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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Pre-MAP Course Website | Pre-MAP GitHub | Google
Plotting with matplotlib
examples in this notebook are based on Nicholas Hunt-Walker's plotting tutorial and Jake VanderPlas' matplotlib tutorial
In this notebook we will learn how to make basic plots like scatter plots, histograms and line plots in using matplotlib in python.
The gallery
If you know what you want a plot to look like, but you don't know the code to make it, go to the matplotlib gallery, where you can see examples and see the source code that generated them.
Basic Plot Commands
Some of the basic plotting commands include
python
plt.plot()         # all purpose plotting function
plt.errorbar()     # plotting with errorbars
plt.loglog(), plt.semilogx(), plt.semilogy()   # plotting in logarithmic space
Step1:  Let's make some sample x and y data, and plot it with the plt.plot command
Step2:  You can customize a bunch of features within the plot
Step3:  Let's plot a sine function
Step4:  Let's plot a figure with errorbars
Step5:  There are three options for log-plots
Step6:  To add a legend to your plot, include the label argument in the plot command, then call plt.legend() at the end of the plotting commands, before plt.show().
Step7:  To save figures in python you just use plt.savefig()
Step8:  Let's make a log-log plot displaying Kepler's law
Step9:  Scatter Plots
Step10:  SIDE NOTE
Step11:  The plot is starting to look better, but there is one really important thing that is missing
Step12:  We can also change things like the axis limits with plt.xlim() and plt.ylim(). For these we just want to feed it a range of values for each axis
Step13:  The axis labels are easy to read, but the numbers and tick marks on the axis are pretty small. We can tweak lots of little things about how the tick marks look, how they are spaced, and if we want to have a grid to guide the reader's eyes. I will give just a couple of examples here
Step14:  By default the figure is square, but maybe this is not the best way to represent our data. If this is the case we can change the size of the figure
Step15:  The last thing I'll mention here is how to put text on plots. This too is simple as long as you specify (x,y) coordinates for the text.
Step16:  Histograms
Histograms can be a great way to visualize data, and they are (surprise) easy to make it python! The basic command is 
python
    num, bins, patches = plt.hist(array, bins=number)
Num refers to the number of elements in each bin, and bins refers to each bin on the x-axis. Note that bins actually gives you bin EDGES, so there will always be num+1 number of bins. We can ignore patches for now. As arguments plt.hist() takes an array and the number of bins you would like (default is bins=10). Some other optional arguments for plt.hist are
Step17:  Subplots
Subplots are a way put multiple plots in what amounts to the same figure; think of subplots like an array of plots! The following picture is helpful for understanding how matplotlib places subplots based on row, column, and figure number
Step18:  You can do fancier things with subplots like have different plots share the same axis, put smaller plots as insets to larger plots, etc. Again, take a look at things like the matplotlib library for examples of different plots. 
Plotting Exoplanets
Let's try to make some plots with a new dataset. The file that we'll use is taken from exoplanets.eu.
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Python Code:
# we use matplotlib and specifically pyplot
# the convention is to import it like this:
import matplotlib.pyplot as plt 
# We'll also read some data using astropy, so let's import that
import numpy as np 
from astropy.io import ascii
# I'm also using this "magic" function to make my plots appear in this notebook
# Only do this when working with notebooks
%matplotlib inline
Explanation: Pre-MAP Course Website | Pre-MAP GitHub | Google
Plotting with matplotlib
examples in this notebook are based on Nicholas Hunt-Walker's plotting tutorial and Jake VanderPlas' matplotlib tutorial
In this notebook we will learn how to make basic plots like scatter plots, histograms and line plots in using matplotlib in python.
The gallery
If you know what you want a plot to look like, but you don't know the code to make it, go to the matplotlib gallery, where you can see examples and see the source code that generated them.
