-of-a-matrix