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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
Generate and return the Kullback-Leibler Divergence (KLD) \(D_{KL}(P \parallel Q)\) of a given univariate Normal distribution \(Q\) from a reference Normal distribution \(P\). More...
Generate and return the Kullback-Leibler Divergence (KLD) \(D_{KL}(P \parallel Q)\) of a given univariate Normal distribution \(Q\) from a reference Normal distribution \(P\).
The Kullback-Leibler Divergence, also known as the relative entropy, of a univariate Normal distribution \(Q\) from a reference univariate Normal distribution \(P\) is defined as,
\begin{equation} \large D_{KL}(P \parallel Q) = \frac{(\mu_P - \mu_Q)^2}{2\sigma_Q^2} + \frac{1}{2}\bigg( \frac{\sigma_P}{\sigma_Q} - \ln\big(\frac{\sigma_P}{\sigma_Q}\big) - 1 \bigg) ~, \end{equation}
where \(\mu\) and \(\sigma\) represent the respective standard deviations of the Normal distributions.
| [in] | meanDiffSq | : The input scalar or array of the same shape as other array-like arguments of the same type kind as the output kld, representing the difference-squared of the mean parameters of the two Normal distributions ( \((P, Q)\)).(optional, default = 0., that is, the two distributions have the same mean.) |
| [in] | varP | : The input scalar or array of the same shape as other array-like arguments, of the same type and kind as the output kld representing the variance of the reference Normal distribution \(P\).(optional, default = 1., it must be present if and only if varQ is also present.) |
| [in] | varQ | : The input scalar or array of the same shape as other array-like arguments, of the same type and kind as meanDiffSq representing the variance of the target Normal distribution \(Q\).(optional, default = 1., it must be present if and only if varP is also present.) |
kld : The input scalar or array of the same shape as input array-like arguments, of,
representing the Kullback-Leibler divergence of the target distribution with respect to the reference.
Possible calling interfaces ⛓
0 <= meanDiffSq must hold for the corresponding input arguments.0 < varP must hold for the corresponding input arguments.0 < varQ must hold for the corresponding input arguments.CHECK_ENABLED=1.pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.pure in release build and impure in debug and testing builds.elemental.
Example usage ⛓
ifort compiler ⛓ ifort compiler ⛓ gfortran compiler ⛓ log1mexp for better accuracy.
Final Remarks ⛓
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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
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Definition at line 3942 of file pm_distNorm.F90.
1.9.3