# An introduction to Python syntax and plotting

In this tutorial, we will learn some of the basics of programming in Python. While this will all become muscle memory, it’s useful to keep this as a reference. To follow along with this tutorial, launch a Jupyter notebook as described in tutorial 0b and type along as we go into the code cells.

## Basic shell commands

In Tutorial 0a and tutorial 0b, you learned how to launch an IPython interpreter from a terminal. Having knowledge of some basic UNIX command line skills, such as moving between directories, listing files in a given directory, and making new directories, is imperative to becoming a computational scientist. Please see this wonderful tutorial by Justin Bois for a primer on using the command line. Briefly, you will only need to know three commands.

1. cd - “Change directories”. By typing this command, you will be able to move from where you currently are to another folder. You can do this by specifically typing a path, such as cd /Users/gchure/bige105. You can also move relative to where you currently are by using some shorthand notation. Typing cd ../ will move you up one directory, cd ../../ will move you up two directories, and cd ~/ will move you to your home directory.

2. ls - “List files and directories”. Typing this command in your terminal will list all files and directories in your current working directory.

3. mkdir - “Make directory”. This is useful for making new directories on your computer without having to open Finder or Windows Explorer. For example, I can make a data folder in my BiGe105 root directory by typing mkdir data. I could make another folder called good_data two directories up from my current folder by typing mkdir ../../data.

With these three commands memorized, you should be able to navigate around your computer without leaving the terminal.

## Hello, world

As is typical when learning any programming language, we’ll start by making our computer speak to us. We’ll do this by using one of the many standard functions in Python, the print function.

 input
print('Hello, world')

 output
Hello, world


In the above code, we called the print function and passed the text Hello, world. surrounded by single quotation marks ''. The text was passed as an argument to the print function by placing it in the parentheses. The quotation marks determined the type of the argument to be text, known as a string. While we used single quotations in the above code, we could also use double quotations "". These are exchangeable in Python.

While our 'Hello, world.' is a string, this function can also be used to print other types such as integers (int), decimals (float), and True/False (bool) by passing them as arguments to the print function.

 input
print(10)
print(3.14159)
print(True)

 output
10
3.14159
True


In the above code, it would be nice to be able to add a comment about what the type of each variable is that we are printing, but we don’t want this comment to be interpreted by Python. By adding a pound symbol (#) before a line of code, we can force Python to ignore it.

 input
# Print an integer
print(10)

# Print a float
print(3.14159)

# Print a bool
print(True)

 output
10
3.14159
True


We see that we get the same result.

## Basic math

### Arithmetic

The crux of scientific programming is the ability to perform mathematical operations. Python can do a variety of simple mathematical functions by default.

 input
print(1 + 1) # this should be 2
print(4 / 2) # this should be 2
print(40 - 38) # this should be 2
print(2^4) # this should be 16

 output
2
2.0
2
6


Everything looks good, but what happened at the end? In Python, you exponentiate terms using a double asterisk (**) and not a carrot (^). The carrot executes a bitwise operation which is completely different than exponentiation.

 input
print(2**4) # this should be 16

 output
16


Note that the all mathematical operations other than addition (+) can only be done on ints, floats, or bool. The addition operator can be performed on strings too! Let’s say we want to stitch together two components of a sequence together.

 input
print('AATAGGCGATAG' + 'tttgaggcgggggc')

 output
AATAGGCGATAGtttgaggcgggggc


While all of these operations are simple, we would like some way in which can store a number for further use. We can do this by assigning the output of an operation to a variable.

 input
# Assign our sequences to variables.
seq_1 = 'AATAGGCGATAG'
seq_2 = 'tttgaggcgggggc'
stitched_seq = seq_1 + seq_2
print(stitched_seq)

 output
AATAGGCGATAGtttgaggcgggggc


We can call methods on some data types in Python. For example, we can convert our stiteched string into all upper or lower case using the upper() or lower() method.

 input
# Convert the stitched sequences to all upper and all lower case.
upper_seq = stitched_seq.upper()
lower_seq = stitched_seq.lower()
print(upper_seq)
print(lower_seq)

 output
AATAGGCGATAGTTTGAGGCGGGGGC
aataggcgatagtttgaggcgggggc


We can also count the occurrences of a given character in a string by using the count() method.

 input
# Count the number of the different bases in the stitched DNA sequence.
num_A = upper_seq.count('A')
num_T = upper_seq.count('T')
num_C = upper_seq.count('C')
num_G = upper_seq.count('G')

