Stacking

The universal method to build matrices from a couple of (matching) submatrices is concatenate. Its syntax is:

concatenate((a1, a2, ...), axis = 0)

This command stacks the submatrices vertically (on top of each other) when axis=0 is specified. With the axis=1 argument, they are stacked horizontally, and this generalizes according to arrays with more dimensions. This function is called by several convenient functions, as follows:

• hstack: Used to stack matrices horizontally
• vstack: Used to stack matrices vertically
• columnstack: Used to stack vectors in columns

Stacking vectors

One may stack vectors row-wise or column-wise using vstack and column_stack, as illustrated in the following figure:

Tip

hstack would produce the concatenation of v1 and v2. 

Let us consider the symplectic permutation as an example for vector stacking: We have a vector of size 2n. We want to perform a symplectic transformation of a vector with an even number of components, that is, exchange the first half with the second...