comp 690 data fusion matplotlib notes albert esterline fall 2008

COMP 690 Data FusionMatplotlib Notes

Albert Esterline

Fall 2008

Documentation Homepage

http://matplotlib.sourceforge.net/ Short descriptions of and links to documentation on all plotting functions

PyplotTutorial (8 pp.)

http://matplotlib.sourceforge.net/users/pyplot_tutorial.html Start here Pyplot is a collection of command style functions that make matplotlib work

like matlab User’s Guide

http://matplotlib.sourceforge.net/users_guide_0.98.3.pdf Refer to as needed

Cookbook / Matplotlib http://www.scipy.org/Cookbook/Matplotlib Lots of good examples Shows figure, link to page giving code and explanation

Examples

http://matplotlib.sourceforge.net/examples/

Just a directory listing, but subdirectory names are descriptive

The “What's new” page

http://matplotlib.sourceforge.net/users/whats_new.html

Every feature ever introduced into matplotlib is listed here under the version that introduced it

Often with a link to an example or documentation

Global Module Index

http://matplotlib.sourceforge.net/modindex.html Documentation on the various modules

This and the next are often the only places to find something

The Matplotlib API

http://matplotlib.sourceforge.net/api/

Documentation on the various packages

Matplotlib Backends See http://matplotlib.sourceforge.net/api/index_backend_api.html Matplotlib uses a backend to produce device-independent output (e.g., pdf,

ps, png)

For backends without a GUI, only output is an explicitly-saved image file

File

…\site-packages\matplotlib\mpl-data\matplotlibrc

sets the default backend with a line for the backend option

The Windows distribution has

backend : TkAgg Specifies the agg backend (for rendering) for Tkinter Tkinter is a Python binding to the Tk GUI toolkit

Still the most popular Python GUI toolkit Other toolkits: wxPython

Tk is an open source, cross-platform widget toolkit—library of basic elements for building a GUI

The antigrain geometry (Agg) library is a platform independent library

Provides efficient antialiased rendering with a vector model

Doesn't depend on a GUI framework Used in web application servers and for generating images in

batch scripts

Matplotlib includes its own copy of Agg

Aliasing is an effect that causes different continuous signals to become indistinguishable (aliases of one another) when sampled Also refers to the resulting distortion Anti-aliasing is the technique of minimizing this distortion

Used in digital photography, computer graphics, digital audio, etc.

matplotlib.pyplot vs. pylab Package matplotlib.pyplot provides a MATLAB-like plotting

framework

Package pylab combines pyplot with NumPy into a single namespace

Convenient for interactive work

For programming, it’s recommended that the namespaces be kept separate

See such things as

import pylab

Or

import matplotlib.pyplot as plt The standard alias

import numpy as np

The standard alias

Also

from pylab import *

Or

from matplotlib.pyplot import *

from numpy import *

We’ll use

from pylab import *

Some examples don’t show this—just assume it

Batch and Interactive Use In a script,

import the names in the matplotlib namespace (pylab)

then list the commands

Example: file E:\SomeFolder\mpl1.py

from pylab import *

plot([1,2,3,4])

show()

Executing

E:\SomeFolder>mpl1.py

produces the figure shown

The command line hangs until the figure is dismissed (click ‘X’ in the upper right)

plot()

Given a single list or array, plot() assumes it’s a vector of y-values

Automatically generates an x vector of the same length with consecutive integers beginning with 0

Here [0,1,2,3]

To override default behavior, supply the x data: plot(x,y )

where x and y have equal lengths

show()

Should be called at most once per script

Last line of the script

Then the GUI takes control, rendering the figure

In place of show(), can save the figure to with, say,

savefig(‘fig1.png’)

Saved in the same folder as the script

Override this with a full pathname as argument—e.g.,

savefig('E:\\SomeOtherFolder\\fig1.png')

Supported formats: emf, eps, pdf, png, ps, raw, rgba, svg, svgz

If no extension specified, defaults to .png

With the TkAgg backend, can use matplotlib from an arbitrary python (interactive) shell

Supposedly requires the matplotlibrc file to have interactive set to True (as well as backend to TkAgg )

In the matplotlibrc file with the Windows distribution, the interactive setting (to False) is commented out

TkAgg sets interactive mode to True when show() or draw() executed

In batch mode (running scripts), interactive mode can be slow

Redraws the figure with each command.

Matplotlib from the Shell Using matplotlib in the shell, we see the objects produced

>>> from pylab import *

>>> plot([1,2,3,4])

[<matplotlib.lines.Line2D object at 0x01A3EF30>]

>>> show()

Hangs until the figure is dismissed or close() issued

show() clears the figure: issuing it again has no result

If you construct another figure, show() displays it without hanging

draw() Clear the current figure and display a blank figure without hanging

Results of subsequent commands added to the figure

>>> draw()

>>> plot([1,2,3])[<matplotlib.lines.Line2D object at 0x01C4B6B0>]

>>> plot([1,2,3],[0,1,2])[<matplotlib.lines.Line2D object at 0x01D28330>]

Shows 2 lines on the figure

Use close() to dismiss the figure and clear it

clf() clears the figure (also deletes the white background) without dismissing it

Figures saved using savefig() in the shell by default are saved in

C:\Python25 Override this by giving a full pathname

Interactive Mode In interactive mode, objects are displayed as soon as they’re created

Use ion() to turn on interactive mode, ioff() to turn it off

Example Import the pylab namespace, turn on interactive mode and plot a line

>>> from pylab import *

>>> ion()

>>> plot([1,2,3,4])

[<matplotlib.lines.Line2D object at 0x02694A10>]

A figure appears with this line on it

The command line doesn’t hang

Plot another line

>>> plot([4,3,2,1])

