tokens: a zoom-in of the convolution kernel. Redder wavelengths have a larger kernel width due to . Positive redshifts move the position of the diagonal convolution to the right. The final model spectrum is shown compared to a low-resolution () spectrum of a solar-like star with S/N per pixel. The additional nuisance parameters f , p b , v b only contribute during the calculation of the likelihood , and do not affect the data generated by the model. Figure 2. A faux observed spectrum (black) of and S/N of ∼20 per pixel, which was used in the toy model test. The recovered maximum a posteriori model spectrum is shown in red. The construction of constitutes a non-negligible component to the total computational budget for each probability evaluation. For this reason a few (optional) approximations have been implemented to minimize this cost. A least-recently used cacher is employed by default to minimize the number of matrix constructions. This uses a small portion of random access memory to retain the N most common sets of . If is required and is sufficiently small (i.e., below some prescribed tolerance) such that , then future calls of within the range will return the previously calculated matrix instead of reconstructing it. The tolerances are configurable, and default to the sub-km s −1 level for and z , and . Alternatively, the construction of can be completely avoided by approximating the convolution with a single kernel width σ at all , where an interpolation routine is used to calculate the expected intensity at . The extent of approximation that can be afforded will vary on the scientific objectives, but the default behavior in sick is balanced to be computationally efficient, and suitable for most scientific applications. I have produced the expected intensities for some arbitrary that can fairly represent any rotational broadening of the source, the object’s redshift, as well as the resolving power of the instrument and the location of the CCD pixels. However, these intensities are not representative of real world data. The height (i.e., photon counts) and shape of an observed spectrum is a function of the source magnitude, exposure time, instrument sensitivities, atmospheric conditions, interstellar extinction, and a host of unaddressed effects. For these reasons a function is required to normalize 3 3 The normalization process is frequently abused by stellar spectroscopists in the literature. Wherever possible, data should not be transformed. One should seek to fit a model to the data, not the other way around. the model to the data. Although the function incorporates a number of effects (e.g., source blackbody temperature, dust, instrument sensitivities), they are phenomena that usually cannot be separated without additional information, and here I only care about their combined effect. The continuum is modeled as a polynomial that enters multiplicatively,where the maximum polynomial degree is specified by the user. For data spanning
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O