# Print them to the screen for good measure.
print(num_A)
print(num_T)
print(num_C)
print(num_G)

 output
6
5
3
12


### Lists and tuples

So far, we’ve learned about floats, ints, bools, and strings as well as how to assign them to variables. But what about when we want to work with a series of these kinds of values? There are a few ways in which we can do this $-$ lists (values within brackets []), tuples (values within parenthesis ()), and arrays (which we’ll learn about in the next section).

 input
# Generate some lists and arrays.
example_list = [1, 2, 3]
example_tuple = (1, 2, 3)
list_of_lists = [[1, 2, 3]]
tuple_of_lists = ([1, 2, 3], [200, 2], 1)
mixed_type_list = [1, 2, 'biology', 'geology', 10.028]


Note that lists and arrays can have mixed types. Once we have a list or a tuple, we can extract a single value or a range of values by indexing.

 input
# Index some values.
print(example_list[0])  # should be 1
print(example_tuple[2])  # should be 3
print(example_list[0:2]) # should be 1 and 2
print(example_list[-1])  # This will give the last entry of the list

 output
1
3
[1, 2]
3


To get the first value of the list, I started with zero. In Python, indexing begins at 0. This is different than in other programming languages such as MATLAB which begins at 1.

So what exactly is the difference between tuples and lists? Lists are mutable. Tuples are not. This means once a value in a tuple is set in place, it can’t be changed without redefining the tuple. Let’s demonstrate this by trying to change the first value of our example_list and example_tuple.

 input
# Change the first entry to 1000
example_list[0] = 1000
print(example_list)
example_tuple[0] = 1000
print(example_tuple)

 output
[1000, 2, 3]

---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-15-a399fb3f8313> in <module>
2 example_list[0] = 1000
3 print(example_list)
----> 4 example_tuple[0] = 1000
5 print(example_tuple)

TypeError: 'tuple' object does not support item assignment


Python yelled at me and told me that I can’t assign a current value in a tuple. This is a very important point. For example, if you want to have some process output a series of values you don’t want to change, put them in a tuple. Otherwise, put them in a list or an array.

Lists are mutable, but we have to be careful with performing arithmetic operations on them. For example, the operators +,-, **, and / will give you errors. However, the * operator will concatenate a list with itself.

 input
# Do list arithmetic.
next_list = [2, 4, 6]
print(next_list * 2)  # Should be [2, 4, 6, 2, 4, 6]
print(next_list * 5)  # Should be the same list repeated five times.

 output
[2, 4, 6, 2, 4, 6]
[2, 4, 6, 2, 4, 6, 2, 4, 6, 2, 4, 6, 2, 4, 6]


So how do we do more complicated mathematical operations on a series of numbers? How can I multiply each element of an array by five? How do I take the exponential of each element? How do I perform a dot product between two series? To perform such tasks, we will have to import another python module, NumPy.

## Importing modules and working with NumPy

When you open a Python interpreter or run a script, you are only loading the ‘standard’ Python packages. This means that you are not loading everything you could possibly want, but only the packages you need to perform the task. To perform more elaborate computation in Python, we will need to import an external module called NumPy.

 input
# Import the NumPy module and give it an alias
import numpy as np


Whenever you write a Python script, you should always import the modules you will need at the very beginning. That way, all of the required packages will be loaded and ready to go when you start loading them.

Let’s talk about the syntax of the above line. I told the Python interpreter that it should import the module called numpy and give it the alias of np. This means whenever I have to call a Numpy associated function, I can do so by typing np.function_name instead of numpy.function_name. The alias can be whatever you would like it to be, but you should stick by the community standards so your code is clear to everyone who is trying to figure out what you are doing.

Numpy is the premier numerical computing module for Python. With it, we have myriad functions for peforming numerical operations.

 input
# Demonstrate the power of numpy.
print(np.exp(-1))
print(np.sin(1))
print(np.cos(2 * np.sin(5)))
print(np.sin(2 * np.pi))

 output
0.36787944117144233
0.8414709848078965
-0.3401272599624713
-2.4492935982947064e-16


With numpy comes a new data type called numpy arrays. These are series of values which are mutable (just like lists) which cannot have a mixed data type (unlike lists and tuples). We can also perform mathematical operations on arrays.

 input
# Demonstrate the magic of numpy arrays
my_array = np.array([1, 2, 3])