[<matplotlib.lines.Line2D object at 0x00D68C30>]

This line is shown on the figure as soon as the command is issued

Turn off interactive mode and plot another line

>>> ioff()

>>> plot([3,2.5,2,1.5])

[<matplotlib.lines.Line2D object at 0x00D09090>] The figure remains unchanged—no new line

Update the figure

>>> show()

The figure now has all 3 lines

The command line is hung until the figure is dismissed

Matplotlib in Ipython Recommended way to use matplotlib interactively is with ipython

In the Ipython drop-down menu, select pylab

Ipython’s pylab mode detects the matplotlibrc file

Makes the right settings to run matplotlib with your GUI of choice in interactive mode using threading

Ipython in pylab mode knows enough about matplotlib internals to make all the right settings

Plots items as they’re produce without draw() or show()

Default folder for saving figures on file

C:\Documents and Settings\current user

Toolbar In interactive mode, at the bottom left of the figure

Not included when a figure is written to file

From right to left

Save: Launches a file save dialog, initially at

C:\Documents and Settings\current user with .png as default

All *Agg backends know how to save image types: PNG, PS, EPS, SVG

Subplot configuration

Adjust the left, bottom, right, or top margin of the figure

With text, control spacing

The Zoom to rectangle:

Define a rectangle by pressing the left mouse button to define one vertex and dragging out to the opposite vertex and releasing

Content of the rectangle occupies the entire space for the figure

The Pan/Zoom: 2 modes

Pan Mode Press the left mouse button, drag it to a new position The figure is pulled along within the frame

Extended by blank area if needed

Zoom Mode Press the right mouse button, drag it to a new position Figure is stretched proportional to the distance dragged in the direction

dragged up and to the right. Shrunk proportional to the distance dragged down and to the left

Use modifier keys x, y or Ctrl to constrain the zoom to the x or y axis or to preserve the aspect ratio preserve, resp.

Forward and Back.

Navigate back and forth between previously defined views

Analogous to forward and back buttons of a web browser

Home

Return to the first (default) view

More Curve Plotting plot() has a format string argument specifying the color and line type

Goes after the y argument (whether or not there’s an x argument)

Can specify one or the other or concatenate a color string with a line style string in either order

Default format string is 'b-' ( solid blue line)

Some color abbreviations

b (blue), g (green), r (red), k (black), c (cyan)

Can specify colors in many other ways (e.g., RGB triples)

Some line styles that fill in the line between the specified points

- (solid line), -- (dashed line), -. (dash-dot line), : (dotted line)

Some line styles that don’t fill in the line between the specified point

o (circles), + (plus symbols), x (crosses), D (diamond symbols)

For a complete list of line styles and format strings,

http://matplotlib.sourceforge.net/api/pyplot_api.html#module-matplotlib.pyplot Look under matplotlib.pyplot.plot()

The axis() command takes a list

[xmin, xmax, ymin, ymax]

and specifies the view port of the axes

ExampleIn [1]: plot([1,2,3,4], [1,4,9,16], 'ro')

Out[1]: [<matplotlib.lines.Line2D object at 0x034579D0>]

In [2]: axis([0, 6, 0, 20])

Out[2]: [0, 6, 0, 20]

Other arguments for the axis() command

‘off’ turns off the axis lines and labels

‘equal’ changes the limits of the x and y axes so that equal increments of x and y have the same length

‘scaled’ achieves the same result as ‘equal’ by changing the dimensions of the plot box instead of the axis limit

‘tight’ changes the axis limits to show all the data and no more

‘image’ is scaled with the axis limits equal to the data limits

axis() with no argument returns the current axis limits,

[xmin, xmax, ymin, ymax]

Generally work with arrays, not lists All sequences are converted to NumPy arrays internally

plot() can draw more than one line at a time Put the (1-3) arguments for one line in the figure

Then the (1-3) arguments for the next line

And so on

Can’t have 2 lines in succession specified just by their y arguments

matplotlib couldn’t tell whether it’s a y then the next y or an x then the corresponding y

The example (next slide) illustrates plotting several lines with different format styles in one command using arrays

In [1]: t = arange(0.0, 5.2, 0.2)

In [2]: plot(t, t, t, t**2, 'rs', t, t**3, 'g^')

Out[2]:

[<matplotlib.lines.Line2D object at 0x02A6D410>,

<matplotlib.lines.Line2D object at 0x02A6D650>,

<matplotlib.lines.Line2D object at 0x02A6D8D0>]

If the y for plot() is 2-dimensional, then the columns are plotted—e.g.,

In [1]: a = linspace(0, 2*pi, 13)

In [2]: b_temp = array([sin(a), cos(a)])

In [3]: b = b_temp.transpose()

In [4]: plot(a, b)

Out[4]:

[<matplotlib.lines.Line2D object at 0x02A770D0>,

<matplotlib.lines.Line2D object at 0x02A77150>]

Controlling Line Properties Lines you encounter are instances of the Line2D class

Instances have the following propertiesProperty Values

alpha The alpha transparency on 0-1 scale

antialiased True | False - use antialised rendering

color a matplotlib color arg

label a string optionally used for legend

linestyle One of -- : -. -

linewidth a float, the line width in points

marker One of + , o . s v x > < ^

markeredgewidth The line width around the marker symbol

markeredgecolor The edge color if a marker is used

markerfacecolor The face color if a marker is used

markersize The size of the marker in points

alpha = 0.0 is complete transparency, alpha = 1.0 is complete opacity

Markers Some of the line types in a format

string give continuous lines

A marker is a symbol displayed at only the specified points on a continuous line

In the format string, indicate a marker with a 3rd symbol One of +, o, s, v, x, >, <, ^

