4.7.1 Stacking vectors

You may stack vectors row-wise or column-wise using vstack and column_stack, as illustrated in Figure 4.3:

Figure 4.3: Difference between vstack and column_stack

Note that hstack would produce the concatenation of v1 and v2. 

Let's consider the symplectic permutation as an example for vector stacking: we have a vector of size . 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 half of the vector with sign change:

This operation is resolved in Python as follows:

# v is supposed to have an even length.
def symp(v):
    n = len(v) // 2 # use the integer division //
    return hstack([v[-n:], -v[:n]])