slides_python_ for basic operation of it

Matplotlib: Python Plotting
Hendrik Speleers

Lab Calc
2024-2025
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Overview
– Anatomy of a figure
●
Figures and axes
– 2D plotting
●
Standard line plotting
●
Other plotting + text annotation
– 3D plotting
●
3D axes + 3D line/surface plotting
– Other plotting
●
Contours + image visualization

Lab Calc
2024-2025
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Matplotlib
– Mathematical plotting library
– Python extension for graphics
●
Suited for visualization of data and creation of high-quality figures
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Extensive package for 2D plotting, and add-on toolkits for 3D plotting
●
Pyplot: MATLAB-like procedural interface to the object-oriented API
– Import convention
from matplotlib import pyplot as plt
import matplotlib.pyplot as plt

Lab Calc
2024-2025
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Matplotlib
– Mathematical plotting library
– Interactive matplotlib sessions
●
IPython console
●
Jupyter notebook
%matplotlib
%matplotlib inline
%matplotlib notebook

Lab Calc
2024-2025
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A simple plot
– Syntax is array-based
– If not interactive, also write:
In [1]: x = np.linspace(0, 2.0*np.pi, 100)
In [2]: cx, sx = np.cos(x), np.sin(x)
In [3]: plt.plot(x, cx)
...: plt.plot(x, sx)
...: plt.show()

Lab Calc
2024-2025
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A simple plot
– Default settings (see also plt.rcParams)
In [3]: plt.figure(figsize=(6.0, 4.0), dpi=72.0)
...: plt.subplot(1, 1, 1)
...: plt.plot(x, cx, color='#1f77b4',
...: linewidth=1.5, linestyle='-')
...: plt.plot(x, sx, color='#ff7f0e',
...: linewidth=1.5, linestyle='-')
...: plt.xlim(-0.1*np.pi, 2.1*np.pi)
...: plt.xticks(np.linspace(0, 6, 7))
...: plt.ylim(-1.1, 1.1)
...: plt.yticks(np.linspace(-1, 1, 9))

Lab Calc
2024-2025
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Anatomy

Lab Calc
2024-2025
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Anatomy
– Hierarchical structure
– Figure
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The overall window on which everything is drawn
●
Components: one or more axes, suptitle, ...
plt.figure(num=None, figure index, 1-based
figsize=None, (width, height) in inches
dpi=None, resolution
facecolor=None, background color
...)

Lab Calc
2024-2025
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Anatomy
– Axes
●
The area on which the data is plotted
● Belongs to a figure, placed arbitrarily (axes) or in grid (subplot)
●
Components: x/y-axis, ticks, spines, labels, title, legend, ...
●
All methods of active axes are directly callable via Pyplot interface
plt.axes((left, bottom, width, height), **kwargs)
plt.subplot(nrows, ncols, index, **kwargs)
**kwargs: facecolor=None, polar=False, ...

Lab Calc
2024-2025
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Anatomy
– Axes components
● Get or set limits: plt.xlim, plt.ylim, plt.axis
– left, right = plt.xlim()
– plt.xlim(left, right)
– plt.axis((left, right, bottom, top)), plt.axis('equal')
● Get or set ticks: plt.xticks, plt.yticks
– locs, labels = plt.xticks()
– plt.xticks(np.arange(3), ('a', 'b', 'c'))
● Set labels: plt.xlabel(txt), plt.ylabel(txt)
● Set title: plt.title(txt)
● Others: plt.box(), plt.grid(), ...

Lab Calc
2024-2025
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Anatomy
– Example
In [1]: plt.figure(facecolor='silver')
...: plt.title('subplot')
...: plt.axes((0.4, 0.3, 0.4, 0.4))
...: plt.xlim(1, 5)
...: plt.ylim(-5, -1)
...: plt.title('axes')

Lab Calc
2024-2025
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2D plotting
– Standard line plotting: basic syntax
●
Connect data points (x, y) with optional format string
● Color (c): b, g, r, c, m, y, k, w
● Linestyle (l): -, --, -., :
● Marker (m): o, *, ., +, x, s, d, ^, <, >, p, h, ...
plt.plot(y)
plt.plot(x, y)
plt.plot(x, y, 'clm')

Lab Calc
2024-2025
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2D plotting
– Standard line plotting: advanced syntax
– Multiple plots per axes possible
– Legend:
plt.plot(x, y, **kwargs)
**kwargs: color, linestyle, linewidth, marker,
markeredgecolor, markeredgewidth,
markerfacecolor, markersize, label, ...
plt.legend(('a', 'b', 'c'), loc='upper right')

Lab Calc
2024-2025
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2D plotting
– For full plot details, check out plt.plot?
– Example
In [1]: t = np.arange(0.0, 2.0, 0.01)
...: s = 1.0 + np.sin(2.0*np.pi*t)
In [2]: plt.axes(facecolor='silver')
...: plt.plot(t, s, 'r')
...: plt.xlabel('time (s)')
...: plt.ylabel('voltage (mV)')
...: plt.title('About as simple as it gets')
...: plt.grid()