The 3 symbols can occur in any order No ambiguity: a marker can’t

be used with a non-continuous line type

In [50]: plot([0,1,2,3], 'g:o')

Out[50]: [<matplotlib.lines.Line2D object at 0x03017BB0>]

Three Ways to Set Line Properties One way: Use keyword line properties as keyword arguments—e.g.,

plot(x, y, linewidth=2.0)

Another way: Use the setter methods of the Line2D instance

For every property prop, there’s a set_prop() method that takes an update value for that property

To use this, note that plot() returns a list of lines—e.g.,

line1, line2 = plot(x1,y1,x2,x2)

The following example has 1 line with tuple unpacking

line, = plot(x, y, 'o')

line.set_antialiased(False)

The 3rd (and final) way to set line properties: use function setp()

1st argument can be an object or sequence of objects

The rest are keyword arguments updating the object’s (or objects’) properties

The following sets the color and linewidth properties of two lines

lines = plot(x1, y1, x2, y2)

setp(lines, color='r', linewidth=2.0)

setp() also accepts property-value pairs of arguments with property names as strings—e.g.,

setp(lines, 'color', 'r', 'linewidth', 2.0)

Multiple Figures and Axes Pylab has the concepts of the current figure and the current axes

An instance of class Figure contains all the plot elements

An instance of class Axes contains most of the figure elements:

instances of Axis, Tick, Line2D, Text, Polygon, …

But 1 figure may have multiple instances of Axes (“graphs”)

All plot and text label commands apply to the current axes

Function gca() returns the current axes as an Axes instance

Function gcf() returns the current figure as a Figure instance

Normally, all is taken care of behind the scenes

Function figure() returns an instance of Figure

Can take a number of arguments

Most have reasonable defaults set in the matplotlibrc file

Typically called with 1 (the figure number) or none

Called with none, the figure number is incremented and a new, current figure returned The figure number starts at 1 A Figure instance has a number property

Called with an integer argument,

if there’s a figure with that number, it becomes the current figure

If not, a new figure with that number is created

Example using multiple figures

figure(1)

plot([1,2,3])

figure(2)

plot([4,5,6])

figure(1) # make figure 1 current

title('Easy as 1,2,3')

In ipython, this opens 2 figure windows

Now consider close() more generally

Takes 1 or no argument; if the argument is

None, closes the current figure

A number, closes the figure with that number

A Figure instance, closes that figure

‘all’, closes all figures

Text The text commands are self-explanatory

xlabel() ylabel() title() text()

In simple cases, all but text() take just a string argument

text() needs at least 3 arguments:

x and y coordinates (as per the axes) and a string

All take optional keyword arguments or dictionaries to specify the font properties

They return instances of class Text

plot([1,2,3])

xlabel('time')

ylabel('volts')

title('A line')

text(0.5, 2.5, 'Hello world!')

Three ways to specify font properties: using setp object oriented methods font dictionaries

Controlling Text Properties with setp Use setp to set any property

t = xlabel('time')

setp(t, color='r', fontweight='bold')

Also works with a list of text instances E.g., to change the properties of all the tick labels

labels = getp(gca(), 'xticklabels')

setp(labels, color='r', fontweight='bold')

Controlling Text Using Object Methods setp is just a wrapper around the Text set methods

Can prepend set_ to the text property and make a normal instance method call

t = xlabel('time')

t.set_color('r')

t.set_fontweight('bold')

Controlling Text Using Keyword Arguments & Dictionaries

All text commands take an optional dictionary argument and keyword arguments to control font properties

E.g., to set a default font theme and override individual properties for given text commands

font = {'fontname' : 'Courier',

'color' : 'r',

'fontweight' : 'bold',

'fontsize' : 11}

plot([1,2,3])

title('A title', font, fontsize=12)

text(0.5, 2.5, 'a line', font, color='k')

xlabel('time (s)', font)

ylabel('voltage (mV)', font)

Legends A legend is a box (by default in upper right) associating labels with lines

(displayed as per their formats)

legend(lines, labels)

where lines is a tuple of lines, labels a tuple of corresponding strings

from pylab import *

lines = plot([1,2,3],'b-',[0,1,2],'r--')

legend(lines, ('First','Second'))

savefig('legend')

If there’s only 1 line, be sure to include the commas in the tuples

lengend((line1,), (‘Profit’,))

Use keyword argument loc to override the default location Use predefined strings or integer codes

‘upper right’ 1

‘upper left’ 2

‘lower left’ 3

‘lower right’ 4

‘right’ 5

‘center left’ 6

‘center right’ 7

‘lower center’ 8

‘upper center’ 9

‘center’ 10

E.g.,

legend((line,), (‘Profit’,) , loc=2)

Writing Mathematical Expressions Can use TeX markup in any text element

For usage, requirements, backend info, see mathtext documentation

http://matplotlib.sourceforge.net/api/mathtext_api.html

Use raw strings (precede the quotes with an 'r')

Surround the string text with $’s (as in TeX)

title(r'$\alpha > \beta$')

Regular text and mathtext can be interleaved within the same string

To make subscripts and superscripts use '_' and '^‘—e.g.,

title(r'$\alpha_i > \beta_i$')

Can use many TeX symbols, e.g.,

\infty, \leftarrow, \sum, \int

The over/under subscript/superscript style is supported

E.g., to write the sum of xi, i from 0 to ,

text(1, -0.6, r'$\sum_{i=0}^\infty x_i$')

Default font is italics for mathematical symbols

To change fonts, e.g., to write “sin” in Roman, enclose the text in a font command—e.g.,

text(1,2, r's(t) = $\mathcal{A}\mathrm{sin}(2 \omega t)$')

