spectral-cube and CASA operations: performance comparisons

[e-koch]

Tutorial and overview of comparing dask and CASA performance.

[e-koch]

Bokeh plots are not being rendered on binder.

[e-koch]

@astrofrog @keflavich I've added a CASA to spectral-cube conversion tutorial for basic cube operations and fitting:

Moved to #15

Everything won't work until radio-astro-tools/spectral-cube#656, radio-astro-tools/spectral-cube#665, and radio-astro-tools/spectral-cube#666 are merged in spectral-cube.

The performance tutorial above is still a WIP.

[e-koch]

This is also noted in the tutorial and demonstrated, but I think this could be a common discrepancy users may find so I'll retiterate it here:

The biggest spectral-cube to CASA difference is CASA's definition of the second moment along the spectral dimension. spectral-cube uses the correct formal definition (i.e., the variance) and then defines the sqrt as the "linewidth_sigma". If noisy lines of sight are included, some of the moment 2 values can be negative (because the variance is being weighted by negative values in places) and so the square root ends up being a NaN. This is likely the most "fair" way of handling these cases as a negative moment 2 is definitely dominated by noise features and not the actual signal. To correct for this, signal masking should be applied before computing the moment 2.

In CASA, the moment2 from immoments is spectral-cube's "linewidth_sigma" (https://casa.nrao.edu/casadocs/casa-6.1.0/global-task-list/task_immoments/about). However, CASA will also apply an absolute value before taking the square root. This will lead to overestimates of the line width and further hide where some lines-of-sight have an erroneous negative moment 2 value. In the CASA-to-SC conversion tutorial, I show that the line widths are overestimated by 5 times in the tutorial data when using this method versus first applying an appropriate signal mask.

If you need to reproduce the CASA behaviour for the second moment in spectral-cube, use this:

moment2 = cube.moment2()
moment2_quant = moment2.quantity
moment2_quant = np.abs(moment2_quant)
lwidth_abs = np.sqrt(moment2_quant)

[astrofrog]

Could you remove the output cells from the notebooks? (otherwise one of the notebooks is too large to comment on - and anyway we should not store outputs in the repo)

[astrofrog]

typo: operations

[astrofrog]

Also I'm not sure about calling this a tutorial, maybe just referring to it as a 'notebook' would make more sense? (and linking to the other notebook in this PR for the average user)

[astrofrog]

Put casatools and casatasks on same line, and also simplify imports above by removing ones that are redundant?