create sparse upper triangular matrix with only 1s

Hello. I want to create a sparse upper triangular with size 10^5x10^5. Is it possible?

m = triu(ones(10^5);

and

 m = sparse(triu(ones(10^5));

exceed maximum array size preference. Thanks.

Answer 1

[James Tursa]

A sparse version of the full triangular matrix will have slightly over 1/2 of the values, plus some extra overhead for the explicit index numbers that are saved. A comparison of memory usage is:

n = number of rows & columns

full memory = 8*n^2 bytes

sparse memory = (8 + (4 or 8))*n*(n+1)/2 + (4 or 8)*(n+1) bytes

The (4 or 8) will depend on whether the indexing is saved as 4 or 8 byte integers on your machine.

So, if we assume 8 byte integers on your machine and n = 10^5, the memory comparison is:

full memory = 8e10 bytes

sparse memory = 8.0001600008e+10 bytes

The sparse version of this triangular matrix will actually consume more data memory than the full version.

A logical version of this matrix will consume this amount of data memory:

sparse logical memory = (1 + (4 or 8))*n*(n+1)/2 + (4 or 8)*(n+1) bytes

So for 8 byte indexing and n = 10^5 as above, you would get:

sparse logical memory = 4.5001250008e+10 bytes

Still 56% the size of the full double version, so probably not what you need.

You need to find another way to solve your problem.