# working with large matrices

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Bram Stegeman 2019년 3월 6일
댓글: Stephan Koschel 2020년 3월 17일
I have to work with large matrices (e.g. A = 8000 x 100.000, all non-zero values).
I want to calculate T= ((A'*A) + lamda*speye(n))\(A'*A); with lamda =e.g. 1-e-3.
I have installed 64 gb ddr and as expected I run out of memory (also when I introduce a threshold and force A to be sparse, and then create sparse(A) and sparse (A') and try to calculate T.
Are there alternative ways to calculate T without out of memory issues?
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Bram Stegeman 2019년 3월 7일
Hello David,
That is correct. 1e5 x 1e5 could already results in memory issues is my experience.
Forget to mension that I'm only interested in the diagonal values of T.
Stephan Koschel 2020년 3월 17일
You are only interested in the diagonals of a matrix multiplication?
I would implement an iteration over the diagonal elements and load the corresponding columns and rows from the two matrices. The entry on the diagonal becomes something like sum(current_row .* current_col)
The iteration could slow down the process, but you only need to load two vectors into memory.

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### 채택된 답변

Munish Raj 2019년 3월 18일
Hello Bram,
You could look at implementing Tall Arrays.
The documentation link can be found here.

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