Scientific Data Analysis
Syllabus
Unix
File Systems
List Files Directories
More On Directories
Working With Files
Git
Versioning Filesystem
Introduction To Git
Setup
Anatomy Of Git
Recording Changes
Viewing History
Undo
Python
Memory Model
Aggregate Types
Functional Programming
Map
Filter
Reduce
Numpy
Create Ndarrays
Operations
Indexing
Boolean Operations
Transposing And Axes Reordering
Aggregation
Other Numpy Functions
Persistent Storage
Pandas
Getting Started
Dataframe
Groupby And Merge
Plots
{}

Index

Visualization of Data

Visualization

In [1]:
import numpy as np
import matplotlib.pyplot as pl

Line plots

In [70]:
x = np.linspace(-5, 5, 100)
y = np.sin(x)

pl.plot(x, y);
In [15]:
# We can control the styling
pl.plot(x, y, color='r', linestyle='--');
In [14]:
#
# We can superimpose multiple lines
#
x2 = np.linspace(-5, 5, 10)
y2 = np.sin(x2)

pl.plot(x, y, color='r')
pl.plot(x2, y2, marker='o', linestyle="");
In [22]:
#
# We can also add text annotations
#
x1 = 2.1; y1 = np.sin(x1)
x2 = np.pi + 0.1; y2 = np.sin(x2)

pl.plot(x, y)
pl.text(x1, y1, 'higher')
pl.text(x2, y2, 'lower')
Out[22]:
Text(3.241592653589793, -0.09983341664682811, 'lower')
In [72]:
#
# Manually set the limits
#
x1 = 2.1; y1 = np.sin(x1)
x2 = np.pi + 0.1; y2 = np.sin(x2)

pl.plot(x, y)
pl.text(x1, y1, 'higher')
pl.text(x2, y2, 'lower')

pl.xlim(-10, 10)
pl.ylim(-2, 2);

Area plots

In [23]:
xs = np.linspace(-5, 5, 100)
def f1(x):
    return x * x
def f2(x):
    return 3*x + 4
In [25]:
pl.plot(xs, f1(xs))
pl.plot(xs, f2(xs))
Out[25]:
[<matplotlib.lines.Line2D at 0x7f0624ff6750>]
In [27]:
pl.plot(xs, f1(xs))
pl.plot(xs, f2(xs))
pl.fill_between(xs, f1(xs), f2(xs), color='gray');
In [29]:
pl.plot(xs, f1(xs))
pl.plot(xs, f2(xs))
pl.fill_between(xs, f1(xs), f2(xs), where=f1(xs) < f2(xs), color='gray');
In [43]:
#
# A limitation
#
x1 = np.linspace(-5, 5, 40)
x2 = np.linspace(-4, 4, 80)
y1 = np.sin(x1)
y2 = np.cos(x2)

pl.plot(x1, y1, marker='o')
pl.plot(x2, y2, linestyle='--', marker='o');
In [44]:
#
# This fails because y2 and y1 are different lengths.
#
pl.plot(x1, y1)
pl.plot(x2, y2, linestyle='--')
pl.fill_between(x1, y1, y2)

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-44-b5ce3afb3f03> in <module>
      4 pl.plot(x1, y1)
      5 pl.plot(x2, y2, linestyle='--')
----> 6 pl.fill_between(x1, y1, y2)

~/anaconda3/lib/python3.7/site-packages/matplotlib/pyplot.py in fill_between(x, y1, y2, where, interpolate, step, data, **kwargs)
   2590     return gca().fill_between(
   2591         x, y1, y2=y2, where=where, interpolate=interpolate, step=step,
-> 2592         **({"data": data} if data is not None else {}), **kwargs)
   2593 
   2594 

~/anaconda3/lib/python3.7/site-packages/matplotlib/__init__.py in inner(ax, data, *args, **kwargs)
   1597     def inner(ax, *args, data=None, **kwargs):
   1598         if data is None:
-> 1599             return func(ax, *map(sanitize_sequence, args), **kwargs)
   1600 
   1601         bound = new_sig.bind(ax, *args, **kwargs)

