Revision: 6336
http://matplotlib.svn.sourceforge.net/matplotlib/?rev=6336&view=rev
Author: jdh2358
Date: 2008-10-26 14:33:36 +0000 (Sun, 26 Oct 2008)
Log Message:
-----------
added glass dots skel
Modified Paths:
--------------
trunk/py4science/examples/glass_dots1.py
trunk/py4science/examples/glass_dots2.py
Added Paths:
-----------
trunk/py4science/examples/glass_dots1_skel.py
Modified: trunk/py4science/examples/glass_dots1.py
===================================================================
--- trunk/py4science/examples/glass_dots1.py 2008-10-25 07:06:53 UTC (rev
6335)
+++ trunk/py4science/examples/glass_dots1.py 2008-10-26 14:33:36 UTC (rev
6336)
@@ -6,10 +6,9 @@
See L. Glass. 'Moire effect from random dots' Nature 223, 578580 (1969).
"""
import cmath
-from numpy import cos, sin, pi, matrix
-import numpy as npy
+import numpy as np
import numpy.linalg as linalg
-from pylab import figure, show
+import matplotlib.pyplot as plt
def myeig(M):
@@ -18,10 +17,16 @@
Solve quadratic:
- lamba^2 - tau*lambda + Delta = 0
+ lamba^2 - tau*lambda +/- Delta = 0
where tau = trace(M) and Delta = Determinant(M)
-
+
+ if M = | a b |
+ | c d |
+
+ the trace is a+d and the determinant is a*d-b*c
+
+ Return value is lambda1, lambda2
"""
a,b = M[0,0], M[0,1]
@@ -32,31 +37,29 @@
lambda1 = (tau + cmath.sqrt(tau**2 - 4*delta))/2.
lambda2 = (tau - cmath.sqrt(tau**2 - 4*delta))/2.
return lambda1, lambda2
-
+
# 2000 random x,y points in the interval[-0.5 ... 0.5]
-X1 = matrix(npy.random.rand(2,2000)
- )-0.5
+X1 = np.random.rand(2,2000)-0.5
-name = 'saddle'
-sx, sy, angle = 1.05, 0.95, 0.
+#name = 'saddle'
+#sx, sy, angle = 1.05, 0.95, 0.
-#name = 'center'
-#sx, sy, angle = 1., 1., 2.5
+name = 'center'
+sx, sy, angle = 1., 1., 2.5
#name= 'stable focus' # spiral
#sx, sy, angle = 0.95, 0.95, 2.5
-theta = angle * pi/180.
+theta = angle * cmath.pi/180.
+S = np.array([[sx, 0],
+ [0, sy]])
-S = matrix([[sx, 0],
- [0, sy]])
+R = np.array([[np.cos(theta), -np.sin(theta)],
+ [np.sin(theta), np.cos(theta)],])
-R = matrix([[cos(theta), -sin(theta)],
- [sin(theta), cos(theta)],])
+M = np.dot(S, R) # rotate then stretch
-M = S*R # rotate then stretch
-
# compute the eigenvalues using numpy linear algebra
vals, vecs = linalg.eig(M)
print 'numpy eigenvalues', vals
@@ -66,17 +69,17 @@
print 'analytic eigenvalues', avals
# transform X1 by the matrix
-X2 = M*X1
+X2 = np.dot(M, X1)
# plot the original x,y as green dots and the transformed x, y as red
# dots
-fig = figure()
+fig = plt.figure()
ax = fig.add_subplot(111)
-x1 = X1[0].flat
-y1 = X1[1].flat
-x2 = X2[0].flat
-y2 = X2[1].flat
+x1 = X1[0]
+y1 = X1[1]
+x2 = X2[0]
+y2 = X2[1]
ax = fig.add_subplot(111)
line1, line2 = ax.plot(x1, y1, 'go', x2, y2, 'ro', markersize=2)
@@ -85,4 +88,4 @@
fig.savefig('glass_dots1.png', dpi=100)
fig.savefig('glass_dots1.eps', dpi=100)
-show()
+plt.show()
Added: trunk/py4science/examples/glass_dots1_skel.py
===================================================================
--- trunk/py4science/examples/glass_dots1_skel.py
(rev 0)
+++ trunk/py4science/examples/glass_dots1_skel.py 2008-10-26 14:33:36 UTC
(rev 6336)
@@ -0,0 +1,80 @@
+"""
+Moire patterns from random dot fields
+
+http://en.wikipedia.org/wiki/Moir%C3%A9_pattern
+
+See L. Glass. 'Moire effect from random dots' Nature 223, 578580 (1969).