Many commonly used function names typeset in a Roman font have shortcuts

The above could be written as

text(1,2, r's(t) = $\mathcal{A}\sin(2 \omega t)$')

Font choices

Roman \mathrm

italics \mathit

caligraphy \mathcal

typewriter \mathtt

Accents :

\hat, \breve, \grave, \bar, \acute, \tilde, \vec, \dot, \ddot

E.g., overbar on an “o”: \bar{o}

from pylab import *

t = arange(0.0, 2.0, 0.01)

s = sin(2*pi*t)

plot(t,s)

title(r'$\alpha_i > \beta_i$', fontsize=20)

text(1, -0.6, r'$\sum_{i=0}^\infty x_i$', fontsize=20)

text(0.6, 0.6, r'$\mathcal{A}\mathrm{sin}(2 \omega t)$',

fontsize=20)

xlabel('time (s)')

ylabel('volts (mV)')

savefig('mathtext_tut', dpi=50)

Axes Properties There’s a current instance of Axes in the current figure

Contains all the graphical elements

gca() returns the current instance of Axes

cla() clears it

The following are a few get_ methods, all with no arguments

Most self-explanatory

get_legend()

get_lines()

get_title()

For the x axis

get_xlabel()

get_xbound() Returns the x-axis numerical bounds in the form of a tuple

(lbound, ubound)

get_xlim() Like get_xbound(), but returns an array

Similar get_ methods for the y axis

Corresponding commands for setting Axes properties

Use object methods (set_) or setp()

If a 2-element tuple or array is returned, method takes 2 corresponding arguments

Grids Use grid() function or grid() Axes method

With no arguments, gives a dotted black line at each tick on both axes

To suppress the grid, use grid(None)

Or simply grid() when there’s already a grid

Takes keyword arguments

grid(color='r', linestyle='-', linewidth=2)

Axes get_ methods

get_xgridlines()

get_ygridlines()

Corresponding set_ methods, or use setp()

Axis Scales Scale of either axis can be linear or log (default base 10)

Axes methods

set_xscale(s)

set_yscale(s) s either ‘linear’ or ‘log’

Corresponding set_ methods, or use setp()

from pylab import *

gca().set_yscale('log')

plot([1,10,100])

savefig('logscale')

Multiple Axes For control over axes placement, use function axes()

Can be initialized with a rectangle [left, bottom, width, height] in relative figure coordinates

(0, 0) is the bottom left of the of the figure canvas

Its width and height are 1

Several ways to use axes(); all return an Axes instance

axes()

Creates a default full window axis or returns the current Axes instance

axes([0.25, 0.25, 0.5, 0.5], axisbg=’g’)

Creates and displays a new axis offset by ¼ of the figure width and height on all sides

axes(ax)

where ax is an Axes instance, makes ax current

Allows multiple axes in the same figure

Objects are placed in the current Axes instance

from pylab import *

plot([0.2, 0.4, 0.6, 0.8, 3])

ax1 = gca()

ax2 = axes([0.25,0.45,0.25,0.25], axisbg='y')

axes(ax1)

plot([0.1,0.2,0.3,0.4,2], 'r--')

axes(ax2)

plot([1,2,3])

savefig('axes')

Multiple Subplots Functions axes() and subplot() both used to create axes

subplot() used more often

subplot(numRows, numCols, plotNum)

Creates axes in a regular grid of axes numRows by numCols

plotNum becomes the current subplot Subplots numbered top-down, left-to-right

1 is the 1st number

Commas can be omitted if all numbers are single digit

Subsequent subplot() calls must be consistent on the numbers or rows and columns

subplot() returns a Subplot instance

Subplot is derived from Axes

Can call subplot() and axes() in a subplot

E.g., have multiple axes in 1 subplot

See the Tutorial for subplots sharing axis tick labels

from pylab import *

subplot(221)

plot([1,2,3])

subplot(222)

plot([2,3,4])

subplot(223)

plot([1,2,3], 'r--')

subplot(224)

plot([2,3,4], 'r--')

subplot(221)

plot([3,2,1], 'r--')

savefig('subplot')

Event Handling All GUIs provide event handling to determine things like key

presses, mouse position, button clicks

matplotlib supports several GUIs

Provides an interface to the GUI event handling via the connect() and disconnect() methods of the pylab interface

matplotlib uses a callback event handling mechanism

Register an event that you want to listen for

The figure canvas calls a user defined function when that event occurs

E.g., to print to the console where the user clicks a mouse on your figure, define a function

def click(event):

print 'you clicked', event.x, event.y

Then register it with the event handler

connect('button_press_event', click)

When the user clicks in the figure canvas, the function is called and passed a MplEvent instance

The event instance has the attributes shown in the next slide

x x position - pixels from left of canvas

y y position - pixels from bottom of canvas

button button pressed None, 1, 2, 3

inaxes the Axes instance if mouse is over axes (or None)

xdata x coord of mouse in data coords (None if mouse isn't over axes)

ydata y coord of mouse in data coords (None if mouse isn't over axes)

name The string name of the event

canvas The FigureCanvas instance the event occurred in

key The key pressed if any, e.g., 'a', 'b', '1'. Also records 'control' and 'shift'

Can connect to events

‘button_press_event’

‘button_release_event’

‘motion_notify_event’

Complete example

from pylab import *

plot(arange(10))

def click(event):

if event.inaxes: print "(%-5.2f, %5.2f)" % (event.xdata, event.ydata)

connect('button_press_event', click)

show()

Bar Charts Function bar() creates a bar chart

Most of the arguments may be either scalars or sequences

Say in […] what they normally are

Required arguments

left x coordinates of the left sides of the bars [sequence]

height height of the bars [sequence]

