List comprehensions and matrices (raws) - python-3.x

Question

Please, have a look at this constriction:
M = [[1,2,3],
[4,5,6],
[7,8,9]]
T = [row[1] for row in M]
print(T)
The result is [2, 5, 8]
I managed to find something here:
http://docs.python.org/py3k/tutorial/datastructures.html#nested-list-comprehensions
But I'm not satisfied with my understanding of this scheme with 'raw'.
Could you tell me where else in the documentation can I read about it?
By the way, why raw? It seems to be a column?

Answer 1

T = [row[1] for row in M]
This is a list comprehension. List comprehensions basically allow you to create lists on the fly while iterating through other iterables (in this case M).
The code above is more or less identical to this:
T = [] # create empty list that holds the result
for row in M: # iterate through all 'rows' in M
cell = row[1] # get the second cell of the current row
T.append(cell) # append the cell to the list
This is all just put together into a single line and a bit more efficient, but the basic idea is the same.
M is a matrix, but the internal representation you chose is a list of lists; or a list of rows. And in T you want to select a single column of the matrix although you have no direct access to columns in the matrix T. So you basically go through each row, take the cell of the column you are interested in and create a new list with the cells of your columns (as lists are usually horizontally aligned, you are strictly getting the transposed vector of your column).

Answer 2

You iterate through the rows and take second element of the row. Then you collect the extracted elements from the rows. It means that you have extracted the column.
Read the list comprehension from the right to the left. It says:
Loop through the matrix M to get the row each time (for row in M).
Apply the expression to the row to get what you need (here row[1]).
Iterate through the constructed results and build the list of them ([...]).
The last point makes it the list comprehension. The thing between the [ and ] is called a generator expression. You can also try:
column = list(row[1] for row in M)
And you get exactly the same. That is because the list() construct a list from any iterable. And the generator expression is such iterable thing. You can also try:
my_set = set(row[1] for row in M)
to get the set of the elements that form the column. The syntactically brief form is:
my_set = {row[1] for row in M}
and it is called set comprehension. And there can be also a dictionary comprehension like this:
d = { row[1]: True for row in M }
Here rather artificially, the row[1] is used as the key, the True is used as the value.