+"""
+import cmath
+import numpy as np
+import numpy.linalg as linalg
+import matplotlib.pyplot as plt
+
+# search for TODO to find the places you need to fix
+TODO = None
+
+def myeig(M):
+ """
+ compute eigen values and eigenvectors analytically
+
+ Solve quadratic:
+
+ lamba^2 - tau*lambda +/- Delta = 0
+
+ where tau = trace(M) and Delta = Determinant(M)
+
+ if M = | a b |
+ | c d |
+
+ the trace is a+d and the determinant is a*d-b*c
+
+ Return value is lambda1, lambda2
+
+ Return value is lambda1, lambda2
+ """
+ # TODO : compute the real values here. 0, 1 is just a place holder
+ return 0, 1
+
+# Generate and shape (2000,2) random x,y points in the
+# interval [-0.5 ... 0.5]
+X1 = TODO
+
+# these are the scaling factor sx, the scaling factor sy, and the
+# rotation angle 0
+name = 'saddle'
+sx, sy, angle = 1.05, 0.95, 0.
+
+# OPTIONAL: try and find other sx, sy, theta for other kinds of nodes:
+# stable node, unstable node, center, spiral, saddle
+
+# convert theta to radians: theta = angle * pi/180
+theta = TODO
+
+# Create a 2D scaling array
+# S = | sx 0 |
+# | 0 sy |
+S = TODO
+
+# create a 2D rotation array
+# R = | cos(theta) -sin(theta) |
+# | sin(theta) cos(theta) |
+R = TODO
+
+# do a matrix multiply M = S x R where x is *matrix* multiplication
+M = TODO
+
+# compute the eigenvalues using numpy linear algebra
+vals, vecs = linalg.eig(M)
+print 'numpy eigenvalues', vals
+
+# compare with the analytic values from myeig
+avals = myeig(M)
+print 'analytic eigenvalues', avals
+
+# transform X1 by the matrix
+# X2 = M x X1 where x is *matrix* multiplication
+X2 = np.dot(M, X1)
+
+# plot the original x,y as green dots and the transformed x, y as red
+# dots
+TODO
Modified: trunk/py4science/examples/glass_dots2.py
===================================================================
--- trunk/py4science/examples/glass_dots2.py 2008-10-25 07:06:53 UTC (rev
6335)
+++ trunk/py4science/examples/glass_dots2.py 2008-10-26 14:33:36 UTC (rev
6336)
@@ -1,4 +1,4 @@
-import numpy as npy
+import numpy as np
import numpy.linalg as linalg
from pylab import figure, show
@@ -12,15 +12,15 @@
self.axes = axes
self.canvas = axes.figure.canvas
self.canvas.mpl_connect('button_press_event', self.press)
- self.canvas.mpl_connect('button_release_event', self.release)
- self.canvas.mpl_connect('motion_notify_event', self.move)
+ self.canvas.mpl_connect('button_release_event', self.release)
+ self.canvas.mpl_connect('motion_notify_event', self.move)
- X1 = self.X1 = npy.matrix(npy.random.rand(2,2000))-0.5
+ X1 = self.X1 = np.random.rand(2,2000)-0.5
- x1 = X1[0].flat
- y1 = X1[1].flat
- x2 = X1[0].flat # no transformation yet
- y2 = X1[1].flat
+ x1 = X1[0]
+ y1 = X1[1]
+ x2 = X1[0] # no transformation yet
+ y2 = X1[1]
self.line1, self.line2 = ax.plot(x1, y1,'go', x2, y2, 'ro',
markersize=2)
self.xlast = None
self.ylast = None
@@ -37,37 +37,37 @@
self.xlast = None
self.ylast = None
self.draw()
-
+
def draw(self):
sx, sy, theta = self.sx, self.sy, self.theta
- a = sx*npy.cos(theta)
- b = -sx*npy.sin(theta)
- c = sy*npy.sin(theta)
- d = sy*npy.cos(theta)
- M = npy.matrix([[a,b],[c,d]])
+ a = sx*np.cos(theta)
+ b = -sx*np.sin(theta)
+ c = sy*np.sin(theta)
+ d = sy*np.cos(theta)
+ M = np.array([[a,b],[c,d]])
- X2 = M*self.X1
- x2 = X2[0].flat
- y2 = X2[1].flat
+ X2 = np.dot(M, self.X1)
+ x2 = X2[0]
+ y2 = X2[1]
self.line2.set_data(x2,y2)
self.canvas.draw()
-
+
def move(self, event):
if not event.inaxes: return # not over axes
if self.xlast is None: return # no initial data
if not event.button: return # no button press
-
+
dx = event.xdata - self.xlast
- dy = event.ydata - self.ylast
+ dy = event.ydata - self.ylast
if event.button==1:
self.theta += dx
elif event.button==3:
self.sx += dx
self.sy += dy
-
+
self.title.set_text('sx=%1.2f, sy=%1.2f, theta=%1.2f'%(self.sx,
self.sy, self.theta))
self.draw()
self.xlast = event.xdata
@@ -75,9 +75,9 @@
-
-from pylab import subplot, show
-fig = figure()
+
+import matplotlib.pyplot as plt
+fig = plt.figure()
ax = fig.add_subplot(111)
t = Transformer(ax)
-show()
+plt.show()
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