Some optional keyword arguments

orientation orientation of the bars (‘vertical’ | ‘horizontal’)

width width of the bars [scalar]

color color of the bars [scalar]

xerr if not None,

generates error ticks on top the bars [sequence]

yerr if not None,

generates errorbars on top the bars [sequence]

ecolor color of any errorbar [scalar]

capsize length (in points) of errorbar caps (default 2) [scalar]

log False (default) leaves the orientation axis as is,

True sets it to log scale

For the following example, need the following

yticks(seq, labels)

Make the ticks on the y axis at y-values in seq with labels the corresponding elements of labels

Without labels, number as per seq

xticks(seq, labels)

Same, but for the x axis

xlim(xmin, xmax)

The values on the x axis go from xmin to xmax

from pylab import *

labels = ["Baseline", "System"]

data = [3.75, 4.75]

yerror = [0.3497, 0.3108]

xerror = [0.2, 0.2]

xlocations = array(range(len(data)))+0.5

width = 0.5

csize = 10

ec = 'r'

bar(xlocations, data, yerr=yerror, width=width,

xerr=xerror, capsize=csize, ecolor=ec)

yticks(range(0, 8))

xticks(xlocations + width/2, labels)

xlim(0, xlocations[-1]+width*2)

title("Average Ratings on the Training Set")

savefig('bar')

An Aside: Artists, Patches, & Collections When we execute this bar chart example in ipython, command

bar(xlocations, data, yerr=yerror, width=width, xerr=xerror,

capsize=csize, ecolor=ec)

returns

[<matplotlib.patches.Rectangle object at 0x01C9F930>,

<matplotlib.patches.Rectangle object at 0x02AC0A90>]

That is, each bar in the graph is an instance of the class

matplotlib.patches.Rectangle

The Patches class has subclasses for geometric figures

The 3 Conceptual Parts of the matplotlib Code The matplotlib code is divided conceptually into 3 parts:

1. the matlab interface

Module pylab is mainly code to manage the multiple figure windows across backends to provide a thin, procedural wrapper around the object oriented

plotting code

2. the matplotlib Artists

a series of classes that derive from matplotlib.artist.Artist

So named because they're the objects that actually draw into the figure

3. the backend renderers, each implementing a common drawing interface that actually puts the ink on the paper—e.g.,

create a postscript document

call the gtk drawing code

The matplotlib Artist hierarchy

The primitive Artists are classes Patch, Line2D, Text, AxesImage, FigureImage and Collection

All other artists are composites of these

E.g., a Tick is comprised of a Line2D instance (tick line) and a Text instance (tick label)

The Artist Containment Hierarchy

Attribute names in lower case Object type listed below in upper case

If the attribute is a sequence, the connecting edge is labeled 0. . .n the object type is in [..]

Some redundant information omitted—e.g.,

yaxis contains the equivalent objects that xaxis contains

minorTicks have same containment hierarchy as majorTicks

Some matplotlib.patches ClassesCircle(xy, radius, **kwargs) A circle of the given radius centered at xy, a tuple (x, y )

Some keyword arguments

edgecolor (or ec) any matplotlib color

facecolor (or fc) any matplotlib color

fill True | False

Rectangle(xy, width, height, **kwargs) A rectangle with lower left corner at xy of the given width and height

Same keyword arguments as Circle

Polygon(xys, **kwargs) xys is a NumPy array of shape N 2, where N is the number of vertices

Same keyword arguments as Circle

Keyword argument zorder Default drawing order (what’s on top of what) for axes is patches,

lines, text

Within same class, by default, what’s specified later is on top what’s drawn earlier

Override this with the zorder argument, with integer values

Higher z-orders are on top lower

zorder must be defined for all graphical objects for it to have an effect

Drawing Patches If p is a patch, it must be added to the axes with the Axes instance

method add_patch(p)

For patches to appear, must invoke draw()

from matplotlib.patches import Rectangle, Circle

from pylab import *

ax = gca()

r = Rectangle((0.1,0.1), 0.5, 0.5, fill=False, zorder=2, ec="r")

ax.add_patch(r)

c = Circle((0.7,0.7), 0.25, zorder=1, fc="y")

ax.add_patch(c)

draw()

savefig('my_patches')

Collections of Patches Package matplotlib.collections contains classes for efficiently drawing

collections of objects sharing most properties

http://matplotlib.sourceforge.net/api/collections_api.html

PatchCollection is derived from class Collection

PatchCollection(patches, match_original=False, **kwargs)

patches is a sequence of Patch objects

If match_original is True, use colors and line-widths of original patches If False, can use the standard keyword arguments (edgecolor,

facecolor, …), applying to patches Can’t use abbreviations (e.g., ec)

If ps is a patch collection, must use Axes instance method add_collection(ps)

No need for draw()

from matplotlib.patches import Polygon

from matplotlib.collections import PatchCollection

from pylab import *

poly1 = Polygon([[0.4,0.4],[0.8,0.3],[0.9,0.9],[0.3,0.5]])

poly2 = Polygon([[0.1,0.1],[0.4,0.4],[0.1,0.4]])

ps = PatchCollection([poly1,poly2], edgecolor='b', facecolor='y')

gca().add_collection(ps)

savefig('my_patch_collection')

Histogramshist(x, bins=n )

Computes and draws a histogram

x: a sequence of numbers (usually with many repetitions)

If keyword argument bins is an integer, it’s the number of (equally spaced) bins

Default is 10

from pylab import *

import numpy

x = numpy.random.normal(2, 0.5, 1000)

hist(x, bins=50)

savefig('my_hist')

hist() returns a tuple (n, bins, patches ), where

n is an array of the bin values,

bins is an array of the bin limits, and

patches is an array of the rectangles plotted

In the shell (with x determined as above),

hist(x, bins=5)

returns

(array([ 1, 35, 406, 483, 75]), array([-0.34300571, 0.40693226, 1.15687024, 1.90680822,

2.65674619, 3.40668417]),

<a list of 5 Patch objects>)

bins can be a sequence of floating point numbers Each is the x valued of a bin edge

So the 1st bin is from bins[0] to bins[1], etc.

