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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def compute_photometry(catalog, photmode):
 """ Compute magnitudes for sources from catalog based on observations photmode. Parameters catalog : `~astropy.table.Table` Astropy Table with 'source_sum' column for the measured flux for each source. photmode : str Specification of the observation filter configuration used for the exposure as reported by the 'PHOTMODE' keyword from the PRIMARY header. Returns ------- phot_cat : `~astropy.table.Table` Astropy Table object of input source catalog with added column for VEGAMAG photometry (in magnitudes). """

    # Determine VEGAMAG zero-point using pysynphot for this photmode
    photmode = photmode.replace(' ', ', ')
    vega = S.FileSpectrum(VEGASPEC)
    bp = S.ObsBandpass(photmode)
    vegauvis = S.Observation(vega, bp)
    vegazpt = 2.5 * np.log10(vegauvis.countrate())

    # Use zero-point to convert flux values from catalog into magnitudes
    # source_phot = vegazpt - 2.5*np.log10(catalog['source_sum'])
    source_phot = vegazpt - 2.5 * np.log10(catalog['flux'])
    source_phot.name = 'vegamag'
    # Now add this new column to the catalog table
    catalog.add_column(source_phot)

    return catalog