#Basic arithmetic
print(my_array * 2)  # Element-wise multiplication
print(my_array / 3)  # Element-wise division
print(my_array * my_array)  # Element-wise multiplication
print(np.dot(my_array, my_array)) # Dot product of two arrays

 output
[2 4 6]
[0.33333333 0.66666667 1.        ]
[1 4 9]
14


Numpy arrays are not limited to being one-dimensional. We can create n-dimensional numpy arrays with ease.

 input
# Create multi-dimensional arrays
one_dimensional_array = np.array([1, 2, 3, 4])
two_dimensional_array = np.array([[1, 2, 3, 4],
[5, 6, 7, 8]])

print(one_dimensional_array)
print(two_dimensional_array)

 output
[1 2 3 4]
[[1 2 3 4]
[5 6 7 8]]


We can even make numpy make series of values for us! This will be very useful once we start manipulating images and making plots.

 input
# Automatically generate series of values.
linear_spaced = np.linspace(0, 10, 1000)  # Generates 1000 points between 0 and 10
log_spaced = np.logspace(-1, 1, 200) # Generates 200 points logarithmically spaced
# between .1 and 10
aranged = np.arange(0, 50, 2)  # Generates values between 0 and 50 taking steps of
# two.


It is impossible to perform scientific computing in Python without using numpy.

## Checking type, length, and shape

It’s useful to be able to see some properties of variables we assign. Let’s look back at the sequence strings we made earlier and extract some of their properties.

 input
# Generate some variable with different types.
string_type = 'AATGATTCG'
float_type = 3.14159
bool_type = True
int_type = 3
list_type = ['Escherichia coli', 'Salmonella enterica', 10]
tuple_type = ('Geospiza fortis', 3)
nparray_type = np.ones_like(tuple_type)

# Print their types
print(type(string_type))
print(type(float_type))
print(type(bool_type))
print(type(int_type))
print(type(list_type))
print(type(tuple_type))
print(type(nparray_type))

 output
<class 'str'>
<class 'float'>
<class 'bool'>
<class 'int'>
<class 'list'>
<class 'tuple'>
<class 'numpy.ndarray'>


Note that even though the elements of our list_type and tuple_type have mixed types, this command tells us what the type of the object is (i.e. list and tuple). We can force changes in the type of a variable with ease. To demonstrate, let’s break up our stitched sequence into the individual basepairs.

 input
# Change the type of a varible
basepairs = list(stitched_seq)
print(basepairs)

 output
['A', 'A', 'T', 'A', 'G', 'G', 'C', 'G', 'A', 'T', 'A', 'G', 't', 't', 't', 'g', 'a', 'g', 'g', 'c', 'g', 'g', 'g', 'g', 'g', 'c']


We can also convert numbers to strings. This is useful if we want to print a sentence including the output from some other operation. Let’s check the length of our two DNA sequences and print it in a sentence.

 input
# Determine the lengths of the two sequences.
seq_1_len = len(seq_1)
seq_2_len = len(seq_2)
print("The length of our sequence is " + str(seq_1_len + seq_2_len) + ' bases')

 output
The length of our sequence is 26 bases


We’ve created a lot of variable so far in this tutorial. It’s nice to be able to look at what variables exist in our environment as well as get some information. Let’s take a look at everything we’ve made so far.

 input
whos

 output
Variable                Type       Data/Info
--------------------------------------------
aranged                 ndarray    25: 25 elems, type int64, 200 bytes
basepairs               list       n=26
bool_type               bool       True
example_list            list       n=3
example_tuple           tuple      n=3
float_type              float      3.14159
int_type                int        3
linear_spaced           ndarray    1000: 1000 elems, type float64, 8000 bytes
list_of_lists           list       n=1
list_type               list       n=3
log_spaced              ndarray    200: 200 elems, type float64, 1600 bytes
lower_seq               str        aataggcgatagtttgaggcgggggc
mixed_type_list         list       n=5
my_array                ndarray    3: 3 elems, type int64, 24 bytes
next_list               list       n=3
np                      module     <module 'numpy' from '/Us<...>kages/numpy/__init__.py'>
nparray_type            ndarray    2: 2 elems, type <U15, 120 bytes
num_A                   int        6
num_C                   int        3
num_G                   int        12
num_T                   int        5
one_dimensional_array   ndarray    4: 4 elems, type int64, 32 bytes
seq_1                   str        AATAGGCGATAG
seq_1_len               int        12
seq_2                   str        tttgaggcgggggc
seq_2_len               int        14
stitched_seq            str        AATAGGCGATAGtttgaggcgggggc
string_type             str        AATGATTCG
tuple_of_lists          tuple      n=3
tuple_type              tuple      n=2
two_dimensional_array   ndarray    2x4: 8 elems, type int64, 64 bytes
upper_seq               str        AATAGGCGATAGTTTGAGGCGGGGGC


We see that we get a relatively nicely ordered list of all of our variables, the type of the variable, and then information about their contents. We can see for our lists and arrays it tells us the number of rows and columns, how many elements there are, what the type of those elements are and so forth.

## Functions

Functions are arguably the most important components of efficient and effective programming. Functions are sections of code that are written to take an argument, perform some manipulation, and return the manipulated argument. In Python, these functions can be written in the same script where you want to use them.

In Python, spacing and indentation matters. When we define a function and perform looping, we have to be very aware of where our code exists in the script. Once you define a function, all operations that are to take place in that function should be indented from the rest of the code.

The best way to learn is by doing. Let’s write a function to add two DNA sequences together and determine its GC content, the percentage of the DNA that is either guanine or cytosine.

 input
def compute_gc(seq_a, seq_b, print_seq=True):
"""
Stitches together two DNA sequences (seq_a and seq_b) into a single sequence
then computes the GC content. This is defined as the number of G's and C's in
the sequence divided by the total sequence length.
"""

# Merge the sequences together.
merged_sequence = seq_a + seq_b

# Determine if the new string should be printed.
if print_seq == True:
print(merged_sequence)

# Make the merged string all upper-case.
merged_upper = merged_sequence.upper()

# Count the number of G's and C's.
num_G = merged_upper.count('G')
num_C = merged_upper.count('C')

# Compute the length of the sequence and the GC content.
seq_len = len(merged_upper)
gc_content = (num_G + num_C) / seq_len

# Return the gc_content
return gc_content


We did a lot of complicated procedures in this code, so let’s go through it piece by piece.

1. We defined the function as compute_gc which takes the arguments seq_a and seq_b as well as a keyword argument print_sequence which has a default value of True.
2. We wrote some information about the what the function does and what arguments it takes. The tripple quoation marks (""") allows us to write strings that go over multiple lines in the code cell.
3. We then performed the operation by adding together seq_a and seq_b and assigning it to a new variable called merged_sequence.
4. We tested if the function should print the resut to the screen. We did this by using an if statement. This tested if print_seq was equal to True. If it that was the case, the print function was called and printed the value of merged_sequence.
5. The GC content is computed and the function is told to return the value.

Each line in this function was one-tab away from the definition statement of the function. Note that we were never specific about what the value of seq_a and what seq_b are.

 input
# Add some various values together.
all_A = 'aaaa'
all_T = 'Tttt'
all_C = 'CcCC'
all_G = 'GgGg'
AT_only = compute_gc(all_A, all_T)
GC_only = compute_gc(all_G, all_C)
AC_only = compute_gc(all_A, all_C)
# Print the variables we assigned them to.
print(AT_only, GC_only, AC_only)

 output
aaaaTttt
GgGgCcCC
aaaaCcCC
0.0 1.0 0.5


We should be pleased to see that AT_only has a GC content of 0, GC_only has a GC content of 1.0, and AC_only has a value of 0.5, as we predicted. Since we added the automatic printing of values as a keyword argument, we can easily tell our function to stop printing things.

 input
AT_only = compute_gc(all_A, all_T, print_seq=False)
GC_only = compute_gc(all_G, all_C, print_seq=False)
AC_only = compute_gc(all_A, all_C, print_seq=False)
# Print the variables we assigned them to.
print(AT_only, GC_only, AC_only)

 output
0.0 1.0 0.5


Being able to write functions to automate tasks will be very valuable in the future $-$ especially when we start working with images.

## Our first for loop

Rather than using “boring” simple operations to learn some syntax, let’s learn about the for loop by using a biological example.

Let’s say that we have a cell sitting in a tube of growth medium. If we place this tube at the right temperature, the cells will grow exponentially. We can write down a very simple model that as long as the cells are well below the carrying capacity of their environment, they will grow as $N(d) = 2^{d},$

where $N(d)$ is the number of cells at division $d$. To test this model, we’ll write a very short simulation to test that the a cell would grow exponentially.

Before we think of how the specific code should be written, let’s write out what our thought process should be.

1. We should first define the initial number of cells as well as the number of divisions to simulate.
2. For each cell division, we should multiply the number of cells that we had in the last division event.
3. After each division, we should keep track of how many cells there are.

