statistics on a matrix's column

[NASA_SimDeveloper]

I have a 2000 x 400 (rows x cols) double precision floating point matrix. I want to find the sigma, and mean of each column using the GPU. Is this a good job for MAGMA? If so, what is a good approach? I am using MAGMA 2.5 on Linux. It seems that coalescing would be important.

[mgates3]

MAGMA doesn't have functions to do this. It has the Level 1 BLAS functions to find vector norms:

• magma_dasum = sum_i abs( x_ i )
• magma_idamax = argmax_i abs( x_i )
• magma_dnrm2 = norm( x )_2 = sqrt( sum_i abs( x_i )^2 )

But not the mean and standard deviation.
-mark

[mgates3]

If you want to write GPU kernels to compute the mean and stddev, you can model them after magmablas/dnrm2.cu, which computes the 2-norm of each column of an m-by-n matrix dA on the GPU. (You can ignore the adjust functions for updating 2-norms.) It is easiest to do in 2 kernels, one for mean, one for stddev. For mean, I think from the dnrm2 kernel code, you would just replace

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    double re = dx[j];
    lsum += re*re;

with

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    lsum += dx[j];

and then divide the final result by n, replacing

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        dxnorm[ blockIdx.x ] = sqrt( sum[0] );

with

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        dxnorm[ blockIdx.x ] = sum[0] / n;

For stddev, it would take the mean from above as an argument, then use

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    double tmp = dx[j] - mean;
    lsum += tmp*tmp;

and

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        dxnorm[ blockIdx.x ] = sqrt( sum[0] / (n-1) );

The dnrm2 code reads data in a coalesced manner by blocks. It may improve performance to have an lda that is a multiple of 32. In your case, rounding up yields lda = 2016. Your matrix would be the first 2000 rows of a 2016 x 400 array.

-mark