This document discusses data visualization capabilities in SageMath. It provides over 90 built-in functions for advanced graphing and plotting data. These functions allow importing data from files, lists, and online sources and generating various types of graphs and plots including scatter plots, line graphs, 3D plots, and more. Complex graphs can also be created by fitting models to data and performing operations like interpolation. Graphs are exportable to common formats like PNG, SVG, and PDF. SageMath provides a powerful yet flexible toolset for mathematical data visualization.

1. Dat
Visualizati n
Le funzionalità matematiche di Sage per la
visualizzazione dei dati
Andrea Lazzarotto
http://andrealazzarotto.com

2. Caratteristiche
Oltre 90 componenti
Grafica avanzata
Linguaggio Python

3. Interfaccia web

4. Non un banale foglio di calcolo

5. Percorso
Importare i dati
Funzioni built-in
Grafici complessi

6. Importare
i dati

7. infile = open('bunny.txt','r')
d = []
for l in infile:
d.append(l.split(' '))
.txt

8. infile = open('bunny.csv','r')
import csv
d = list(csv.reader(infile))
.csv

9. html(
table(
[['x','y','z']] +
d[:10],
header_row = True
)
)

10. import urllib2 as U
infile = U.urlopen('http://example.com/data.txt')
d = []
for l in infile:
d.append(l.split(' '))

11. Le liste
a = [1,2,3,4]
b = [[1,3], [6], [1,2,5]]
c = [(5,8,6), 'linux', 7.352]

12. [i^2 + 3 for i in a]
↓
[4, 7, 12, 19]

13. Funzioni
built-in

14. v = [random() for i in [0..9]]
list_plot(v, transparent=True, size=40)

15. coords = enumerate(v)
line(coords, transparent=True)

16. scatter_plot(california, edgecolor=[.4,.4,.4,1],
marker='+', markersize=1, aspect_ratio='1',
axes_labels=['Lon','Lat'], transparent=True)

17. Solo due dimensioni?
Funzioni precedenti → point3d
point3d(bunny[::10], size=20, color='brown')
http://graphics.stanford.edu/data/3Dscanrep/

19. m = random_matrix(ZZ, 5, 5)
matrix_plot(m, cmap='autumn', transparent=True)

20. Opzioni
color='red'
axes=False
frame=True
thickness=8
...

21. Esportazione
g = scatter_plot(d)
g.save('graficobellissimo.png')
g.save('graficobellissimo.svg')
g.save('graficobellissimo.pdf')

22. Grafici
complessi

23. Fitting
v = [(i, random()*0.5-0.25 + i^2+i+1)
for i in srange(0,4,0.2)]
# v -> simulazione di x^2 + x + 1
var('a b c')
f(x) = a*x^2 + b*x + c
sol = find_fit(v, f, solution_dict=True)
A = scatter_plot(v)
B = plot(f.subs(sol), (x, 0, v[-1][0]))
(A+B).show(transparent=True)

25. Interpolazione
points = [[x,y] for [x,y,z] in bunny]
values = [z for [x,y,z] in bunny]
xv = [float(x) for [x,y] in points]
yv = [float(y) for [x,y] in points]
import numpy as np
grid_x, grid_y = np.mgrid[min(xv):max(xv):200jr,
min(yv):max(yv):200jr]
from scipy.interpolate import griddata
grid_z = griddata(points, values,
(grid_x, grid_y), method='linear')
http://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html

26. matrix_plot(grid_z.T, origin='lower',
cmap='BrBG_r', transparent=True)

27. Matplotlib con Pylab
import matplotlib.pyplot as plt
from pylab import figure, savefig
def twobar(dA, dB, xlabel, ylabel, ticks, suff):
fig = figure()
ax = fig.add_subplot(1,1,1)
i = range(len(dA))
ax.bar(i, dB, align='center', linewidth=4,
facecolor='#bb0000', edgecolor='white')
ax.bar(i, dA, fill=False, align='center',
edgecolor='#666666')

28. ax.set_xticks(i)
ax.set_xticklabels([str(d) + suff
for d in ticks])
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.xaxis.labelpad = 12
savefig("output.png", transparent=True)
twobar(datiA, datiB, 'Percentuale', 'Elementi',
[2,4,6,8], "%")

30. Conclusione
Numerosi elementi base
Infinite varianti
Vari livelli di complessità

31. ?