With this idea in place, let’s go through the code.

 input
# Set the initial number of cells in the experiment.
number_of_cells = 1

# Set the number of division cycles for the experiment.
number_of_divisions = 10

# Set a list of number of cells at division d and start with 1 cell
N_d = [number_of_cells]

# Loop through each division event
for i in range(number_of_divisions):
# Make the cells duplicate
number_of_cells = number_of_cells * 2

# Add the new number of cells to our storage list.
N_d.append(number_of_cells)



We covered a lot of syntax in that cell, so let’s take a look at it piece by piece.

• number_of_cells = 1: We assigned our starting number of cells to a variable.
• number_of_divisions = 10: We assigned a value for the total number of divisions to a variable.
• N_d = [number_of_cells] We made a list where the first entry (our starting point) only has one cell.

Now we enter the for loop, which exectues our simulation.

• for i in range(number_of_divisions): This starts the for loop. We are using the variable i as an iterator (basically a counter). Each time we go through the loop, i will take on the next value of the range function. The range function generates a list of integers starting from 0 to number_of_divisions which we set as 10.
• number_of_cells = number_of_cells * 2: This performed the cell division, doubling the number of cells. We also reassigned the value of this variable. Through the next iteration of the loop, the number will double again.
• N_d.append(number_of_cells): This is using the append method of the N_d list to add the number of cells at each division to our list before we go on to the next round of the loop.

Also notice that, just like in functions, the code is indented. Everything that is indented to the same level will execute within the loop.

Let’s take a look at our N_d list and see how the number of cells changed over time.

 input
# Print the result of our simulation.
print(N_d)

 output
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]


It looks like our function worked! But can we tell this is exponential growth? Because this is a simple case, we can see that the number of cells are doubling at each division. However, It would be very useful to plot these results.

## Plotting using matplotlib

There are many plotting utilities available for Python. Some notable examples include Bokeh for interactive plotting, Seaborn and Altair for statistical visualization, and a Python port of the popular R programming language plotting utility ggplot. While interactive plotting is likely the visualization tool of the future, the most common (and full featured) plotting utility for Python as of this writing is matplotlib. It was designed with the plotting syntax and style of MATLAB in mind and many of the commands are similiar. As is the case with numpy, matplotlib is not within the standard libray of Python and must be imported.

 input
# Load the plotting utility matplotlib with an alias plt.
import matplotlib.pyplot as plt

# The following line allows for plots to be rendered in this notebook.
%matplotlib inline


We would like to see if our simulated cells appear to grow exponentially with time. To do so, we would like to plot the number of cells we have at division number $d$ as a function of $d$. Before we do any plotting, let’s generate a vector of division times that matches the size of our N_d vector. We can do this using some of the arrangement methods that we used earlier with numpy. Since we had measure at $d=0$, our new division vector must have a length of number_of_divisions + 1.

 input
# Establish a vector of the division cycles
division_vector = np.arange(0, number_of_divisions + 1, 1)


Now all that is left is to plot it! We can use the plot function of matplotlib to generate our scatterplot. We’ll choose small circles as our markers and provide the approriate $x$ and $y$ labels as we always should. We’ll also add a legend to our plot to show that these data poitns are from a simulation.

 input
# Generate the plot.
plt.plot(division_vector, N_d, 'o', label='simulation')

# Set the axis labels.
plt.xlabel('number of divisions')
plt.ylabel('number of cells')

plt.legend()

 output
<matplotlib.legend.Legend at 0x1174df610>


In calling the plt.plot() function, we first passed it the $x$ and $y$ data, told it to plot the points as circles (through the 'o' argument), and finally gave it a label.

To me, this plot is pretty ugly. Every aspect of this plot can be stylized to your liking, althought it will take a little bit of work. However, we can import the seaborn plotting utility which will stylize all of our plots and make them much clearer to interpret.

 input
import seaborn as sns
sns.set()


With this imported, let’s go ahead and remake the plot from above. We’ll also save it using the plt.savefig function. With this, you’ll be able to insert your plots into the PDF assignments you will turn in.

 input
# Generate the plot.
plt.plot(division_vector, N_d, 'o', label='simulation')

# Set the axis labels.
plt.xlabel('number of divisions')
plt.ylabel('number of cells')

plt.legend()
plt.savefig('growth_simulation.pdf')

 output

That’s much better!

While we have covered a lot of Python syntax, I don’t expect you will have all of it memorized! Every module (nearly) that you will use has a well constructed documentation that explains how functions should be used. Some great examples of this are the documentation pages for NumPy and SciPy, seaborn, and scikit-image.

