Hi,

Is there a built in function that can get the sum of the upper secondary diagonals of a matrix? some times called the skew:



I can call each by its element, but I would like it to work for any a1n & an1, I can do tr(reverse) to find the secondary diagonal, after each reduction of the matrix by 1 row/column:



matrix multiplier.sm (15 KiB) downloaded 29 time(s).

Thanks in advance
Ian

Lets say the matrix is 10 x 10, I don't want the user to have to "manually" create all the steps to get to the tr(reverse), this is a lot of work and could introduce errors. What I want is a simple (if it is indeed simple!) loop to do it.
Your solutions certainly speed up the process and wonder if they could be implemented?

Ian

Hello

Maybe you can do this




Best Regards

Carlos

File not found.File not found.

(the first is more a "proof of concept", is very inefficient because it does a lot useless calculations)

Wrote

... your image red arrows represents the *.JPEG destruction.
JPG does not compress, it destroys the details bottom-right up top left.
What's the relationship between your JPG image and your attempt ?

Image jpeg.sm (53 KiB) downloaded 26 time(s).

Hi Jean,

The image was just to illustrate the direction of the summation, the primary diagonal is top left to bottom right.

Hi Carlos and Davide,

These look like interesting solutions, let me try on the larger matrix.

Thanks once again
Ian

Interesting results on the speed of calculation:
Main Matrix:

Method Carlos:

Method Davide:

Comments?

Wrote

(the first is more a "proof of concept", is very inefficient because it does a lot useless calculations)

You should try the 2nd method in my file.
As stated in the previous post the first method is really inefficient, since for each iteration it calculates all the sums from the first value up to the n-th diagonal.

BTW with a random set of values and small matrices, doesn't seems so slow in my machine (WIN7PRO/AMD PRO A10/16GB RAM). With bigger matrices the difference is huge (for a 100x100 matrix, 26.1s with first method, 0.028s with second method)





The method to check the sum of [r,c] coordinates can be used more efficently in a double loop, though (here it is extended to the whole matrix).

Hi,

Second method now as quick as the first by Carlos.

Jean, many opportunities for engineering!

Thanks to all

Ian

Wrote

Jean, many opportunities for engineering !

w/o abstract: of little interest for common visitor.

Matrix DIAGONAL.sm (11 KiB) downloaded 28 time(s).