Basic Plot Commands
Some of the basic plotting commands include
python
plt.plot()         # all purpose plotting function
plt.errorbar()     # plotting with errorbars
plt.loglog(), plt.semilogx(), plt.semilogy()   # plotting in logarithmic space
End of explanation
# Sample data
x = np.arange(10)
y = np.arange(10, 20)
# Make the plot, then show the plot
plt.plot(x, y)
plt.show()
Explanation: Let's make some sample x and y data, and plot it with the plt.plot command:
End of explanation
plt.plot(x, y, '.', markersize=20, color='red')  
plt.show()
Explanation: You can customize a bunch of features within the plot:
* markersize sets the symbol size 
* color sets the color
* The first argument after y sets the marker shape. Try: x, ., o, +, --, -., :
End of explanation
# Let's make x go from zero to 4*pi
x = np.linspace(0, 4*np.pi, 50)
y = np.sin(x)
# This will be a thick dashed line:
plt.plot(x, y, linestyle='--', linewidth=5) 
# Add labels to the axes
plt.xlabel('Xlabel') 
plt.ylabel('Ylable')
# Set the plot title
plt.title('Sine Curve')
plt.show()
Explanation: Let's plot a sine function:
End of explanation
# Let's plot y=x^3
x = np.arange(10)
y = x**3
# Let's make up some errorbars in x and y
xerr_values = 0.2 * np.sqrt(x)
yerr_values = 5 * np.sqrt(y)
# Call the errorbar function 
plt.errorbar(x, y, xerr=xerr_values, yerr=yerr_values)
plt.show()
Explanation: Let's plot a figure with errorbars:
End of explanation
x = np.linspace(0, 20)
y = np.exp(x)
plt.semilogy(x, y) 
plt.show()
Explanation: There are three options for log-plots: plt.loglog(), plt.semilogx(), plt.semilogy()
End of explanation
xred = np.random.rand(100)
yred = np.random.rand(100)
xblue = np.random.rand(20)
yblue = np.random.rand(20)
plt.plot(xred, yred, '^', color='red', markersize=8, 
         label='Red Points')
plt.plot(xblue, yblue, '+', color='blue', markersize=12, 
         markeredgewidth=3, label='Blue Points')
plt.xlabel('Xaxis')
plt.ylabel('Yaxis')
plt.legend()
# You can also place the legend in different places using this: 
# plt.legend(loc='lower left')
plt.show()
Explanation: To add a legend to your plot, include the label argument in the plot command, then call plt.legend() at the end of the plotting commands, before plt.show().
End of explanation
x = np.linspace(0, 10)
y = np.sin(x)
plt.plot(x, y)
plt.title('sin')
plt.xlabel('Xaxis')
plt.ylabel('Yaxis')
# just give savefig the file name, or path to file name that you want to write
plt.savefig('sineplot.png') 
plt.show()
Explanation: To save figures in python you just use plt.savefig():
End of explanation
# Semimajor-axis in units of AU:
a_AU = np.array([0.387, 0.723, 1. , 1.524, 5.203, 9.537, 19.191, 30.069, 39.482])
# Orbital period in units of years
T_yr = np.array([0.24, 0.62, 1., 1.88, 11.86, 29.46, 84.01, 164.8, 247.7])
# Let's set gravity and mass of the sun in [cgs] units:
G = 6.67e-8
Msun = 1.99e+33 
plt.loglog(a_AU, T_yr, 'o')
plt.xlabel('Semi-Major Axis [AU]')
plt.ylabel('Period [yrs]')
plt.show()
# now plot a function over the data
# as you work more in python you will learn how to actually fit models to your data 
def keplers_third_law(a, M):
    return np.sqrt((4*np.pi**2 * a**3) / (G * M))
# Convert semimajor-axis into centimeters
a_cm = a_AU * 1.496e+13 
# Convert period into seconds
T_s = T_yr * 3.154e+7
plt.loglog(a_cm, T_s, 'o')
plt.loglog(a_cm, keplers_third_law(a_cm, Msun), '--', 
           label='Keplers Third Law') # try swapping out Msun with something else and see what it looks like 
plt.xlabel('Semi-Major Axis [cm]')
plt.ylabel('Period [s]')
plt.legend(loc=2)
plt.show()    
Explanation: Let's make a log-log plot displaying Kepler's law:
End of explanation
# first let's read in some data to use for plotting
galaxy_table = ascii.read('data/mygalaxy.dat')
galaxy_table[:5]
# simple scatter plot
plt.scatter(galaxy_table['col1'], galaxy_table['col2'])
plt.show()
Explanation: Scatter Plots
End of explanation
plt.scatter(galaxy_table['col1'], galaxy_table['col2'], 
            color='blue', s=1, edgecolor='None', marker='o')
plt.show()
# here would be the equivalent statement using plt.plot(), note that the syntax is a little different 
plt.plot(galaxy_table['col1'], galaxy_table['col2'], 'o', 
         color='blue', markersize=1, markeredgecolor='None')
plt.show()
Explanation: SIDE NOTE: If you are running things in the IPython environment or from a script you would want to do something like the following to get your plots to show up in a new window:
python
plt.scatter(galaxy_table['col1'], galaxy_table['col2'])
plt.show()
In an IPython Notebook, you will see the plot outputs whether or not you call plt.show() because we've used the %matplotlib inline magic function.
Let's break down these basic examples:
- We are running functions called "plot" or "scatter" that take specific arguments.
- The most basic arguments that these functions take are in the form of (x,y) values for the plot, and we get these from a data table. 
- We can use more specific arugments like 'o' to customize things like the plot symbol (marker) that we are using. 
With plt.scatter() you can change things like point color, point size, point edge color and point type. The argument syntax for adding these options are as follows: 
color = 'colorname'; could be 'b' for blue, 'k' for black, 'r' for red
s = number; changes marker size
markeredgecolor = None or 'colorname'
marker = 'symbolname', i.e. 's' for square, 'o' for circle, '+' for cross, 'x' for x, '*' for star, '^' for triangle, etc.
Let's do an example:
End of explanation
plt.scatter(galaxy_table['col1'], galaxy_table['col2'], color='blue', 
            s=1, edgecolor='None', marker='o')
plt.xlabel('Galactic Longitude (degrees)', 
           fontweight='bold', size=16)
plt.ylabel('Galactic Latitude (degrees)', 
           fontweight='bold', size=16)
plt.show()
Explanation: The plot is starting to look better, but there is one really important thing that is missing: axis labels. These are very easy to put in in matplotlib using plt.xlabel() and plt.ylabel(). These functions take strings as their arguments for the labels, but can also take other arguments that case the text format:
End of explanation
plt.scatter(galaxy_table['col1'], galaxy_table['col2'], 
            color='blue', s=1, edgecolor='None', marker='o')
plt.xlabel('Galactic Longitude (degrees)', 
           fontweight='bold', size=16)
plt.ylabel('Galactic Latitude (degrees)', 
           fontweight='bold', size=16)
plt.xlim([-180,180])
plt.ylim([-90,90])
plt.show()
Explanation: We can also change things like the axis limits with plt.xlim() and plt.ylim(). For these we just want to feed it a range of values for each axis:
End of explanation
plt.scatter(galaxy_table['col1'], galaxy_table['col2'], 
            color='blue', s=1, edgecolor='None', marker='o')
# Labels
plt.xlabel('Galactic Longitude (degrees)', 
           fontweight='bold', size=16)
plt.ylabel('Galactic Latitude (degrees)', 
           fontweight='bold', size=16)
# Set limits
plt.xlim([-180,180])
plt.ylim([-90,90])
# Choose axis ticks
plt.xticks(range(-180,210,60), fontsize=16, fontweight='bold') # change tick spacing, font size and bold
plt.yticks(range(-90,120,30), fontsize=16, fontweight='bold')
# turn on minor tick marks 
plt.minorticks_on()
plt.grid() # turn on a background grip to guide the eye 
plt.show()
Explanation: The axis labels are easy to read, but the numbers and tick marks on the axis are pretty small. We can tweak lots of little things about how the tick marks look, how they are spaced, and if we want to have a grid to guide the reader's eyes. I will give just a couple of examples here:
End of explanation
plt.figure(figsize=(10,4)) # change figure size 
plt.scatter(galaxy_table['col1'], galaxy_table['col2'], 
            color='blue', s=1, edgecolor='None', marker='o')
# Labels
plt.xlabel('Galactic Longitude (degrees)', 
           fontweight='bold', size=16)
plt.ylabel('Galactic Latitude (degrees)', 
           fontweight='bold', size=16)
# Set limits
plt.xlim([-180,180])
plt.ylim([-90,90])
# Choose axis ticks
plt.xticks(range(-180,210,60), fontsize=16, fontweight='bold') # change tick spacing, font size and bold
plt.yticks(range(-90,120,30), fontsize=16, fontweight='bold')
# turn on minor tick marks 
plt.minorticks_on()
plt.grid() # turn on a background grip to guide the eye 
plt.show()
Explanation: By default the figure is square, but maybe this is not the best way to represent our data. If this is the case we can change the size of the figure:
End of explanation
plt.figure(figsize=(10,4)) # change figure size 
plt.scatter(galaxy_table['col1'], galaxy_table['col2'], 
            color='blue', s=1, edgecolor='None', marker='o')
# the next three lines put text on the figure at the specified coordinates
plt.text(-90, -50, 'LMC', fontsize=20) 
plt.text(-60, -60, 'SMC', fontsize=20)
plt.text(0, -30, 'MW Bulge', fontsize=20)
plt.xlabel('Galactic Longitude (degrees)', 
           fontweight='bold', size=16)
plt.ylabel('Galactic Latitude (degrees)', 
           fontweight='bold', size=16)
plt.xlim([-180,180])
plt.ylim([-90,90])
plt.xticks(range(-180,210,60), fontsize=16, fontweight='bold') # change tick spacing, font size and bold
plt.yticks(range(-90,120,30), fontsize=16, fontweight='bold')
plt.minorticks_on() # turn on minor tick marks 
plt.grid() # turn on a background grip to guide the eye 
plt.show()
Explanation: The last thing I'll mention here is how to put text on plots. This too is simple as long as you specify (x,y) coordinates for the text.
End of explanation
# plots histogram where the y-axis is counts 
x = np.random.randn(10000)
num, bins, patches = plt.hist(x, bins=50)
plt.xlabel('Bins')
plt.ylabel('Counts')
plt.show()
# plots histogram where the y-axis is a probability distribution 
plt.hist(x, bins=50, normed=True)
plt.xlabel('Bins')
plt.ylabel('Probability')
plt.show()
# plots a histogram where the y-axis is a fraction of the total 
weights = np.ones_like(x)/len(x)
plt.hist(x, bins=50, weights=weights)
plt.ylabel('Fraction')
plt.xlabel('Bins')
plt.show()
# print out num and bins and see what they look like! what size is each array?
# how would you plot this histogram using plt.plot? what is the x value and what is the y value? 
Explanation: Histograms
Histograms can be a great way to visualize data, and they are (surprise) easy to make it python! The basic command is 
python
    num, bins, patches = plt.hist(array, bins=number)
Num refers to the number of elements in each bin, and bins refers to each bin on the x-axis. Note that bins actually gives you bin EDGES, so there will always be num+1 number of bins. We can ignore patches for now. As arguments plt.hist() takes an array and the number of bins you would like (default is bins=10). Some other optional arguments for plt.hist are: 
range: lower and upper range of bins 
normed: set to 'True' or 'False.' If true it will return a normalized probability distribution instead of just raw number counts for the y-axis. 
histtype: can be step to something like 'step', 'stepfilled', or 'bar' for the histogram style. 
weights: an array of values that must be of the same size as the number of bins. It controls the factor by which the number counts are weighted, i.e. it makes your number counts into number_counts*weight.
