[New feature] Conditionning

Fixes #150

First draft

src/ConditionalDistribution.jl

@@ -0,0 +1,68 @@
+struct ConditionalDistribution{d,p,D,T,TD} <: Distributions.ContinuousMultivariateDistribution
+    X::TD
+    dims::Ntuple{p,Int64}
+    xs::NTuple{p, T}
+    function ConditionalDistribution(X,dims,xs)
+
+        # Get dimensions: 
+        D = length(rand(X))
+        p = length(xs)
+        d = D - p
+        @assert length(dims) == p
+        @assert all(dims .<= D)
+        xs = Tuple(xs...)
+        T = eltype(xs)
+        TD = typeof(X)
+        return new{d,p,D,T,TD}(X,dims,xs)
+    end
+end
+
+function ConditionalDistribution(X::SklarDist{TC,Tm},dims,xs) where {TC<:GaussianCopula, Tm}
+    # If the copula is gaussian, then the conditional distribution has a closed form formula. 
+    # It is also a SklarDist with a Gaussian copula, but not exactly the same one. 
+    # invert the xs to z-scale
+    Z = Normal()
+    zs = similar(xs)
+    for (i,di) in enumerate(dims)
+        zs[i] = quantile(Z,cdf(X.m[di],xs[i]))
+    end
+
+    # Now we simply need to condition a gaussian random vector and apply back 
+end
+
+
+function ConditionalDistribution(X::SklarDist{IndependentCopula{d},Tm},dims,xs) where {d,Tm}
+    # If the copula is the independence, conditionning is just subsetting. 
+    otherdims = (i for i in d if !(i in dims))
+    return subsetdims(X,otherdims)
+end
+
+function _v(u,j,uj)
+    return [(i == j ? uj : u[i]) for i in eachindex(u)]
+end
+function _der(X,dims,u)
+    if length(dims)==1
+        j = dims[1]
+        return ForwardDiff.derivative(uj -> cdf(X,_v(u,j,uj)), u[j])
+    else
+        j = pop!(dims)
+        return ForwardDiff.derivative(uj -> _der(X,dims,_v(u,j,uj)), u[j])
+    end
+end
+function Distributions.cdf(X::ConditionalDistribution{d,p,D,T,TD},u) where {d,p,D,T,TD}
+    # So we need the derivative of the original cdf. 
+
+    # Make the full vector x :
+    x = zeros(D)    
+    j = 1
+    for i in 1:D
+        if !(i in X.dims)
+            x[i] = u[j]
+            j += 1
+        end
+    end
+    x[X.dims...] .= X.xs
+
+    # Now derivate the cdf: 
+    return _der(C.C, C.dims, x)
+end