1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
|
#!/usr/bin/env python
# Copyright (C) 2011, 2012 Povilas Kanapickas <povilas@radix.lt>
#
# This file is part of cppreference-doc
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see http://www.gnu.org/licenses/.
import matplotlib.pyplot as plt
import os
from numpy import *
from bisect import *
#
# DATA - array of items describing data to plot
# Each item consists of the following parts
#
# 1 : string : name of the function
# 2 : array of 4 items : xmin, xmax, ymin, ymax
# 3 : array of N items : X coordinates for the N points to plot.
# Points outside [xmin, xmax] won't be plotted
# 4 : array of N items : Y coordinates for the N points to plot.
# Points outside [ymin, ymax] won't be plotted
# 5 : array of M items : Points where the function is discontinuous.
# Each of the items contains 6 elements:
# * x,y of the beginning of the discontinuity region
# * 'T' or 'F' depending on whether the function has
# a real value at that point
# * x,y of the end of the discontinuity region
# * 'T' or 'F' depending on whether the function has
# a real value at that point
#
DATA = (
( 'floor',
( -3.5, 3.5, -3.5, 3.5 ),
arange(-4, 4, 0.02),
floor(arange(-4, 4, 0.02)),
( (-3, -4, 'F', -3, -3, 'T'),
(-2, -3, 'F', -2, -2, 'T'),
(-1, -2, 'F', -1, -1, 'T'),
( 0, -1, 'F', 0, 0, 'T'),
( 1, 0, 'F', 1, 1, 'T'),
( 2, 1, 'F', 2, 2, 'T'),
( 3, 2, 'F', 3, 3, 'T')
)
),
( 'ceil',
( -3.5, 3.5, -3.5, 3.5 ),
arange(-4, 4, 0.02),
ceil(arange(-4, 4, 0.02)),
( (-3, -3, 'T', -3, -2, 'F'),
(-2, -2, 'T', -2, -1, 'F'),
(-1, -1, 'T', -1, 0, 'F'),
( 0, 0, 'T', 0, 1, 'F'),
( 1, 1, 'T', 1, 2, 'F'),
( 2, 2, 'T', 2, 3, 'F'),
( 3, 3, 'T', 3, 4, 'F')
)
),
( 'trunc',
( -3.5, 3.5, -3.5, 3.5 ),
arange(-4, 4, 0.02),
trunc(arange(-4, 4, 0.02)),
( (-3, -3, 'T', -3, -2, 'F'),
(-2, -2, 'T', -2, -1, 'F'),
(-1, -1, 'T', -1, 0, 'F'),
( 1, 0, 'F', 1, 1, 'T'),
( 2, 1, 'F', 2, 2, 'T'),
( 3, 2, 'F', 3, 3, 'T'),
)
),
( 'round_away_zero',
( -3.5, 3.5, -3.5, 3.5 ),
arange(-4, 4, 0.02),
around(arange(-4, 4, 0.02)),
( (-3.5, -4, 'T', -3.5, -3, 'F'),
(-2.5, -3, 'T', -2.5, -2, 'F'),
(-1.5, -2, 'T', -1.5, -1, 'F'),
(-0.5, -1, 'T', -0.5, 0, 'F'),
( 0.5, 0, 'F', 0.5, 1, 'T'),
( 1.5, 1, 'F', 1.5, 2, 'T'),
( 2.5, 2, 'F', 2.5, 3, 'T'),
( 3.5, 3, 'F', 3.5, 4, 'T')
)
),
( 'sin',
( -6.3, 6.3, -1, 1),
arange(-6.3, 6.3, 0.02),
sin(arange(-6.3, 6.3, 0.02)),
()
),
( 'cos',
( -6.3, 6.3, -1, 1),
arange(-6.3, 6.3, 0.02),
cos(arange(-6.3, 6.3, 0.02)),
()
),
( 'tan',
( -6.3, 6.3, -4, 4),
arange(-6.3, 6.3, 0.02),
tan(arange(-6.3, 6.3, 0.02)),
( ( -4.72, 100, 'F', -4.70, -100, 'F'),
( -1.59, 100, 'F', -1.57, -100, 'F'),
( 1.57, 100, 'F', 1.59, -100, 'F'),
( 4.70, 100, 'F', 4.72, -100, 'F')
)
)
)
font = {'family' : 'DejaVu Sans',
'weight' : 'normal',
'size' : 9}
plt.rc('font', **font)
for i in xrange(len(DATA)):
(name,lim,xdata,ydata,discont) = DATA[i]
#make a single array from the data
data = list()
for j in xrange(len(xdata)):
data.append({'type' : 'c', 'x' : xdata[j], 'y' : ydata[j]})
data.sort(key = lambda it: it['x'])
for j in xrange(len(discont)):