End of explanation
# make two side by side plots 
x1 = np.linspace(0.0, 5.0)
x2 = np.linspace(0.0, 2.0)
y1 = np.cos(2 * np.pi * x1) * np.exp(-x1)
y2 = np.cos(2 * np.pi * x2)
plt.figure(figsize=[15,3])
plt.subplot(1,2,1) # 1 row, 2 columns, 1st figure 
plt.plot(x1,y1)
plt.xlabel('Xlabel')
plt.ylabel('Ylabel')
plt.subplot(1,2,2) # 1 row, 2 columsn, 2nd figure 
plt.plot(x2,y2)
plt.xlabel('Xlabel')
plt.ylabel('Ylabel')
plt.show()
# stack two plots on top of one another
plt.subplot(2,1,1) # 1 row, 2 columns, 1st figure 
plt.plot(x1,y1)
plt.xlabel('Xlabel')
plt.ylabel('Ylabel')
plt.subplot(2,1,2) # 1 row, 2 columsn, 2nd figure 
plt.plot(x2,y2)
plt.xlabel('Xlabel')
plt.ylabel('Ylabel')
plt.show()
Explanation: Subplots
Subplots are a way put multiple plots in what amounts to the same figure; think of subplots like an array of plots! The following picture is helpful for understanding how matplotlib places subplots based on row, column, and figure number:
<img src="images/subplot-grid.png">
End of explanation
# don't worry about this way to read in files right now 
import pandas as pd 
exoplanets = pd.read_csv('data/exoplanet.eu_catalog_1022.csv')
# get rid of some rows with missing values to be safe
exoplanets = exoplanets[np.isfinite(exoplanets['orbital_period'])]
# let's see what the data table looks like
exoplanets.head()
# plot distance from host star versus mass (in jupiter masses) for each exoplanet 
plt.loglog(exoplanets['semi_major_axis'], exoplanets['mass'],'.')
plt.annotate("Earth", xy=(1,1/317.), size=12)
plt.annotate("Jupiter", xy=(5,1), size=12)
plt.xlabel('Semi-Major Axis [AU]',size=20)
plt.ylabel('Mass [M$_{Jup}$]', size=20)
# let's try to find out if the blobs above separate out by detection type
import seaborn as sns; sns.set()
transits = exoplanets[exoplanets['detection_type'] == 'Primary Transit']
radial_vel = exoplanets[exoplanets['detection_type'] == 'Radial Velocity']
imaging = exoplanets[exoplanets['detection_type'] == 'Imaging']
ttv = exoplanets[exoplanets['detection_type'] == 'TTV']
plt.loglog(transits['semi_major_axis'], transits['mass'], '.', label='Transit',markersize=12)
plt.loglog(radial_vel['semi_major_axis'], radial_vel['mass'], '.', label='Radial Vel', markersize=12)
plt.loglog(imaging['semi_major_axis'], imaging['mass'], '.', label='Direct Imaging', markersize=16)
plt.loglog(ttv['semi_major_axis'], ttv['mass'], '.', label='TTV', color='cyan', markersize=16)
plt.annotate("Earth", xy=(1,1/317.), size=12)
plt.annotate("Jupiter", xy=(5,1), size=12)
plt.xlabel('Semi-Major Axis [AU]', size=20)
plt.ylabel('Mass [M$_{Jup}$]', size=20)
plt.legend(loc=4, prop={'size':16})
# and now just for fun an xkcd style plot! 
plt.xkcd()
plt.scatter(exoplanets['discovered'], exoplanets['radius']*11)
plt.xlabel('Year Discovered')
plt.ylabel('Radius [R_Earth]')
Explanation: You can do fancier things with subplots like have different plots share the same axis, put smaller plots as insets to larger plots, etc. Again, take a look at things like the matplotlib library for examples of different plots. 
Plotting Exoplanets
Let's try to make some plots with a new dataset. The file that we'll use is taken from exoplanets.eu.
End of explanation
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