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EIDOS models the primary beam of radio astronomy antennas. The code can be used to create MeerKAT L-band beams from both holographic (AH) observations and EM simulations within a maximum diameter of 10 degrees. The beam model is less accurate at higher frequencies, and performs much better below 1400 MHz. The diagonal terms of the model beam Jones matrix are much better known than the off-diagonal terms. The performance of EIDOS is dependent on the quality of the given AH and EM datasets; as more accurate AH models and EM simulations become available, this pipeline can be used to create more accurate sparse representation of primary beams using Zernike polynomials.