softmax(χ::Vector{T}) where T<:Real

Given a real vector of $k$ non-negative scores $χ=c_1,...,c_k$, return the vector $π=p_1,...,p_k$ of their softmax probabilities, as per

$p_i=\frac{\textrm{e}^{c_i}}{\sum_{i=1}^{k}\textrm{e}^{c_i}}$.

Examples

χ=[1.0, 2.3, 0.4, 5.0]
π=softmax(χ)

std(metric::Metric, ν::Vector{T};
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statistics.jl
Unit for statistics, probability and related functions.
Category
Output
1. Probability
functions relating to probability
2. Descriptive Statistics
functions relating to decriptive statistics
Probability
Function
Description
softmax
compute softmax probabilities
PosDefManifold.softmax — Function
softmax(χ::Vector{T}) where T<:Real
Given a real vector of $k$ non-negative scores $χ=c_1,...,c_k$,  return the vector $π=p_1,...,p_k$ of their  softmax probabilities,  as per
$p_i=\frac{\textrm{e}^{c_i}}{\sum_{i=1}^{k}\textrm{e}^{c_i}}$.
Examples
χ=[1.0, 2.3, 0.4, 5.0]
π=softmax(χ)
source
Descriptive Statistics
Function
Description
mean
scalar mean of real or complex numbers according to the specified metric
std
scalar standard deviation of real or complex numbers according to the specified metric
mean(metric::Metric, ν::Vector{T}) where T<:RealOrComplex
See bottom of documentation of general function mean
Statistics.std — Function
std(metric::Metric, ν::Vector{T};
>>>>>>> dev
    corrected::Bool=true,
    mean=nothing) where T<:RealOrComplex
Standard deviation of $k$ real or complex scalars,  using the specified metric  of type Metric::Enumerated type and the  specified mean if provided.
Only the Euclidean and Fisher  metric are supported by this function. Using the Euclidean  metric return the output of standard Julia  std  function. Using the Fisher metric return the scalar geometric standard deviation,  which is defined such as,
$\sigma=\text{exp}\Big(\sqrt{k^{-1}\sum_{i=1}^{k}\text{ln}^2(v_i/\mu})\Big)$.
If corrected is true, then the sum is scaled with $k-1$,  whereas if it is false the sum is scaled with $k$.
Examples
using PosDefManifold
# Generate 10 random numbers distributed as a chi-square with 2 df.
ν=[randχ²(2) for i=1:10]
arithmetic_sd=std(Euclidean, ν) # mean not provided
geometric_mean=mean(Fisher, ν)
<<<<<<< HEAD
geometric_sd=std(Fisher, ν, mean=geometric_mean) # mean provided
source
Settings
Theme
documenter-lightdocumenter-dark
This document was generated with Documenter.jl version 0.27.17 on Friday 13 May 2022. Using Julia version 1.7.2.
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geometric_sd=std(Fisher, ν, mean=geometric_mean) # mean provided