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
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
|
from Numeric import *
from plplot import *
XPTS = 35
YPTS = 46
XSPA = 2./(XPTS-1)
YSPA = 2./(YPTS-1)
#polar plot data
PERIMETERPTS = 100
RPTS = 40
THETAPTS = 40
#potential plot data
PPERIMETERPTS = 100
PRPTS = 40
PTHETAPTS = 64
tr = array((XSPA, 0.0, -1.0, 0.0, YSPA, -1.0))
def mypltr(x, y, data):
result0 = data[0] * x + data[1] * y + data[2]
result1 = data[3] * x + data[4] * y + data[5]
return array((result0, result1))
def polar():
#polar contour plot example.
plenv(-1., 1., -1., 1., 0, -2,)
plcol0(1)
# Perimeter
t = (2.*pi/(PERIMETERPTS-1))*arange(PERIMETERPTS)
px = cos(t)
py = sin(t)
plline(px, py)
# create data to be contoured.
r = arange(RPTS)/float(RPTS-1)
r.shape = (-1,1)
theta = (2.*pi/float(THETAPTS-1))*arange(THETAPTS-1)
xg = r*cos(theta)
yg = r*sin(theta)
zg = r*ones(THETAPTS-1)
lev = 0.05 + 0.10*arange(10)
plcol0(2)
plcont(zg, lev, pltr2, xg, yg, 2)
# ^-- :-). Means: "2nd coord is wrapped."
plcol0(1)
pllab("", "", "Polar Contour Plot")
def potential():
#shielded potential contour plot example.
# create data to be contoured.
r = 0.5 + arange(PRPTS)
r.shape = (-1,1)
theta = (2.*pi/float(PTHETAPTS-1))*(0.5+arange(PTHETAPTS-1))
xg = r*cos(theta)
yg = r*sin(theta)
rmax = max(r.flat)
xmin = min(xg.flat)
xmax = max(xg.flat)
ymin = min(yg.flat)
ymax = max(yg.flat)
x0 = (xmin + xmax)/2.
y0 = (ymin + ymax)/2.
#perturbed (expanded) limits
peps = 0.05
xpmin = xmin - abs(xmin)*peps
xpmax = xmax + abs(xmax)*peps
ypmin = ymin - abs(ymin)*peps
ypmax = ymax + abs(ymax)*peps
# Potential inside a conducting cylinder (or sphere) by method of images.
# Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
# Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
# Also put in smoothing term at small distances.
eps = 2.
q1 = 1.
d1 = rmax/4.
q1i = - q1*rmax/d1
d1i = rmax**2/d1
q2 = -1.
d2 = rmax/4.
q2i = - q2*rmax/d2
d2i = rmax**2/d2
div1 = sqrt((xg-d1)**2 + (yg-d1)**2 + eps**2)
div1i = sqrt((xg-d1i)**2 + (yg-d1i)**2 + eps**2)
div2 = sqrt((xg-d2)**2 + (yg+d2)**2 + eps**2)
div2i = sqrt((xg-d2i)**2 + (yg+d2i)**2 + eps**2)
zg = q1/div1 + q1i/div1i + q2/div2 + q2i/div2i
zmin = min(zg.flat)
zmax = max(zg.flat)
# print "%.15g %.15g %.15g %.15g %.15g %.15g %.15g %.15g \n" % \
# (q1, d1, q1i, d1i, q2, d2, q2i, d2i)
# print "%.15g %.15g %.15g %.15g %.15g %.15g \n" % \
# (xmin, xmax, ymin, ymax, zmin, zmax)
# Positive and negative contour levels.
nlevel = 20
dz = (zmax-zmin)/float(nlevel)
clevel = zmin + (arange(20)+0.5)*dz
try:
#This works with numpy 20.3
clevelpos = compress(clevel > 0., clevel)
clevelneg = compress(clevel <= 0., clevel)
except:
#Eventually eliminate this as we quit supporting old numpy versions.
print "Calculate negative and positive contours the old-fashioned way"
clevelpos = zeros(20,"double")
clevelneg = zeros(20,"double")
nclevelpos = 0
nclevelneg = 0
for i in range(20):
if clevel[i] > 0.:
clevelpos[nclevelpos] = clevel[i]
nclevelpos = nclevelpos+1
else:
clevelneg[nclevelneg] = clevel[i]
nclevelneg = nclevelneg+1
clevelpos = clevelpos[0:nclevelpos]
clevelneg = clevelneg[0:nclevelneg]
#Colours!
