Merge pull request #902 from stan-dev/fix-column-major-explanation

Correct explanation of column-major order, example output

Author: bob-carpenter

src/cmdstan-guide/stan_csv_apdx.qmd

@@ -47,9 +47,10 @@ element index is $1$ and the last element index is $N$.
 Container variables are serialized in
 [column major order](https://eli.thegreenplace.net/2015/memory-layout-of-multi-dimensional-arrays),
 a.k.a. "Fortran" order.
-In column major-order, all elements of column 1 are listed in ascending order,
+In column major-order for a 2-D container, all elements of column 1 are listed in ascending order,
 followed by all elements of column 2, thus the
-first index changes the slowest and the last index changes the fastest.
+column index changes the slowest and the row index changes the fastest. For higher dimensions,
+this generalizes to the last index changing the slowest and first index changing the fastest.
 
 To see how this works, consider a 3-dimensional variable with dimension sizes 2, 3, and 4,
 e.g., an array of matrices, a 2-D array of vectors or row_vectors, or a 3-D array of scalars.
@@ -60,11 +61,11 @@ Given a Stan program with model parameter variable:
 The Stan CSV file will require 24 columns to output the elements of `foo`.
 The first 6 columns will be labeled:
 ```
-foo.1.1.1, foo.1.1.2, foo.1.1.3, foo.1.1.4, foo.1.2.1, foo.1.2.2
+foo.1.1.1,foo.2.1.1,foo.1.2.1,foo.2.2.1,foo.1.3.1,foo.2.3.1
 ```
 The final 6 columns will be labeled:
 ```
-foo.2.2.3, foo.2.2.4, foo.2.3.1, foo.2.3.2, foo.2.3.3, foo.2.3.4
+foo.1.1.4,foo.2.1.4,foo.1.2.4,foo.2.2.4,foo.1.3.4,foo.2.3.4
 ```
 
 To see how a tuple would be laid out, consider the following variable: