How to check whether two lists are circularly identical in Python

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For instance, I have lists:

a[0] = [1, 1, 1, 0, 0]
a[1] = [1, 1, 0, 0, 1]
a[2] = [0, 1, 1, 1, 0]
# and so on

They seem to be different, but if it is supposed that the start and the end are connected, then they are circularly identical.

The problem is, each list which I have has a length of 55 and contains only three ones and 52 zeros in it. Without circular condition, there are 26,235 (55 choose 3) lists. However, if the condition "circular" exists, there are a huge number of circularly identical lists

Currently I check circularly identity by following:

def is_dup(a, b):
    for i in range(len(a)):
        if a == list(numpy.roll(b, i)): # shift b circularly by i
            return True
    return False

This function requires 55 cyclic shift operations at the worst case. And there are 26,235 lists to be compared with each other. In short, I need 55 * 26,235 * (26,235 - 1) / 2 = 18,926,847,225 computations. It"s about nearly 20 Giga!

Is there any good way to do it with less computations? Or any data types that supports circular?

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Is there a list of Pytz Timezones?

3 answers

I would like to know what are all the possible values for the timezone argument in the Python library pytz. How to do it?

834

Answer #1

You can list all the available timezones with pytz.all_timezones:

In [40]: import pytz
In [41]: pytz.all_timezones
Out[42]: 
["Africa/Abidjan",
 "Africa/Accra",
 "Africa/Addis_Ababa",
 ...]

There is also pytz.common_timezones:

In [45]: len(pytz.common_timezones)
Out[45]: 403

In [46]: len(pytz.all_timezones)
Out[46]: 563

Python strptime() and timezones?

3 answers

I have a CSV dumpfile from a Blackberry IPD backup, created using IPDDump. The date/time strings in here look something like this (where EST is an Australian time-zone):

Tue Jun 22 07:46:22 EST 2010

I need to be able to parse this date in Python. At first, I tried to use the strptime() function from datettime.

>>> datetime.datetime.strptime("Tue Jun 22 12:10:20 2010 EST", "%a %b %d %H:%M:%S %Y %Z")

However, for some reason, the datetime object that comes back doesn"t seem to have any tzinfo associated with it.

I did read on this page that apparently datetime.strptime silently discards tzinfo, however, I checked the documentation, and I can"t find anything to that effect documented here.

I have been able to get the date parsed using a third-party Python library, dateutil, however I"m still curious as to how I was using the in-built strptime() incorrectly? Is there any way to get strptime() to play nicely with timezones?

198

Answer #1

I recommend using python-dateutil. Its parser has been able to parse every date format I"ve thrown at it so far.

>>> from dateutil import parser
>>> parser.parse("Tue Jun 22 07:46:22 EST 2010")
datetime.datetime(2010, 6, 22, 7, 46, 22, tzinfo=tzlocal())
>>> parser.parse("Fri, 11 Nov 2011 03:18:09 -0400")
datetime.datetime(2011, 11, 11, 3, 18, 9, tzinfo=tzoffset(None, -14400))
>>> parser.parse("Sun")
datetime.datetime(2011, 12, 18, 0, 0)
>>> parser.parse("10-11-08")
datetime.datetime(2008, 10, 11, 0, 0)

and so on. No dealing with strptime() format nonsense... just throw a date at it and it Does The Right Thing.

Update: Oops. I missed in your original question that you mentioned that you used dateutil, sorry about that. But I hope this answer is still useful to other people who stumble across this question when they have date parsing questions and see the utility of that module.

Fitting empirical distribution to theoretical ones with Scipy (Python)?

3 answers

INTRODUCTION: I have a list of more than 30,000 integer values ranging from 0 to 47, inclusive, e.g.[0,0,0,0,..,1,1,1,1,...,2,2,2,2,...,47,47,47,...] sampled from some continuous distribution. The values in the list are not necessarily in order, but order doesn"t matter for this problem.

PROBLEM: Based on my distribution I would like to calculate p-value (the probability of seeing greater values) for any given value. For example, as you can see p-value for 0 would be approaching 1 and p-value for higher numbers would be tending to 0.

I don"t know if I am right, but to determine probabilities I think I need to fit my data to a theoretical distribution that is the most suitable to describe my data. I assume that some kind of goodness of fit test is needed to determine the best model.

Is there a way to implement such an analysis in Python (Scipy or Numpy)? Could you present any examples?

Thank you!

159

Answer #1

Distribution Fitting with Sum of Square Error (SSE)

This is an update and modification to Saullo"s answer, that uses the full list of the current scipy.stats distributions and returns the distribution with the least SSE between the distribution"s histogram and the data"s histogram.

Example Fitting

Using the El Niño dataset from statsmodels, the distributions are fit and error is determined. The distribution with the least error is returned.