Allows for unequally spaced bin

Other Keyword Arguments range Lower and upper range of the bins,

No effect if bins is a sequence

Outliers ignored

normed If True, the array of bin values returned contains the counts

normalized to form a probability density (summing to 1)

cumulative If True, each bin gives the count for that bin plus all bins for smaller

values

histtype: the style drawn

‘bar’: traditional bar style

‘barstacked’: a bar style, multiple data stacked on top each other

‘step’: a line plot by default unfilled

‘stepfilled’: a line plot by default filled

align (values ‘left’, ‘mid’, ‘right’) Whether the bars are centered

on the left bin edges, between bin edges, or on the right bin edges

rwidth Relative width of bars as a fraction of bin width

If None, width automatically computed

Ignored if histtype=’step’

Log If True, axes have a log scale

Empty bins filtered out

Other usual keyword arguments: edgecolor (or ec), facecolor (or fc), fill, linewidth, etc.

NumPy Histogramshistogram (x, **kwargs)

x is as with matplotlib hist(x, **kwargs)

Returns a tuple (n, bins)

Just like the matplotlib function hist(x, **kwargs) returns a tuple (n, bins, patches)

But without the patches

Doesn’t draw a figure

Other keyword arguments:

range (default None)

normed (default 0, i.e., False)

Same as the hist() arguments of the same name

from pylab import *

import numpy

mu, sigma = 2, 0.5

# Vector of 10000 normal deviates with STD 0.5 and mean 2

v = numpy.random.normal(mu,sigma,10000)

hist(v, bins=50, normed=1) # matplotlib version (plot)

(n, bins) = numpy.histogram(v, bins=50, normed=1) # no plot

plot(bins, n, 'r', linewidth=2)

savefig('histnumpy')

For next example, need the numpy function

rand (d1, d2, . . ., dn )

Returns an array of shape (d1, d2, . . . , dn ) of uniform random numbers in the interval [0, 1)

This example constructs a 3030 array of random numbers in the interval [0,1)

Draws histograms of the normalized row and column sums (marginal densities)

from numpy import *

from pylab import *

v = rand(30,30)

csum = v.sum(axis=0)

rsum = v.sum(axis=1)

teen_bins = arange(10,20)

subplot(121)

hist(csum, bins=teen_bins, normed=True)

title('Marginal Density x')

subplot(122)

hist(rsum, bins=teen_bins, normed=True)

title('Marginal Density y')

savefig('twoDhist')

histogram2d(x, y, **kwargs) Keywords arguments again are

bins (default 10)

range (default None)

normed (default False)

Returns a tuple (H, xedges, yedges )

xedges and yedges are arrays of floating point numbers Define the edges of the 2D bins at the x and y values, resp.

H is oriented such that H [i,j ] is the number of samples in binx[j] and biny[i] Associate x with j, y with i

With normed=True, get a density (not a bin-count)

Marginal densities got by summing rows or summing columns

>>> H, xedges, yedges = histogram2d(rand(100),rand(100),bins=5)

>>> print H.sum(axis=0)

[ 21. 26. 13. 20. 20.]

>>> print xedges

[ 0.01034873 0.20348935 0.39662997 0.58977059 0.7829112 0.97605182]

>>> print H.sum(axis=1)

[ 23. 15. 23. 24. 15.]

>>> print yedges

[ 2.86000121e-05 1.99003906e-01 3.97979212e-01 5.96954518e-01 7.95929824e-01 9.94905130e-01]

histogramdd([[x0,0, x0,1, …, x0,D-1], …, [xN-1,0, xN-1,1, …, xN-1,D-1]]), **kwargs)

Generalizes histogram2d()

The 1st argument is a length-N array of length-D arrays (samples)

Scatter Plotsscatter(x, y )

x and y are arrays of numbers of the same length, N

Makes a scatter plot of x vs. y

from pylab import *

N = 20

x = 0.9*rand(N)

y = 0.9*rand(N)

scatter(x,y)

savefig('scatter_dem')

Keyword Argumentss If an integer, size of marks in points2 , i.e., area occupied (default 20)

If an array of length N, gives the sizes of the corresponding elements of x, y

marker Symbol marking the points (default = ‘o’)

Same options as for lines that don’t connect the dots And a few more

c A single color or a length-N sequence of colors

from pylab import *

N = 30

x = 0.9*rand(N)

y = 0.9*rand(N)

area = pi * (10 * rand(N))**2 # 0 to 10 point radius

scatter(x,y,s=area, marker='^', c='r')

savefig('scatter_demo')

Ticks A tick is a cross mark on an axis with an associated label

xticks (on the x axis) and yticks (on the y axis)

xticks() returns a tuple of

an array of tick locations (numbers) on the x axis

an array of corresponding tick labels (text)

yticks() is the same, but for the y axis

>>> plot([1,2,3,4], [1,4,9,16])

[<matplotlib.lines.Line2D object at 0x02AC2190>]

>>> xlocs, xlabs = xticks()

>>> ylocs, ylabs = yticks()

>>> print xlocs, '\n', xlabs, '\n', ylocs, '\n', ylabs

[ 1. 1.5 2. 2.5 3. 3.5 4. ]

<a list of 7 Text xticklabel objects>

[ 0. 2. 4. 6. 8. 10. 12. 14. 16.]