When you are typing away in the notebook or in an iPython terminal, you can pull up the documentation information for any function or attribute by typing the name followed by a question mark (?). For example (assuming you have numpy imported as np, you can get the documentation for the np.random module by typing the following.

 input
np.random?

 output
[0;31mType:[0m        module
[0;31mString form:[0m <module 'numpy.random' from '/Users/gchure/anaconda3/lib/python3.7/site-packages/numpy/random/__init__.py'>
[0;31mFile:[0m        ~/anaconda3/lib/python3.7/site-packages/numpy/random/__init__.py
[0;31mDocstring:[0m
========================
Random Number Generation
========================

Use default_rng() to create a Generator and call its methods.

=============== =========================================================
Generator
--------------- ---------------------------------------------------------
Generator       Class implementing all of the random number distributions
default_rng     Default constructor for Generator
=============== =========================================================

============================================= ===
BitGenerator Streams that work with Generator
--------------------------------------------- ---
MT19937
PCG64
Philox
SFC64
============================================= ===

============================================= ===
Getting entropy to initialize a BitGenerator
--------------------------------------------- ---
SeedSequence
============================================= ===

Legacy
------

For backwards compatibility with previous versions of numpy before 1.17, the
various aliases to the global RandomState methods are left alone and do not
use the new Generator API.

==================== =========================================================
Utility functions
-------------------- ---------------------------------------------------------
random               Uniformly distributed floats over [0, 1)
bytes                Uniformly distributed random bytes.
permutation          Randomly permute a sequence / generate a random sequence.
shuffle              Randomly permute a sequence in place.
choice               Random sample from 1-D array.
==================== =========================================================

==================== =========================================================
Compatibility
functions - removed
in the new API
-------------------- ---------------------------------------------------------
rand                 Uniformly distributed values.
randn                Normally distributed values.
ranf                 Uniformly distributed floating point numbers.
random_integers      Uniformly distributed integers in a given range.
(deprecated, use integers(..., closed=True) instead)
random_sample        Alias for random_sample
randint              Uniformly distributed integers in a given range
seed                 Seed the legacy random number generator.
==================== =========================================================

==================== =========================================================
Univariate
distributions
-------------------- ---------------------------------------------------------
beta                 Beta distribution over [0, 1].
binomial             Binomial distribution.
chisquare            :math:\chi^2 distribution.
exponential          Exponential distribution.
f                    F (Fisher-Snedecor) distribution.
gamma                Gamma distribution.
geometric            Geometric distribution.
gumbel               Gumbel distribution.
hypergeometric       Hypergeometric distribution.
laplace              Laplace distribution.
logistic             Logistic distribution.
lognormal            Log-normal distribution.
logseries            Logarithmic series distribution.
negative_binomial    Negative binomial distribution.
noncentral_chisquare Non-central chi-square distribution.
noncentral_f         Non-central F distribution.
normal               Normal / Gaussian distribution.
pareto               Pareto distribution.
poisson              Poisson distribution.
power                Power distribution.
rayleigh             Rayleigh distribution.
triangular           Triangular distribution.
uniform              Uniform distribution.
vonmises             Von Mises circular distribution.
wald                 Wald (inverse Gaussian) distribution.
weibull              Weibull distribution.
zipf                 Zipf's distribution over ranked data.
==================== =========================================================

==================== ==========================================================
Multivariate
distributions
-------------------- ----------------------------------------------------------
dirichlet            Multivariate generalization of Beta distribution.
multinomial          Multivariate generalization of the binomial distribution.
multivariate_normal  Multivariate generalization of the normal distribution.
==================== ==========================================================

==================== =========================================================
Standard
distributions
-------------------- ---------------------------------------------------------
standard_cauchy      Standard Cauchy-Lorentz distribution.
standard_exponential Standard exponential distribution.
standard_gamma       Standard Gamma distribution.
standard_normal      Standard normal distribution.
standard_t           Standard Student's t-distribution.
==================== =========================================================

==================== =========================================================
Internal functions
-------------------- ---------------------------------------------------------
get_state            Get tuple representing internal state of generator.
set_state            Set state of generator.
==================== =========================================================


## In conclusion…

In this tutorial, we worked through some of the basic syntax of the Python language, learned some crucial programming skills, and even generated a plot of cell growth over time. Through the rest of this course, you will build upon these skills and learn even more interesting and useful tidbits of programming.