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Fast numerical approximation to the PDF of the Voigt distribution with around 1.2% of maximum deviation
ResourceFunction["NPseudoVoigt"][x,b,σ] calculates the approximation at postions x of a Voigt distribution with CauchyDistribution parameter b and NormalDistribution parameter σ. |
NPseudoVoigt always returns numerical results, even for exact inputs:
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NPseudoVoigt compared to the analytic solution:
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NPseudoVoigt automatically threads over lists:
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NPseudoVoigt is approximately normed to 1 for b and σ greater than 0:
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NPseudoVoigt's norm has four additional terms that cancel out for non-extreme values of b and σ:
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NPseudoVoigt's deviation to the analytic solution in the maximum is usually less than ±1% for every parameter combination b and σ:
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NPseudoVoigt's relative deviation increases if b and σ approach one another:
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NPseudoVoigt is also stable against σ being 0:
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NPseudoVoigt can be compiled to obtain faster execution times:
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Negative b parameters can produce imaginary values:
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Negative σ parameters do not yield symmetric values:
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NPseudoVoigt can be used to approximate an atomic absorption spectrum efficiently:
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NPseudoVoigt can be used to show that σ is negligible or even 0, whereas the VoigtDistribution could throw errors:
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This work is licensed under a Creative Commons Attribution 4.0 International License