# Implementation of the Primary Sample Space Sampler in the book Primary Sample Space Sampler

In the Multiplexed Metropolis Light Transport implementation of the book Physically Based Rendering, the proposal samples are generated by the Primary Sample Space Sampler MLTSampler.

In each Markov chain iteration, a random vector $$v$$ is generated, using the MLTSampler class, from which the proposed strategy $$j$$ and a path $$y$$ are formed. $$j$$ depends only on the first component of $$v$$, while $$y$$ only depends on the remaining entries $$v'$$ of $$v$$.

Say $$k$$ is any other possible strategy. Are we somehow able to obtain the random vector $$w'$$ which would have produced the same path $$y$$?

Beyond that I'd need to evaluate the density $$q(u,v)$$ of the underlying proposal kernel, where $$u$$ is the random vector from the previous iteration. Is there any way to do that?