matplotlib-checkins Mailing List for matplotlib

Revision: 6336
 http://matplotlib.svn.sourceforge.net/matplotlib/?rev=6336&view=rev
Author: jdh2358
Date: 2008年10月26日 14:33:36 +0000 (2008年10月26日)
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年10月25日 07:06:53 UTC (rev 6335)
+++ trunk/py4science/examples/glass_dots1.py	2008年10月26日 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年10月26日 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年10月25日 07:06:53 UTC (rev 6335)
+++ trunk/py4science/examples/glass_dots2.py	2008年10月26日 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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