Compare Numpy and Matlab code that uses random permutation - python

I'm having problems to compare the output of two code because of random number state.
I'm comparing the MATLAB randperm function with the output of the equivalent numpy.random.permutation function but, even if I've set the seed to the same value with a MATLAB rand('twister',0) and a python numpy.random.seed(0) I'm obtaining different permutations.
I've to say that the result of MATLAB's rand and numpy numpy.random.rand are the same if the seed are set like above.

This is a common issue. While the random number generator is identical, the function which converts your random number stream into a random permutation is different. There is no specified standard algorithm which describes the expected result.
To solve this issue, you have to use the same library in both tools.

Related

Matching random seed in R for code coming from Python

I am given some python codes which depends on random numbers. This python code use a random_seed = 300.
Now I am trying to replicate this Python code in R. To make sure that the replication is perfect, I need to compare the end results between R and Python. Given that, the code depends on the random numbers, is there any way to know the equivalent random seed to be used in R?
I had a look into Creating same random number sequence in Python, NumPy and R, but it appears to be opposite way implementation i.e. from R to Python.
There is also a R library called reticulate where I could run python code in R, but could not figure out if I could fetch the R-equivalent random seed using this library
Any pointer will be very helpful.
Many thanks,

Total variation implementation in numpy for a piecewise linear function

I would like to use total variation in Python, but I wasn't able to find an existing implementation.
Assuming that I have an array with a finite number of elements, is the implementation with NumPy simply as:
import numpy as np
a = np.array([...], dtype=float)
tv = np.sum(np.abs(np.diff(a)))
My main doubt is how to compute the supremum of tv across all partitions, and if just the sum of the absolute difference might suffice for a finite array of floats.
Edit: My input array represents a piecewise linear function, therefore the supremum over the full set of partitions is indeed the sum of absolute differences between contiguous points.
Yes, that is correct.
I imagine you're confused by the mathy definition on the Wikipedia page for total variation. Have a look at the more practical definition on the Wikipedia page for total variation denoising instead.
For an actual code (even Python) implementation, see e.g. Tensorflow's total_variation(), though this is for one or more (2D, color) images, so the TV is computed for both rows and columns, and then added together.

Numpy: random number generation - breaking loop into chunks

A question regarding the generation of random numbers in Numpy.
I have a code which does the following:
import numpy as np
for i in range(very_big_number):
np.random.randn(5)
# other stuff that uses the generated random numbers
since unfortunately very_big_number can really be a very large number, I wanted to break this loop into chunks, say e.g. call 10 times the same
for i in range(very_big_number/10):
np.random.randn(5)
# other stuff that uses the generated random numbers
and then collate all the output together. However, I want to make sure that this division into blocks preserves the randomness of my generated numbers.
My question is:reading the numpy docuemntation or equivalently
this question on StackOverflow, I would be tempted to think that it is enough to just divide the loops and run the subloops on e.g. ten different cores at the same time. However I would like to know if that is correct or if I should set some random number seed and if so, how.
Dividing the loop.... the randomness is questionable....
Instead go for parallel processing....
Try below said "Joblib" library or any other library if you know for parallel processing....
https://pythonhosted.org/joblib/parallel.html
Joblib provides a simple helper class to write parallel for loops
using multiprocessing

Difference between Numpy's random module and Python? [duplicate]

