### QUCOVAR

Find co-variance of Q and U from a POL2 observation

#### Description:

Calculates the co-variance of Q and U in each map pixel for a POL2 observation. For a single pixel, the returned co-variance is:

sum( W_i$\ast$RQ_i$\ast$RU_i )/(N$\ast$sum( W_i ))

where:

• RQ_I is the ith residual from the Q map, and RU_I is the ith residual from the U map. A residual is the bolometer Q or U sample minus the Q or U map pixel value (the pixel value is the weighted mean of the Q or U sample values that fall in the pixel). These residuals can be dumped by makemap when the Q and U maps are created.

• W_i is the weight for the ith sample. It is the geometric mean of the weights associated with RQ_i and RU_i. These can also be dumped by makemap, but are created initially by calcuq as the residual of the fitting process for each sample.

The input NDFs should be created by running makemap twice on the CALCQU output for a single POL2 observation - once to create a Q map and once to create a U map. On each invocation of makemap, the config should include " exportndf=(res,qua,noi,lut)" . This will causes two extra NDFs to be created by each invocation of makemap with suffixes " QT_con_lut" , " QT_con_res" , " UT_con_lut" and " UT_con_res" . These should be supplied as input to this command.

#### Parameters:

3-D NDF holding Q LUT model (suffix " QT_con_lut" ).
3-D NDF holding Q residuals time-series (suffix " QT_con_res" ).
3-D NDF holding U LUT model (suffix " UT_con_lut" ).
3-D NDF holding U residuals time-series (suffix " UT_con_res" ).