The function about a vec-permutation matrix

[renc]

Thank you, Rick. It is good enough. I got it.

My purpose is to find an information matrix at convergence. To get it, I need to know the relationship between vec(A) and vec(A`), which is only one part of the information matrix.

[Rick_SAS]

In SAS/IML, the SHAPECOL function is used to generate vec(A).  You can use the SHAPE function to generate vec(A`) directly, without using any transpose operators.

Explicitly forming a permutation matrix is usually inefficient because you are using an nxn matrix to represent a permutation on N elements. I avoid permutation matrices whenever possible and use the permutation as a subscript index to map a vector to a permutation of iteself. However, if you insists on it, you can generate a permutation matrix from a permutation vector by using the function in this blog post: Automating the Great Christmas Gift Exchange - The DO Loop