All Distributions

All Fitted Distributions

Best Fit Distribution

Best Fit Distribution

Example Code

%matplotlib inline

import warnings
import numpy as np
import pandas as pd
import scipy.stats as st
import statsmodels.api as sm
from scipy.stats._continuous_distns import _distn_names
import matplotlib
import matplotlib.pyplot as plt

matplotlib.rcParams["figure.figsize"] = (16.0, 12.0)
matplotlib.style.use("ggplot")

# Create models from data
def best_fit_distribution(data, bins=200, ax=None):
    """Model data by finding best fit distribution to data"""
    # Get histogram of original data
    y, x = np.histogram(data, bins=bins, density=True)
    x = (x + np.roll(x, -1))[:-1] / 2.0

    # Best holders
    best_distributions = []

    # Estimate distribution parameters from data
    for ii, distribution in enumerate([d for d in _distn_names if not d in ["levy_stable", "studentized_range"]]):

        print("{:>3} / {:<3}: {}".format( ii+1, len(_distn_names), distribution ))

        distribution = getattr(st, distribution)

        # Try to fit the distribution
        try:
            # Ignore warnings from data that can"t be fit
            with warnings.catch_warnings():
                warnings.filterwarnings("ignore")
                
                # fit dist to data
                params = distribution.fit(data)

                # Separate parts of parameters
                arg = params[:-2]
                loc = params[-2]
                scale = params[-1]
                
                # Calculate fitted PDF and error with fit in distribution
                pdf = distribution.pdf(x, loc=loc, scale=scale, *arg)
                sse = np.sum(np.power(y - pdf, 2.0))
                
                # if axis pass in add to plot
                try:
                    if ax:
                        pd.Series(pdf, x).plot(ax=ax)
                    end
                except Exception:
                    pass

                # identify if this distribution is better
                best_distributions.append((distribution, params, sse))
        
        except Exception:
            pass

    
    return sorted(best_distributions, key=lambda x:x[2])

def make_pdf(dist, params, size=10000):
    """Generate distributions"s Probability Distribution Function """

    # Separate parts of parameters
    arg = params[:-2]
    loc = params[-2]
    scale = params[-1]

    # Get sane start and end points of distribution
    start = dist.ppf(0.01, *arg, loc=loc, scale=scale) if arg else dist.ppf(0.01, loc=loc, scale=scale)
    end = dist.ppf(0.99, *arg, loc=loc, scale=scale) if arg else dist.ppf(0.99, loc=loc, scale=scale)

    # Build PDF and turn into pandas Series
    x = np.linspace(start, end, size)
    y = dist.pdf(x, loc=loc, scale=scale, *arg)
    pdf = pd.Series(y, x)

    return pdf

# Load data from statsmodels datasets
data = pd.Series(sm.datasets.elnino.load_pandas().data.set_index("YEAR").values.ravel())

# Plot for comparison
plt.figure(figsize=(12,8))
ax = data.plot(kind="hist", bins=50, density=True, alpha=0.5, color=list(matplotlib.rcParams["axes.prop_cycle"])[1]["color"])

# Save plot limits
dataYLim = ax.get_ylim()

# Find best fit distribution
best_distibutions = best_fit_distribution(data, 200, ax)
best_dist = best_distibutions[0]

# Update plots
ax.set_ylim(dataYLim)
ax.set_title(u"El Niño sea temp.
 All Fitted Distributions")
ax.set_xlabel(u"Temp (°C)")
ax.set_ylabel("Frequency")

# Make PDF with best params 
pdf = make_pdf(best_dist[0], best_dist[1])

# Display
plt.figure(figsize=(12,8))
ax = pdf.plot(lw=2, label="PDF", legend=True)
data.plot(kind="hist", bins=50, density=True, alpha=0.5, label="Data", legend=True, ax=ax)

param_names = (best_dist[0].shapes + ", loc, scale").split(", ") if best_dist[0].shapes else ["loc", "scale"]
param_str = ", ".join(["{}={:0.2f}".format(k,v) for k,v in zip(param_names, best_dist[1])])
dist_str = "{}({})".format(best_dist[0].name, param_str)

ax.set_title(u"El Niño sea temp. with best fit distribution 
" + dist_str)
ax.set_xlabel(u"Temp. (°C)")
ax.set_ylabel("Frequency")

We hope this article has helped you to resolve the problem. Apart from How to check whether two lists are circularly identical in Python, check other identity-related topics.

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Angelo Innsbruck

Munchen | 2022-12-05

identity is always a bit confusing 😭 How to check whether two lists are circularly identical in Python is not the only problem I encountered. I am just not quite sure it is the best method

Walter Williams

California | 2022-12-05

Thanks for explaining! I was stuck with How to check whether two lists are circularly identical in Python for some hours, finally got it done 🤗. I just hope that will not emerge anymore

Xu Zelotti

Rome | 2022-12-05

Maybe there are another answers? What How to check whether two lists are circularly identical in Python exactly means?. Will use it in my bachelor thesis

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