Lab Calc
2024-2025
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2D plotting
– Plotting methods are actually connected to axes
●
Pyplot provides an interface to the active axes
In [1]: t = np.arange(0.0, 2.0, 0.01)
...: s = 1.0 + np.sin(2.0*np.pi*t)
In [2]: ax = plt.axes()
...: ax.plot(t, s, 'r')
...: ax.set(facecolor='silver',
...: xlabel='time (s)',
...: ylabel='voltage (mV)',
...: title='About as simple as it gets')
...: ax.grid()

Lab Calc
2024-2025
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2D plotting
– Example: data statistics
●
Data in the file “populations.txt” describes the populations of
hares, lynxes and carrots in northern Canada during 20 years
●
Load the data and plot it
●
Compute the mean populations over time
●
Which species has the highest population each year?
# year hare lynx carrot
1900 30e3 4e3 48300
1901 47.2e3 6.1e3 48200
1902 70.2e3 9.8e3 41500
...

Lab Calc
2024-2025
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2D plotting
●
Load the data and plot it
In [1]: data = np.loadtxt('populations.txt')
In [2]: year, hares, lynxes, carrots = data.T
In [3]: plt.axes((0.2, 0.1, 0.6, 0.8))
...: plt.plot(year, hares)
...: plt.plot(year, lynxes)
...: plt.plot(year, carrots)
...: plt.xticks(np.arange(1900, 1921, 5))
...: plt.yticks(np.arange(1, 9) * 10000)
...: plt.legend(('Hare', 'Lynx', 'Carrot'))

Lab Calc
2024-2025
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2D plotting
●
Compute the mean populations over time
●
Which species has the highest population each year?
In [4]: populations = data[:, 1:]
In [5]: populations.mean(axis=0)
Out[5]: array([34080.9524, 20166.6667, 42400.])
In [6]: populations.std(axis=0)
Out[6]: array([20897.9065, 16254.5915, 3322.5062])
In [7]: populations.argmax(axis=1)
Out[7]: array([2, 2, 0, 0, 1, 1, 2, 2, 2, 2, ...])

Lab Calc
2024-2025
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2D plotting
– Other plotting
● Log plots: plt.loglog(x, y), plt.semilogx(x, y), plt.semilogy(x, y)
● Polar plots: plt.polar(theta, r)
● Scatter plots: plt.scatter(x, y)
● Bar graphs: plt.bar(x, height), plt.barh(y, width)
● Pie charts: plt.pie(x)
● Histogram: plt.hist(x, bins=None)
● Filled curves: plt.fill(x, y), plt.fill_between(x, y1, y2=0)
– For full method details, check out plt.method?

Lab Calc
2024-2025
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2D plotting
– Example
In [1]: names = ['a', 'b', 'c', 'd']
...: values = [1, 10, 40, 50]
In [2]: plt.figure(figsize=(3, 9))
...: plt.bar(names, values)
...: plt.scatter(names, values)
...: plt.fill_between(names, values)
...: plt.suptitle(
...: 'categorical plotting', y=0.92)

Lab Calc
2024-2025
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2D plotting
– Text
● Axes text: plt.title(txt), plt.xlabel(txt), plt.ylabel(txt)
● Plain text: plt.text(x, y, txt)
● Annotation: plt.annotate(txt, xy=(x, y), xytext=(xt, yt),
arrowprops={'arrowstyle':'->'})
●
Extensive math rendering engine
– Support for TeX markup inside dollar signs ($)
– Use raw strings (precede the quotes with an 'r')
plt.title('alpha > beta') # normal text
plt.title(r'$alpha > beta$') # math text

Lab Calc
2024-2025
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2D plotting
– Example
In [1]: x = np.linspace(0, 2.0*np.pi, 25)
In [2]: plt.scatter(x, np.sin(x))
...: plt.ylim(-2, 2)
...: plt.text(3, 1, 'sine function',
...: fontsize=18, style='italic')
...: plt.annotate('localnmax',
...: xy=(np.pi/2.0, 1), xytext=(1.3, 0),
...: arrowprops={'arrowstyle':'->'})
...: plt.annotate('localnmin',
...: xy=(np.pi*3.0/2.0, -1), xytext=(4.5, -0.4),
...: arrowprops={'arrowstyle':'->'})

Lab Calc
2024-2025
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3D plotting
– Module mplot3d
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This toolkit adds simple 3D plotting to matplotlib with same “look-and-feel”
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It supplies an axes object that can create a 2D projection of a 3D scene
– Creation of 3D axes object
● Use ax = mplot3d.Axes3D(fig)
●
Use any standard axes creation method
with keyword projection='3d'
– ax = plt.subplot(111, projection='3d')
from mpl_toolkits import mplot3d

Lab Calc
2024-2025
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3D plotting
– 3D axes properties
● Z-axis: ax.set(..., zlabel='z', zticks=(-1,0,1))
● Orientation: ax.view_init(elev=30, azim=45)
In [1]: ax = plt.axes(projection='3d')
...: ax.view_init(elev=30, azim=45)
...: ax.set(xlabel='x', ylabel='y', zlabel='z')