I have a big script in Python. I inspired myself in other people's code so I ended up using the numpy.random module for some things (for example for creating an array of random numbers taken from a binomial distribution) and in other places I use the module random.random.
Can someone please tell me the major differences between the two?
Looking at the doc webpage for each of the two it seems to me that numpy.random just has more methods, but I am unclear about how the generation of the random numbers is different.
The reason why I am asking is because I need to seed my main program for debugging purposes. But it doesn't work unless I use the same random number generator in all the modules that I am importing, is this correct?
Also, I read here, in another post, a discussion about NOT using numpy.random.seed(), but I didn't really understand why this was such a bad idea. I would really appreciate if someone explain me why this is the case.
You have made many correct observations already!
Unless you'd like to seed both of the random generators, it's probably simpler in the long run to choose one generator or the other. But if you do need to use both, then yes, you'll also need to seed them both, because they generate random numbers independently of each other.
For numpy.random.seed(), the main difficulty is that it is not thread-safe - that is, it's not safe to use if you have many different threads of execution, because it's not guaranteed to work if two different threads are executing the function at the same time. If you're not using threads, and if you can reasonably expect that you won't need to rewrite your program this way in the future, numpy.random.seed() should be fine. If there's any reason to suspect that you may need threads in the future, it's much safer in the long run to do as suggested, and to make a local instance of the numpy.random.Random class. As far as I can tell, random.random.seed() is thread-safe (or at least, I haven't found any evidence to the contrary).
The numpy.random library contains a few extra probability distributions commonly used in scientific research, as well as a couple of convenience functions for generating arrays of random data. The random.random library is a little more lightweight, and should be fine if you're not doing scientific research or other kinds of work in statistics.
Otherwise, they both use the Mersenne twister sequence to generate their random numbers, and they're both completely deterministic - that is, if you know a few key bits of information, it's possible to predict with absolute certainty what number will come next. For this reason, neither numpy.random nor random.random is suitable for any serious cryptographic uses. But because the sequence is so very very long, both are fine for generating random numbers in cases where you aren't worried about people trying to reverse-engineer your data. This is also the reason for the necessity to seed the random value - if you start in the same place each time, you'll always get the same sequence of random numbers!
As a side note, if you do need cryptographic level randomness, you should use the secrets module, or something like Crypto.Random if you're using a Python version earlier than Python 3.6.
From Python for Data Analysis, the module numpy.random supplements the Python random with functions for efficiently generating whole arrays of sample values from many kinds of probability distributions.
By contrast, Python's built-in random module only samples one value at a time, while numpy.random can generate very large sample faster. Using IPython magic function %timeit one can see which module performs faster:
In [1]: from random import normalvariate
In [2]: N = 1000000
In [3]: %timeit samples = [normalvariate(0, 1) for _ in xrange(N)]
1 loop, best of 3: 963 ms per loop
In [4]: %timeit np.random.normal(size=N)
10 loops, best of 3: 38.5 ms per loop
The source of the seed and the distribution profile used are going to affect the outputs - if you are looking for cryptgraphic randomness, seeding from os.urandom() will get nearly real random bytes from device chatter (ie ethernet or disk) (ie /dev/random on BSD)
this will avoid you giving a seed and so generating determinisitic random numbers. However the random calls then allow you to fit the numbers to a distribution (what I call scientific random ness - eventually all you want is a bell curve distribution of random numbers, numpy is best at delviering this.
SO yes, stick with one generator, but decide what random you want - random, but defitniely from a distrubtuion curve, or as random as you can get without a quantum device.
It surprised me the randint(a, b) method exists in both numpy.random and random, but they have different behaviors for the upper bound.
random.randint(a, b) returns a random integer N such that a <= N <= b. Alias for randrange(a, b+1). It has b inclusive. random documentation
However if you call numpy.random.randint(a, b), it will return low(inclusive) to high(exclusive). Numpy documentation

Sampling from a huge uniform distribution in Python

I need to select 3.7*10^8 unique values from the range [0, 3*10^9] and either obtain them in order or keep them in memory.
To do this, I started working on a simple algorithm where I sample smaller uniform distributions (that fit in memory) in order to indirectly sample the large distribution that really interests me.
The code is available at the following gist https://gist.github.com/legaultmarc/7290ac4bef4edb591d1e
Since I'm having trouble implementing something more robust, I was wondering if you had other ideas to sample unique values from a large discrete uniform. I'm looking for either an algorithm, a module or an idea on how to manage very large lists directly (perhaps using the hard drive instead of memory).
There is an interesting post, Generating sorted random ints without the sort? O(n) which suggests that instead of generating uniform random ints, you can do a running-sum on exponential random deltas, which gives you a uniform random result generated in sorted order.
It's not guaranteed to give exactly the number of samples you want, but should be pretty close, and much faster / lower memory requirements.
Edit: I found a second post, generating sorted random numbers without exponentiation involved? which suggests tweaking the distribution density as you go to generate an exact number of samples, but I am leery of just exactly what this would do to your "uniform" distribution.
Edit2: Another possibility that occurs to me would be to use an inverse cumulative binomial distribution to iteratively split your sample range (predict how many uniformly generated random samples would fall in the lower half of the range, then the remainder must be in the upper half) until the block-size reaches something you can easily hold in memory.
This is a standard sample with out replacement. You can't divide the range [0, 3*10^9] into equally binned ranges and sample same amount in each bin.
Also, 3 billion is relative large, many "ready to use" codes only handle 32 bit integers, roughly 2 billion(+-). Please take a close look at their implementations.

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