Out of memory error with 8GB and 64bit

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Alexandra on 29 Oct 2015
Commented: Walter Roberson on 30 Oct 2015
Hi,
I am working with lots of memory and I am getting an out of memory error.
>> memory
Maximum possible array: 16146 MB (1.693e+10 bytes) *
Memory available for all arrays: 16146 MB (1.693e+10 bytes) *
Memory used by MATLAB: 1080 MB (1.132e+09 bytes)
Physical Memory (RAM): 8111 MB (8.505e+09 bytes)
* Limited by System Memory (physical + swap file) available.
The model is quite large. It's a script with dozens of matrixes 50k*50k. I know I use intensive functions as copulas, kron function, nested for and if's.
But this model is being developed for a long time and I really need it to run. What can I do?
Am I being inefficient or am I simply asking the impossible? This is a 64bit version.
Thanks a lot,

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Alexandra on 30 Oct 2015
I don't understand what's at stake by changing to single precision. Don't understand the difference..
Stephen Cobeldick on 30 Oct 2015
So named "single" floating point values take up exactly half the memory of "double" floating point values, but have a lower precision, exactly as the documentation states "Because MATLAB stores numbers of type single using 32 bits, they require less memory than numbers of type double, which use 64 bits. However, because they are stored with fewer bits, numbers of type single are represented to less precision than numbers of type double."
Converting to single would be an easy way to use less memory, if the precision requirement of your algorithm and data permit this.
Alexandra on 30 Oct 2015
Ok. I see the difference is in the number of decimals ("32-bit single-precision variables represent data to about seven decimal places, which is less accurate than doubles"). Since I work with €, I have no interest in computing bellow cents and I will try single.
Thanks,

Lessmann on 30 Oct 2015
Hi,
considering the mentioned size of a matrix, the matrix would occupy ~20GB or ~10GB in the case of single precision. With the 16GB available memory you are asking the impossible.
>> M = zeros(50000,50000);
>> whos
Name Size Bytes Class Attributes
M 50000x50000 20000000000 double
To the point what you cando, take a good look at your script and see if the problem can be broken down into smaller pieces (not processing all the data at once).
If the matrix is sparsely populated, you could have a look into sparse matrices.

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Lessmann on 30 Oct 2015
I didn't meant to break down the script but the data. Sometimes it is possible divide the data into chunks, process them independendly of each other and combine the results afterwards.
For example, process 50 times a 1000x50000 matrix.
But if such an approach is feasible depents on the problem at hand.
Alexandra on 30 Oct 2015
Ok thanks, that is more difficult to apply because I apply operations that involve all rows or columns at once, like average, sumif etc. But if I can't solve it I will think about doing that..
Walter Roberson on 30 Oct 2015
sum and average do not require having all of the data available at the same time.
Consider that sum([1 2 3 4]) is 1+2+3+4 which is the same as (1+2)+(3+4) which is sum([1 2])+sum([3 4]). Therefore you can break your data up into smaller blocks, do the sum of each block, and then add the subtotals.
Likewise, average is sum divided by the number of elements, so you can break the data up into blocks, do the sum of each block, add the subtotals, and then divide the total by the number of elements. Also, in the special case that all the blocks are the same size, you can mean() the mean()'s of the blocks (a technique that will not work if any block is a different size than the others.)