# Matrix Multiplication Python — Memory Hungry

Here is a snippet from my python script where I am performing:

1. a dictionary lookup
2. a cartesian multiplication of a list of len=500 against a list of len=60,
3. calculating a cumulative addition for each multiplcation combination
4. repeat this down a 20,000 rows

This is slowing things way down and making it hard to debug with the ~10 min wait times. How can I write this in a more efficient way, and that makes use of more than just one CPU?

ccle_head, dot_prod_total = [], []
with open(ccle_mRNA_file, mode='r') as ccle:
next(ccle)
exp_mat = [line.rstrip().split('\t') for line in ccle]
for row in exp_mat:
if row[0] != 'Name' and row[1] in pat_mRNA: # data row
n_row = [float(s) for s in row[2:]]
# get ready for some slow matrix multiplication:
prod = [p*n for n in n_row for p in pat_mRNA[row[1]]] # slows here
if dot_prod_total:
dot_prod_total = [cum_prod + prod for (cum_prod,prod)
else: dot_prod_total = prod  # first record of matrix products


Here are the docs for the input params:

"""
:param ccle_mRNA_file: text file, rows are gene expression across sample columns
:param pat_head: list, patient id [pat_1(str), pat_2...]
:param pat_mRNA: dict, patient RNA {gene(str):[pat_1(float), pat_2..}
:param cell_interest: set, cells of same tissue {cell_1, cell_2}
"""

• I'm working on an in-depth answer, but the absolute core advice for this type of thing is "use numpy". – lvc Jul 25 '15 at 9:38
• I'm using numpy.stats later to compute a K-S test between two different distributions of these products, but I couldn't find a suitable numpy libraries for the sort of thing I asked above. Thanks, and look forward to your in-depth answer. – Thomas Matthew Jul 25 '15 at 9:43

I'm not sure I completely follow exactly what processing you're doing to your data. The comments in the code suggest it's meant to be a matrix multiplication, the description you've provided above it suggests it's a cartesian product, but your code looks like does the sum of (flattened) outer products of corresponding rows. I'll proceed on the assumption that your code is doing the right thing, but hopefully you can clarify.

There are two general pieces of advice that apply here:

1. Separation of concerns. You're mingling code to parse your data with code to process it once it is parsed. Instead, parse everything into the appropriate data structures first, and then do the processing.

2. Use appropriate libraries and data structures. When you're doing linear algebra, that means numpy. Numpy is a dedicated, LA library that has heavily optimised routines for things like various matrix products, so you don't need to roll your own. Numpy arrays will also use quite a bit less memory than Python lists. However, what you're working with is labelled data (and some of it is labelled in two dimensions), which means the best data structure is probably a pandas dataframe - it's basically like your dict of strings to lists in pat_mRNA, but much more optimised, and fully compatible with numpy's matrix manipulations.

These things together will make your code easier to follow, more maintainable, and often both faster and shorter.

So, start by looking at your core data structure:

exp_mat = [line.rstrip().split('\t') for line in ccle]


This is a list of lists of strings. For most of the rows, you don't seem to care about column 0 at all. Column 1 contains row labels, and corresponding to keys in your dictionary pat_mRNA. The rest of it is numeric data, currently stored as strings. It also contains 'header' rows - you only keep one of those around, so presumably you only expect one to be in there. I'm guessing that is column labels, which a DataFrame lets you include directly in the same data structure.

The only trick parsing this into a DataFrame is that it is a little easier (and, apparently, more efficient) to swap the columns and rows from how you have them currently. That will affect how it prints, and which methods you call to relabel things, but not much else. This is how I would parse it into a DataFrame:

data = pd.DataFrame()
for line in ccle:
row = line.rstrip().split('\t')
if row[0] == 'Name':
elif row[1] in pat_mRNA:
data[row[1]] = [float(f) for f in row[2:]]



Note that I have modified your conditions a little, since yours seemed slightly off. The else branch of your condition effectively says "if the zeroth column is "name" or the first column isn't a match, it must be a header" - I've changed it so that instead, an appropriate value in the zeroth column is a header, and a non-matching first column on is ignored.

I've maintained a temporary 'headers' list, because your code is currently robust against those appearing anywhere in the file. A better way to maintain that robustness would be if you know - or, preferably, can parse from your file before now - how many variables you have data for. Then you could do away with that headers list and do this:

data = pd.DataFrame(index=range(nvars))
for line in ccle:
row = line.rstrip().split('\t')
if row[0] == 'Name':
data.index = row
elif row[1] in pat_mRNA:
data[row[1]] = [float(f) for f in row[2:]]


In either case, I am assuming that you have one header for each variable. If that's a bad assumption, you may need to adjust this code.