ncollin = 11
ncolbox = 1
ncollab = 2
#Finally start plotting this page!
pladv(0)
plcol0(ncolbox)
plvpas(0.1, 0.9, 0.1, 0.9, 1.0)
plwind(xpmin, xpmax, ypmin, ypmax)
plbox("", 0., 0, "", 0., 0)
plcol0(ncollin)
# Negative contours
pllsty(2)
plcont(zg, clevelneg, pltr2, xg, yg, 2)
# Positive contours
pllsty(1)
plcont(zg, clevelpos, pltr2, xg, yg, 2)
# Draw outer boundary
t = (2.*pi/(PPERIMETERPTS-1))*arange(PPERIMETERPTS)
px = x0 + rmax*cos(t)
py = y0 + rmax*sin(t)
plcol0(ncolbox)
plline(px, py)
plcol0(ncollab)
pllab("", "", "Shielded potential of charges in a conducting sphere")
def main():
mark = 1500
space = 1500
clevel = -1. + 0.2*arange(11)
xx = (arrayrange(XPTS) - XPTS/2) / float((XPTS/2))
yy = (arrayrange(YPTS) - YPTS/2) / float((YPTS/2)) - 1.
xx.shape = (-1,1)
z = (xx*xx)-(yy*yy)
# 2.*outerproduct(xx,yy) for new versions of Numeric which have outerproduct.
w = 2.*xx*yy
# Set up grids.
# Note *for the given* tr, mypltr(i,j,tr)[0] is only a function of i
# and mypltr(i,j,tr)[1] is only function of j.
xg0 = mypltr(arange(XPTS),0,tr)[0]
yg0 = mypltr(0,arange(YPTS),tr)[1]
distort = 0.4
cos_x = cos((pi/2.)*xg0)
cos_y = cos((pi/2.)*yg0)
xg1 = xg0 + distort*cos_x
yg1 = yg0 - distort*cos_y
# Need independent copy here so the shape changes for xg0t do not affect
# xg0.
try:
xg0t = xg0.copy()
except:
# old versions of Numpy bundled with python-1.5 do not have the
# copy method for arrays. So if the above fails, do it another way
# (which we will remove as soon as we quit supporting python-1.5)
xg0t = array(xg0)
cos_x.shape = (-1,1)
xg0t.shape = (-1,1)
xg2 = xg0t + distort*cos_x*cos_y
yg2 = yg0 - distort*cos_x*cos_y
# Plot using mypltr (scaled identity) transformation used to create
# xg0 and yg0
# pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
# plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
# plcol0(2)
# plcont(z, clevel, mypltr, tr)
# plstyl([mark], [space])
# plcol0(3)
# plcont(w, clevel, mypltr, tr)
# plstyl([], [])
# plcol0(1)
# pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
plcol0(2)
plcont(z, clevel, mypltr, tr)
plstyl([mark], [space])
plcol0(3)
plcont(w, clevel, mypltr, tr)
plstyl([], [])
plcol0(1)
pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# Plot using 1D coordinate transformation.
pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
plcol0(2)
plcont(z, clevel, pltr1, xg1, yg1)
plstyl([mark], [space])
plcol0(3)
plcont(w, clevel, pltr1, xg1, yg1)
plstyl([], [])
plcol0(1)
pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
# plcol0(2)
# plcont(z, clevel, pltr1, xg1, yg1)
# plstyl([mark], [space])
# plcol0(3)
# plcont(w, clevel, pltr1, xg1, yg1)
# plstyl([], [])
# plcol0(1)
# pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
#
# Plot using 2D coordinate transformation.
plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
plcol0(2)
plcont(z, clevel, pltr2, xg2, yg2)
plstyl([mark], [space])
plcol0(3)
plcont(w, clevel, pltr2, xg2, yg2)
plstyl([], [])
plcol0(1)
pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
# pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# plenv(-1.0, 1.0, -1.0, 1.0, 0, 0)
# plcol0(2)
# plcont(z, clevel, pltr2, xg2, yg2)
# plstyl([mark], [space])
# plcol0(3)
# plcont(w, clevel, pltr2, xg2, yg2)
# plstyl([], [])
# plcol0(1)
# pllab("X Coordinate", "Y Coordinate", "Streamlines of flow")
#
# polar contour examples.
pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
polar()
# pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# polar()
# potential contour examples.
pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
potential()
# pl_setcontlabelparam(0.006, 0.3, 0.1, 1)
# potential()
# Restore defaults
plcol0(1)
pl_setcontlabelparam(0.006, 0.3, 0.1, 0)
main()
|