<a list of 9 Text yticklabel objects>

xticks() and yticks() can also take 1 or 2 (or more) arguments to set tick features

With 1 argument, it’s an array of new locations for the ticks—e.g.,

xticks( arange(6) )

With 2 arguments, they’re the locations (as with 1) and an array of corresponding labels—e.g.,

xticks([1, 2, 3], [‘Al’, ‘Ed’, ‘Ken’])

xticks() and yticks() can also take text keyword arguments

In all cases, xticks() and yticks() return a tuple of an array of locations and an array of labels

Some tick-related Axes instance methods Note: Minor ticks are the (usually smaller) ticks that occur

between the major ticks (the usual ticks)

get_xticklabels(),

get_xmajorticklabels()

get_xminorticklabels()

get_xticklabels(minor=False)

get_xticklines()¶

get_xticks(minor=False) Return the x ticks as a list of locations

Corresponding y methods

Corresponding set_ methods

>>> plot([1,2,3])

[<matplotlib.lines.Line2D object at 0x01C9C110>]

>>> gca().set_xticks([0.25, 0.75, 1.25, 1.75, 2.25, 2.75], minor=True)

[<matplotlib.axis.XTick object at 0x00B3B770>,

<matplotlib.axis.XTick object at 0x02AC9C10>,

<matplotlib.axis.XTick object at 0x02AC9F90>,

<matplotlib.axis.XTick object at 0x02AC9FF0>,

<matplotlib.axis.XTick object at 0x02AD4390>,

<matplotlib.axis.XTick object at 0x02AD47B0>]

>>> draw()

Note the small ticks on the x axis

For the following example:

Text property rotation is the angle of the text object relative to the x axis Values, besides numbers (degrees), can be ‘horizontal’ (default)

and ‘vertical”

from pylab import *

plot([1,2,3,4], [1,4,9,16])

locs, labels = xticks([1,2,3,4], ['Frogs','Hogs','Bogs','Slogs'])

setp(labels, 'rotation', 'vertical')

savefig('ticks_simpler')

Tick Locators and Formatters Module matplotlib.ticker has 2 bases classes: Locator,

Formatter

Each axis (xaxis or yaxis) has

a major and minor tick locator and

The default minor tick locators return the empty list By default, no minor ticks

a major and minor tick formatter

Each can be set independently

A user can create and plug-in a custom tick locator or formatter

Locators handle

autoscaling of the view limits based on the data limits

choosing the tick locations

Class MultipleLocator

Most generally useful tick locator

Initialize it with a base

It picks axis limits and ticks that are multiples of the base

Class AutoLocator

Contains a MultipleLocator instance

Dynamically (& intelligently) updates it based on the data & zoom limits

Class Summary

NullLocator No ticks

IndexLocator Locator for index plots (e.g., where x = range(len(y))

LinearLocator Evenly spaced ticks from min to max

LogLocator Logarithmically ticks from min to max

MultipleLocator Ticks and range are a multiple of base; either integer or float

AutoLocator Choose a MultipleLocator and dynamically reassign

The Basic Tick Locators

To override the default locator,

use a locator and pass it to the x or y axis instance with one of (where ax is the current axes object)

ax.xaxis.set_major_locator( xmajorLocator )

ax.xaxis.set_minror_locator( xminorLocator )

ax.yaxis.set_major_locator( ymajorLocator )

ax.yaxis.set_minor_locator( yminorLocator )

Tick Formatting Formatters control conversion of the numeric tick location into a string

A formatter operates on a single tick value (and its tick position)

Returns a string to the axis

Class Summary

NullFormatter No labels on the ticks

FixedFormatter Set the strings manually for the labels

FuncFormatter User defined function sets the labels

FormatStrFormatter Use a sprintf format string

IndexFormatter Cycle through fixed strings by tick position

ScalarFormatter Default formatter for scalars; autopick the fmt string

LogFormatter Formatter for log axes

DateFormatter Use an strftime string to format the date

The Tick Formatting Classes

To control the major and minor tick label formats,

use one of the following (where ax is an Axes instance)

ax.xaxis.set_major_Formatter( xmajorFormatter )

ax.xaxis.set_minor_Formatter( xminorFormatter )

ax.yaxis.set_major_Formatter( ymajorFormatter )

ax.yaxis.set_minor_Formatter( yminroFormatter )

from pylab import *

# import the tick locator and formatter class

from matplotlib.ticker import MultipleLocator, FormatStrFormatter

majorLocator = MultipleLocator(21) # multiples of 21

majorFormatter = FormatStrFormatter('*%d*')

minorLocator = MultipleLocator(7) # multiples of 7

minorFormatter = FormatStrFormatter('%d')

t = arange(0.0, 100.0, 0.1)

s = sin(0.1*pi*t)*exp(-t*0.01)

plot(t, s)

ax = gca()

ax.xaxis.set_major_locator(majorLocator)

ax.xaxis.set_major_formatter(majorFormatter)

ax.xaxis.set_minor_locator(minorLocator)

ax.xaxis.set_minor_formatter(minorFormatter)

grid(True)

savefig('ticks_simple')

Plotting Dates To plot dates, matplotlib provides converter functions to convert

python datetime objects to and from floating point numbers

Represent days in the Gregorian Calendar UTC time

No daylight savings time or timezone offset

But timezone support is provided See the pytz module (http://pytz.sourceforge.net/)

The supported date range is the same as the Python datetime module: years 0001-9999

3 datetime conversion functions.

date2num() takes a (sequence of) python datetime(s) Returns a (sequence of) float(s)

num2date() does the inverse

drange() takes a start date, end date and datetime timedelta object

Returns a sequence of floats

Function plot_date() plots y-values vs. floating point dates

Uses plot() but picks a date tick locator and a date tick formatter makes an intelligent default choice based on the range of dates