~/anaconda3/lib/python3.7/site-packages/matplotlib/axes/_axes.py in fill_between(self, x, y1, y2, where, interpolate, step, **kwargs)
   5242             where = True
   5243         where = where & ~functools.reduce(np.logical_or,
-> 5244                                           map(np.ma.getmask, [x, y1, y2]))
   5245 
   5246         x, y1, y2 = np.broadcast_arrays(np.atleast_1d(x), y1, y2)

ValueError: operands could not be broadcast together with shapes (40,) (80,)
In [45]:
y1_interp = np.interp(x2, x1, y1)
y1_interp.shape
Out[45]:
(80,)
In [46]:
pl.plot(x1, y1)
pl.plot(x2, y2, linestyle='--')
pl.fill_between(x2, y1_interp, y2, where=y1_interp < y2)
Out[46]:
<matplotlib.collections.PolyCollection at 0x7f0625a5aa10>

Error plots

In [51]:
xs = np.linspace(-5, 5, 10)
ys = np.sin(xs)
errs = np.random.random(len(xs))
errs
Out[51]:
array([0.67437957, 0.65731275, 0.10624474, 0.27883236, 0.55785646,
       0.05681281, 0.04248705, 0.6100362 , 0.68089623, 0.5112584 ])
In [52]:
#
# Each point has error 2*errs.
#
pl.errorbar(xs, ys, yerr=errs, capsize=3);
In [54]:
#
# Asymmetric errors
#
err_low = np.random.random(len(xs)) * 0.2
err_hi = np.random.random(len(xs)) * 0.1
errs = np.array([err_low, err_hi])
errs
Out[54]:
array([[0.09028524, 0.15667844, 0.13270258, 0.08077813, 0.1741719 ,
        0.04341984, 0.06995846, 0.03139628, 0.05228361, 0.18537323],
       [0.02243741, 0.04079118, 0.09860552, 0.02533219, 0.0465428 ,
        0.09717926, 0.06045159, 0.00660893, 0.02009699, 0.03619972]])
In [56]:
pl.errorbar(xs, ys, yerr=errs, capsize=0, elinewidth=5, color='gray')
Out[56]:
<ErrorbarContainer object of 3 artists>

Bar Plots

In [77]:
x = np.linspace(-1, 1, 5)
y1 = np.random.random(len(x))
y2 = np.random.random(len(x))
In [78]:
pl.bar(x, y1, width=0.2);
In [79]:
#
# Side-by-side plots
#
pl.bar(x, y1, width=0.2)
pl.bar(x+0.2, y2, width=0.2);
In [82]:
#
# Adjust bottom
#
pl.bar(x, y2, width=0.2, bottom=0.5);
pl.ylim(0, 2)
Out[82]:
(0, 2)
In [84]:
#
# Adjust bottom
#
pl.bar(x, y1, width=0.2)
pl.bar(x, y2, width=0.2, bottom=y1);
pl.ylim(0, 2)
Out[84]:
(0, 2)

Contour Plots

Consider a 2D grid

(x1,y1) (x2,y1) (x3,y1) ... (xn, y1)
(x1,y2) (x2,y2) (x3,y3) ... (xn, y2)
.
.
.
(x1,ym) (x2,ym) (x3,ym) ... (xn,ym)

At each coordinate (xi,yj), we can have height z[i,j].

Contour plot visualizes the heights as a 2D plot.

In [91]:
x = np.linspace(-10, 10, 100)
y = np.linspace(-10, 10, 100)
xgrid, ygrid = np.meshgrid(x, y)
In [94]:
xgrid.shape
Out[94]:
(100, 100)
In [92]:
z = xgrid * xgrid + ygrid * ygrid
In [93]:
z.shape
Out[93]:
(100, 100)
In [95]:
colormap = pl.get_cmap('jet')
In [98]:
pl.contourf(xgrid, ygrid, z, levels=10, cmap=colormap);
In [103]:
pl.contour(xgrid, ygrid, z, colors='gray');

3D surface plot

In [107]:
from mpl_toolkits.mplot3d import Axes3D
In [108]:
ax = pl.gca(projection ='3d')
ax.plot_wireframe(xgrid, ygrid, z);
In [121]:
#
# Default view is:
#   elevation = 30
#   azimuth = 45
#

elevation = 0
azimuth = 45 - 30
ax = pl.gca(projection ='3d')
ax.view_init(elevation, azimuth)
ax.plot_wireframe(xgrid, ygrid, z);
In [ ]:

Copyright 2020, Ken Pu