How can I turn a matrix into several submatrices and add up certain submarices?

Hi community,

I am wondering how to turn a large matrix (9800x9800) into 49x49 submatrices (each with 200x200 cells). Following that, I want to do the following operations:

1. sum up all matrices on the diagonale
2. sum up all matrices in the lower triangle
3. sum up all matrices in the upper triangle

I have been succesful with the first item using the following code:

for i = 1 : meta.NCOUNTRIES;
    i
    Z_all{i} = Z((i - 1) * meta.NSECTORS + 1 : i * meta.NSECTORS, (i - 1) * meta.NSECTORS + 1 : i * meta.NSECTORS);
end

Z_RoW = zeros(meta.NSECTORS);
for i = 1 : meta.NCOUNTRIES; 
    i
    Z_RoW = Z_RoW + Z_all{i};
end

where

• meta.NCOUNTRIES = 49
• meta.NSECTORS = 200
• meta.Zdim = 9800

I think the above code is not ideal, i.e. it could be done w/o having to use a loop. Also, I have troubles with finding and summing up the elements in the lower/upper triangle.

Thank you!

Answer 1

[Image Analyst]

See the FAQ: http://matlab.wikia.com/wiki/FAQ#How_do_I_split_an_image_into_non-overlapping_blocks.3F

[Paul Wolfram]

Hi Image Analyst,

this is nice for splitting up the matrix. I am still unsure though how to add up certain matrices, e.g. only the matrices in the lower or upper triangle (as shown in yellow shades / green shades in the picture below).

Thank you!