To use custom date tickers and formatters, use plot()

from pylab import *

import datetime

date1 = datetime.date( 1998, 1, 1 )


delta = datetime.timedelta(days=100)

dates = drange(date1, date2, delta)

s = rand(len(dates))

plot_date(dates, s)

locs, labels = xticks()

setp(labels, rotation=45)

grid(True)

fig = gcf()

dsize = fig.get_size_inches()

fig.set_size_inches( 2 * dsize[0], dsize[1] )

savefig('tick_dates_simple')

Locating and Formatting Date LabelsClass Summary

MinuteLocator Locate minutes

HourLocator Locate hours

DayLocator Locate specified days of the month

WeekdayLocator Locate days of the week, e.g., MO, TU

MonthLocator Locate months, e.g., 7 for July

YearLocator Locate years that are multiples of base

RRuleLocator Locate using a matplotlib.dates.rrulewrapper. The rrulewrapper is a simple wrapper around a dateutils.rrule

The Tick Locators Specialized For Date Plots • In the matplotlib.dates module

E.g., for a month tick every quarter, use

months = MonthLocator(range(3,13,3))

For full control of date ticking, use your own rule with the RRuleLocator class

DateFormatter sub-class of Formatter takes a strftime() format string

from pylab import *

import datetime

years = YearLocator(2) # every 2 years

months = MonthLocator(range(3,13,3)) # every quarter

yearsFmt = DateFormatter('%y') # only last 2 digits

ax = gca()

ax.xaxis.set_major_locator(years)

ax.xaxis.set_major_formatter(yearsFmt)

ax.xaxis.set_minor_locator(months)



delta = datetime.timedelta(days=100)

dates = drange(date1, date2, delta)

s = rand(len(dates))

plot_date(dates, s)Continued

locs, labels = xticks()

setp(labels, rotation=45)

grid(True)

fig = gcf()



savefig('tick_dates')

Odds and EndsHorizontal and Vertical Lineshlines(y, xmin, xmax )

Draw horizontal lines at heights given by the numbers in array y

If xmin and xmax are arrays of same length as y, they give the left and right endpoints of the corresponding lines, resp.

If either is a scalar, all lines have the same endpoint, specified by it


linewidth (or lw): line width in points

color: default ‘k’

vlines(x, ymin, ymax ) is similar but for vertical lines

from pylab import *

y = arange(0,3,0.1)

x = 2*y

hlines(y, 0, x, color='b', lw=4)

savefig('hlines')

Axis Lines axhline() draws a line on the x axis spanning the horizontal

extent of the axes

axhline(y ) draws such a line parallel to the x axis at height y


color: default ‘b’

label

linewidth in points

axvline() is similar but w.r.t. the y axis

Grid Lines grid(True) produces grid lines at the tick coordinates

grid(None) suppresses the grid

grid() toggles the presence of the grid


color: default ‘k’

linestyle: default ‘:’

linewidth

Some Axes instance methods

get_xgridlines()

get_ygridlines()

Example:

setp(gca().get_xgridlines(), color='r')

Resizing the Figure Often should make the figure wider or higher so objects aren’t cramped

Use Figure instance methods get_size_inches() and set_size_inches()

To get an array of the 2 dimensions in inches (width then height):

fig = gcf()


E.g., to double the width


See the example in the SciPy Cookbook

http://www.scipy.org/Cookbook/Matplotlib/AdjustingImageSize

3D Matplotlib: mplot3d See http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html

An Axes3D object is created like any other axes, but using the projection='3d' keyword

Create a new matplotlib.figure.Figure and add to it a new axes of type Axes3D

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()

ax = fig.add_subplot(111, projection='3d')

Example: Line PlotsAxes3D.plot(xs, ys, *args, **kwargs)

Plot 2D or 3D data

xs, ys are the arrays of x, y coordinates of vertices

zs is the z value(s), either 1 for all points or (as array) 1 for each point

zdir gives which direction to use as z (‘x’, ‘y’ or ‘z’) when plotting a 2D set

Other arguments are passed on to plot()

Example

import matplotlib as mpl

from mpl_toolkits.mplot3d import Axes3D

import numpy as np

import matplotlib.pyplot as plt

mpl.rcParams['legend.fontsize'] = 10

fig = plt.figure()

ax = fig.gca(projection='3d')

theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)

z = np.linspace(-2, 2, 100)

r = z**2 + 1

x = r * np.sin(theta)

y = r * np.cos(theta)

ax.plot(x, y, z, \ label='parametric curve')

ax.legend()

plt.show()

AnimationThe Old Way To take an animated plot and turn it into a movie,

save a series of image files (e.g., PNG) and

use an external tool to convert them to a movie

Can use mencoder, part of the mplayer suite

See http://www.mplayerhq.hu/design7/news.html

Can download binaries for Windows

Or use ImageMagick’s convert (“the Swiss army knife of image tools”)

See http://www.imagemagick.org/script/convert.php

Matplotlib Animation Matplotlib Animation Tutorial

http://jakevdp.github.com/blog/2012/08/18/matplotlib-animation-tutorial/

Matplotlib animation documentation

http://matplotlib.org/api/animation_api.html

Matplotlib animation examples

http://matplotlib.org/examples/animation/

Official and good, but documentation limited to meager program comments The tutorial (above) goes through several of these

Alias http://matplotlib.sourceforge.net/examples/animation/index.html

This replaces the Cookbook examples

http://www.scipy.org/Cookbook/Matplotlib/Animations

comp 690 data fusion matplotlib notes albert esterline fall 2008

Documents

matplotlib work

orfrom matplotlib

pylabpackage matplotlib

matplotlib namespace

pyplot import

neededcookbook matplotlib

numpy import

pyfrom pylab import