Lab Calc
2024-2025
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3D plotting
– Natural plot extensions
● Line plots: ax.plot(x, y, z), ax.plot3D(x, y, z)
● Scatter plots: ax.scatter(x, y, z), ax.scatter3D(x, y, z)
In [1]: 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)
In [2]: ax = plt.axes(projection='3d')
...: ax.plot(x, y, z, 'r')
...: ax.set(title='parametric curve')

Lab Calc
2024-2025
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3D plotting
– Surface plotting
● Wireframe plot: ax.plot_wireframe(X, Y, Z)
● Surface plot: ax.plot_surface(X, Y, Z)
– Surface options
●
Create coordinate matrices from coordinate vectors
– X, Y = np.meshgrid(x, y, sparse=False, copy=True)
●
Color maps: mapping between numeric values and colors
– Use keyword cmap
– Manipulated via module matplotlib.cm
– Examples: jet, hot, coolwarm, bone, ...

Lab Calc
2024-2025
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3D plotting
– Example
In [1]: x = np.arange(-5, 5, 0.25)
...: y = np.arange(-5, 5, 0.25)
...: X, Y = np.meshgrid(x, y)
...: R = np.sqrt(X**2 + Y**2)
...: Z = np.sin(R)
...: plt.suptitle('surface plots')
...: ax1 = plt.subplot(1, 2, 1, projection='3d')
...: ax1.plot_wireframe(X, Y, Z, color='black')
...: ax2 = plt.subplot(1, 2, 2, projection='3d')
...: ax2.plot_surface(X, Y, Z, cmap='coolwarm')

Lab Calc
2024-2025
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Contour plotting
– Contour lines: basic syntax
– Other contour functions:
● Filled contours: plt.contourf(X, Y, Z, levels)
● Contour identification: plt.clabel(cs), plt.colorbar(cs)
● 3D contour lines (mplot3d): ax.contour(X, Y, Z, levels)
plt.contour(Z)
plt.contour(X, Y, Z)
plt.contour(X, Y, Z, levels)

Lab Calc
2024-2025
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Contour plotting
– Example
In [1]: t = np.arange(-2, 2, 0.01)
...: X, Y = np.meshgrid(t, t)
...: Z = np.sin(X * np.pi / 2)
...: + np.cos(Y * np.pi / 4)
...: cs = plt.contour(X, Y, Z)
...: plt.clabel(cs)
...: cs = plt.contourf(X, Y, Z, cmap='coolwarm')
...: plt.colorbar(cs)

Lab Calc
2024-2025
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Image plotting
– Image
●
A matrix of color intensities (via color map)
●
A matrix of RGB or RGBA colors (3D array of dept = 3 or 4)
– Image plots: basic syntax
– Other matrix visualization:
● Matrix values: plt.matshow(A)
● Matrix sparsity: plt.spy(A)
plt.imshow(img)

Lab Calc
2024-2025
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Image plotting
– Example
In [1]: A = np.diag(np.arange(10, 21))
...: plt.imshow(A, cmap='summer')
...: plt.spy(A, marker='*')

Lab Calc
2024-2025
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Image plotting
– Example: Mandelbrot set
●
Fractal set of complex numbers
● Definition: any c for which zi+1
= zi
2
+ c does
not diverge, starting from z0
= 0
● Property: limi→∞
sup | zi+1
| ≤ 2 for any valid c
In [1]: def mandelbrot(nx, ny, max_it=20):
...: # TODO
...: return M
In [2]: M = mandelbrot(501, 501, 50)
...: plt.imshow(M.T, cmap='flag')
...: plt.axis('off')

Lab Calc
2024-2025
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Image plotting
– Example: Mandelbrot set
In [1]: def mandelbrot(nx, ny, max_it=20):
...: x = np.linspace(-2.0, 1.0, nx)
...: y = np.linspace(-1.5, 1.5, ny)
...: C = x[:,np.newaxis]
...: + 1.0j*y[np.newaxis,:]
...: Z = C.copy()
...: M = np.ones((nx, ny), dtype=bool)
...: for i in range(max_it):
...: Z[M] = Z[M]**2 + C[M]
...: M[np.abs(Z) > 2] = False
...: return M

Lab Calc
2024-2025
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Colors
– Predefined colors
●
abbreviation: b, g, r, c, m, y, k, w
●
full name: blue, green, red, cyan, magenta, yellow, black, white, ...
– RGB/RGBA code
●
tuple of three or four float values in [0, 1]
●
a hexadecimal RGB or RGBA string
– Black and white
●
string representation of a float value in [0, 1]
– All string specifications of color are case-insensitive

Lab Calc
2024-2025
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Lab Calc
2024-2025
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Colormaps

Lab Calc
2024-2025
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Input and output
– Save figures
●
Most backends support png, pdf, eps, svg
– Image I/O
In [1]: plt.plot([1, 2, 4, 2])
...: plt.savefig('plot.png', format='png')
In [1]: img = plt.imread('elephant.png')
In [2]: plt.imshow(img)
In [3]: plt.imsave('new_elephant.png', img)

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