AO prediction

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Example AO telemetry data:

aol0_modeval_ol_15:40:18.088427319.fits

aol0_modeval_ol_15:40:34.115929146.fits

aol0_modeval_ol_15:40:57.955397265.fits

Description

Each file contains 30000 consecutive wavefront measurements acquired a 2 kHz (15 sec total duration per file). The number of modes is 1161: this is the number of values measured at each time step.

The files are 3D images, with the last axis encoding the time step. Each slice is a 2D image of size 1161 x 1. So, the total 3D image size is 1161 x 1 x 30000.

Building Data Matrix

The data matrix is assembled by pasting consecutive measurement vectors together. See pseudo code below

Input  : measurement 3D cube T
Output : data matrix D

Tsize0 = 1161; // number of modes measured
Tsize2 = 30000; // number of time steps in input 3D cube

filterN = 10; // number of time steps in predictive filter


jjmax = Tsize2 - (filterN-1); // number of time steps in output data matrix D

for(jj=0; jj<jjmax; jj++)
{
    for(n=0; n<filterN; n++)
    {
        for(i=0; i<Tsize0; i++)
        {
            ii = n*Tsize0 + i;
            D[ii, jj] = T[i, 1, jj+n];
        }
    }
}

Small matrix test (testing pseudoinv result)

Following script used for testing:

cacao << EOF
loadfits "aol0_modeval_ol_15:40:18.088427319.fits[1:30,*,1:4000]" im00
im3Dto2D im00
imrepshiftx im00 5 mat
imswapaxis2D mat matA
savefits matA "!mat_ssmall.fits"
cudacomppsinv matA matAinv 0.01 100 VTmat
savefits matAinv "!mat_ssmall_psinv.fits"
listim
exitCLI
EOF

Input matrix (size = 150 x 3995) : mat_ssmall.fits

Output pseudoinverse (size = 150 x 3995) : mat_ssmall_psinv.fits

List of eigenvalues : eigenv.dat

Code source: See function int CUDACOMP_magma_compute_SVDpseudoInverse() in file cudacomp.c