(x1,y1,t1, x2,y2,t2) = discont[j]
data_x = [i['x'] for i in data]
imin = bisect_left(data_x, x1)
imax = bisect_right(data_x, x2)
del data[imin:imax]
data.insert(imin, {'type' : 'dend', 'x': x2, 'y' : y2, 't': t2 })
data.insert(imin, {'type' : 'dbeg', 'x': x1, 'y' : y1, 't': t1 })
# make fig
fig = plt.figure(figsize=(200.0/72.0,200.0/72.0))
ax = fig.add_subplot(111)
(xmin,xmax,ymin,ymax) = lim
ax.set_xlim((xmin, xmax))
ax.set_ylim((ymin, ymax))
# functions for range checking
def c_in_lim(cx, cy, px, py):
if cx < xmin and px < xmin:
return False
if cx > xmax and px > xmax:
return False
if cy < ymin and py < ymin:
return False
if cy > ymax and py > ymax:
return False
return True
def d_in_lim(x, y):
if x < xmin - (xmax-xmin)*0.03:
return False
if x > xmax + (xmax-xmin)*0.03:
return False
if y < ymin - (ymax-ymin)*0.03:
return False
if y > ymax + (ymax-ymin)*0.03:
return False
return True
# paint lines
# the lines are painted in batches
paint_batch = list()
for j in xrange(1, len(data)):
prev_t = data[j-1]['type']
curr_t = data[j]['type']
prev_x = data[j-1]['x']
curr_x = data[j]['x']
prev_y = data[j-1]['y']
curr_y = data[j]['y']
is_good = True #whether current segment needs painting
# don't paint out of bounds
if curr_t == 'c':
if not c_in_lim(curr_x, curr_y, prev_x, prev_y):
is_good = False
else:
if not d_in_lim(curr_x, curr_y):
is_good = False
# don't paint within discontinuous region
if (curr_t == 'dend' and prev_t == 'dbeg'):
is_good = False
# append an item to batch if needed
if is_good:
if len(paint_batch) == 0:
paint_batch.append((prev_x, prev_y))
paint_batch.append((curr_x, curr_y))
# we need painting if this is the last data point
if j == len(data) - 1:
is_good = False
# paint the current batch, if any
if (not is_good) and len(paint_batch) > 1:
# merge adjacent segments if they have the same direction
def compute_dir(n):
(x1,y1) = paint_batch[n]
(x2,y2) = paint_batch[n+1]
return (y2-y1)/(x2-x1)
prev_dir = compute_dir(0)
k = 1
while k < len(paint_batch) - 1:
curr_dir = compute_dir(k)
if curr_dir == prev_dir:
del paint_batch[k]
else:
prev_dir = curr_dir
k += 1
# paint
(x,y) = zip(*paint_batch)
l = ax.plot(x, y)
plt.setp(l, 'color', '#0000FF')
plt.setp(l, 'linewidth', 0.5)
paint_batch = []
# paint markers
for j in xrange(0, len(data)):
curr_t = data[j]['type']
curr_x = data[j]['x']
curr_y = data[j]['y']
# paint point marking discontinuous region if needed
if curr_t != 'c':
if not d_in_lim(curr_x, curr_y):
continue
fill = data[j]['t']
l = ax.plot(curr_x, curr_y, marker='o')
plt.setp(l, 'markersize', 7.5)
plt.setp(l, 'markeredgewidth', 0.5)
plt.setp(l, 'markeredgecolor', '#0000FF')
if fill == 'T':
plt.setp(l, 'markerfacecolor', '#0000FF')
else:
plt.setp(l, 'markerfacecolor', 'white')
ax.grid(True)
ax.set_axisbelow(True)
ax.tick_params(pad = 7.5)
ax.set_aspect((xmax-xmin)/(ymax-ymin)) # always produce square plots
outfile = 'output/math-' + name + '.svg'
tmpfile = outfile + '.tmp'
plt.savefig(tmpfile, format='svg')
os.system('xsltproc --novalid fix_svg-math.xsl ' + tmpfile + ' > ' + outfile)
os.system('rm ' + tmpfile)
plt.close()
|