As an aside, as a matter of commonly-accepted Python style (and in accordance with PEP 8), I have placed all of the code for each branch of the if in indented blocks, even if it is only one line. At most, you should only put it immediately after the : if there is only one branch to the if (no else or elifs), and even then, consider an indented block anyway.

I would change pat_mRNA to also be a DataFrame. You could change how you currently build it, or you could just pass the whole dictionary you have at the moment into pd.DataFrame().

Once you've done that, you can use numpy to do your LA work. As written, your entire strange product becomes this:

dot_prod_total = sum(np.outer(data[key], pat_mRNA[key]).flat for key in data)


Which should be quite a lot faster than trying to do it by list comprehensions, and may use multithreading depending on how numpy is compiled.

• @JoeWallis Good point. I've updated the answer to flatten each product before summation, which I believe makes it a closer match to the OPs. – lvc Jul 25 '15 at 11:19
• @Ivc Can't I also use data = pd.read_csv('test_cell.txt',header=2,sep='\t') to read my data file into a DataFrame? And if I do that, how can I set column 1 (rather than column 0) to be the "key" (gene symbol)? – Thomas Matthew Jul 28 '15 at 5:18
• @ThomasMatthew I missed that method in the docs. It looks like you can set the row names by passing index_col=1, but the description reads as though it will leave all the data as strings. pd.read_table looks a bit better - I believe that pd.read_table('test_cell.txt', header=2, col_index=1, dtype=np.float64).T is equivalent to my loop, provided the two lines you skip aren't blank (if they are, you want header=0, which is the default). – lvc Jul 28 '15 at 5:52
• Lines 0 and 1 are basically garbage, so I'll continue with header=0. However compact this solution is, it breaks when I arrive at a row in test_cell.txt that contains NaN. How can I incorporate DataFrame.fillna() when typesetting to float? – Thomas Matthew Jul 28 '15 at 6:11
• @Thomas header=0 is what you want if lines 0 and 1 are blank - read_table doesn't count blank lines. For non-blank garbage, you still want header=2 (non-blank lines before the header line are also skipped). The navalues argument may help you with NaN cells, but otherwise, that may be a question for StackOverflow. – lvc Jul 28 '15 at 6:36

# Style

## PEP8

• It's recommended to not use inline comments.
• Have a space after , in most if not all occurrences.
for i, j in zip(list_1, list_2)

• Don't have the else section on the else:.
else: dot_prod_total = prod is kinda ugly and hard to read.

• Operators need a space either side of them. 2 + 2
The exception to this is to show precedence. 2 + 2*2

• Don't use () unless needed.
[cum_prod + prod for cum_prod, prod in zip(dot_prod_total, prod)]

• When going on a new line have the operator on the previous line. prod for prod in \n prod not prod for prod \n in prod

## Other

• Don't overwrite variables in loops using the variable. [prod for prod in prod], this makes no sense.

index_prod for index_prod in prod makes more sense.
line for line in lines is better, as it uses understandable words. I'm no mRNA researcher, so I don't know the equivalent words.

# Code

Memory Hungry

To fix this with little to no effort, you can use generator comprehensions. There almost the same as list comprehensions.

You use list comprehensions to build lists. There is a way to build generators, which are like memory efficient lists, with the same syntax.
There is a big difference between the two tho, and that is you can't index a generator.

An example of a generator in Python2 is xrange and range in Python3.

ccle_head, dot_prod_total = [], None

with open(ccle_mRNA_file, mode='r') as ccle:
for _ in range(2):
next(ccle)
exp_mat = (line.rstrip().split('\t') for line in ccle)

for row in exp_mat:
if row[0] != 'Name' and row[1] in pat_mRNA:
n_row = (float(s) for s in row[2:])
prod = (p*n for n in n_row for p in pat_mRNA[row[1]])
if dot_prod_total is not None:
dot_prod_total = (cum_prod + prod for cum_prod, prod in
zip(dot_prod_total, prod))
else:
dot_prod_total = prod
else:

Generators are good as they use roughly $O(1)$ memory, rather than lists with $O(n)$.
Some things don't work with generators however, and so you may have to use list(generator). However with most things it will work fine.