# Multiple indexing from a multidimensional array to a vector **URL:** \ **Category:** Modeling\ **Created:** [April 13, 2019, 7:13pm UTC](https://discourse.mc-stan.org/t/multiple-indexing-from-a-multidimensional-array-to-a-vector/8457 "2019-04-13T19:13:17Z")\ **Posts on this page:** 5\ **Page:** 1

**Author:** ![scellus](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/scellus/32/30_2.png) [@scellus](https://discourse.mc-stan.org/u/scellus)\ **Post date:** [April 13, 2019, 7:13pm UTC](https://discourse.mc-stan.org/t/multiple-indexing-from-a-multidimensional-array-to-a-vector/8457/1 "2019-04-13T19:13:17Z")

I have a vector of observations `y` (of length N) with associated indices (ii, jj, kk), each of length N, and an array of parameters `theta[i, j, k]` in my model, and I would like to write a vectorised sampling statement equivalent to ``` for (l in 1:N) y[l] ~ normal(theta[ii[l], jj[l], kk[l]], sigma); ``` Is it possible to vectorise this directly? If not, does it make sense to do it indirectly, somehow, like vectorizing (“raveling”) the three-dimensional array and computing the indices to the vector manually? ---

**Author:** ![bbbales2](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bbbales2/32/77_2.png) [@bbbales2](https://discourse.mc-stan.org/u/bbbales2)\ **Post date:** [April 13, 2019, 8:09pm UTC](https://discourse.mc-stan.org/t/multiple-indexing-from-a-multidimensional-array-to-a-vector/8457/2 "2019-04-13T20:09:23Z")

> [@scellus](#): > > Is it possible to vectorise this directly? Not directly, the multiple indexing in Stan indexes all combinations of inputs. Check out the Matrix Indexing Table here: [6.8 Multiple Indexing and Range Indexing | Stan Reference Manual](https://mc-stan.org/docs/2_19/reference-manual/language-multi-indexing-section.html) (the last row, concerning `a[is, js]`, returns a matrix not a vector). The only comment I would make is that, if this is the only time theta is used, then could theta be a single dimensional vector of length L? In that case vectorization would be possible. Is theta being used elsewhere? ---

Also welcome to the forums! ---

**Author:** ![scellus](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/scellus/32/30_2.png) [@scellus](https://discourse.mc-stan.org/u/scellus)\ **Post date:** [April 13, 2019, 8:44pm UTC](https://discourse.mc-stan.org/t/multiple-indexing-from-a-multidimensional-array-to-a-vector/8457/4 "2019-04-13T20:44:07Z")

> [@bbbales2](#): > > The only comment I would make is that, if this is the only time theta is used, then could theta be a single dimensional vector of length L? In that case vectorization would be possible. Is theta being used elsewhere? Thanks for your reply. Yes, `theta` is used elsewhere. The last index is time, and there is an AR-like model over that index. And later there will be more structure over the other indices, maybe. I saw the Matrix Indexing Table but suspected that there may be another syntax hiding somewhere. ;) There seems to be `to_array_1d`— I guess I’ll try it and compute the index manually. ---

**Author:** ![bbbales2](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bbbales2/32/77_2.png) [@bbbales2](https://discourse.mc-stan.org/u/bbbales2)\ **Post date:** [April 13, 2019, 9:18pm UTC](https://discourse.mc-stan.org/t/multiple-indexing-from-a-multidimensional-array-to-a-vector/8457/5 "2019-04-13T21:18:28Z")

> [@scellus](#): > > Yes, `theta` is used elsewhere. Ah, bummer. For reference (if it helps), 3 dimensional arrays are C++ std::vectors of std::vectors of std::vectors. Stan Matrix and vector types are Eigen Matrix and Vector types. The biggest performance boost from vectorization is when there’s room for lots of shared calculation. I don’t think that’s true for a bunch of scalar normal\_lpdf evaluations, but I don’t have a great feel for what’s gonna be fast and slow here. You could very well get some performance boost by shuffling things around and making the memory happier.