Good to know

Conditional Multivariate Normals

using Distributions
using LinearAlgebra

##

# P(A|B)

Σab = 0.2*randn(3,3)
Σab += Σab'
Σab += diagm([1.0;1.0;1.0])

μ_ab = [10.0;0.0;-1.0]
μ_1 = μ_ab[1:1]
μ_2 = μ_ab[2:3]

Σ_11 = Σab[1:1,1:1]
Σ_12 = Σab[1:1,2:3]
Σ_21 = Σab[2:3,1:1]
Σ_22 = Σab[2:3,2:3]

##

# P(A|B) = P(A,B) / P(B)
P_AB = MvNormal(μ_ab, Σab)                       # likelihood
P_B = MvNormal([-0.5;0.75], [0.75 0.3; 0.3 2.0]) # evidence

# Schur compliment
μ_(b) = μ_1 + Σ_12*Σ_22^(-1)*(b-μ_2)
Σ_ = Σ_11 + Σ_12*Σ_22^(-1)*Σ_21

P_AB_B(a,b) = pdf(P_AB, [a;b]) / pdf(P_B, b)
P_A_B(a,b; mv = MvNormal(μ_(b), Σ_)) = pdf(mv, a) 

##

# probability density: p(a) = P(A=a | B=b)
@show P_A_B([1.;],[0.;0.])
@show P_AB_B([1.;],[0.;0.])

P(A|B=B(.))

Various Internal Function Docs

IncrementalInference._solveCCWNumeric! — Function

_solveCCWNumeric!(ccwl; ...)
_solveCCWNumeric!(ccwl, _slack; perturb)

Solve free variable x by root finding residual function fgr.usrfnc(res, x). This is the penultimate step before calling numerical operations to move actual estimates, which is done by an internally created lambda function.

Notes

Assumes cpt_.p is already set to desired X decision variable dimensions and size.
Assumes only ccw.particleidx will be solved for
small random (off-manifold) perturbation used to prevent trivial solver cases, div by 0 etc.
- perturb is necessary for NLsolve (obsolete) cases, and smaller than 1e-10 will result in test failure
Also incorporates the active hypo lookup

DevNotes

TODO testshuffle is now obsolete, should be removed
TODO perhaps consolidate perturbation with inflation or nullhypo

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