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SF.net SVN: matplotlib: [3977] trunk/py4science
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From: <jd...@us...> - 2007-10-21 20:57:56
|
Revision: 3977
http://matplotlib.svn.sourceforge.net/matplotlib/?rev=3977&view=rev
Author: jdh2358
Date: 2007-10-21 13:57:54 -0700 (Sun, 21 Oct 2007)
Log Message:
-----------
added glass moire pattern example
Added Paths:
-----------
trunk/py4science/examples/glass_dots1.py
trunk/py4science/examples/skel/glass_dots_skel.py
trunk/py4science/workbook/fig/glass_dots1.eps
trunk/py4science/workbook/fig/glass_dots1.png
Added: trunk/py4science/examples/glass_dots1.py
===================================================================
--- trunk/py4science/examples/glass_dots1.py (rev 0)
+++ trunk/py4science/examples/glass_dots1.py 2007-10-21 20:57:54 UTC (rev 3977)
@@ -0,0 +1,95 @@
+"""
+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).
+"""
+from numpy import cos, sin, pi, matrix
+import numpy as npy
+import numpy.linalg as linalg
+from pylab import figure, show
+
+def csqrt(x):
+ """
+ sqrt func that handles returns sqrt(x)j for x<0
+ """
+ if x<0: return complex(0, npy.sqrt(abs(x)))
+ else: return npy.sqrt(x)
+
+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)
+
+ """
+
+ a,b = M[0,0], M[0,1]
+ c,d = M[1,0], M[1,1]
+ tau = a+d # the trace
+ delta = a*d-b*c # the determinant
+
+ lambda1 = (tau + csqrt(tau**2 - 4*delta))/2.
+ lambda2 = (tau - csqrt(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
+
+name = 'saddle'
+#sx, sy, angle = 1.05, 0.95, 0.
+
+#name = 'focus'
+#sx, sy, angle = 1.05, 0.95, 2.6
+
+#name = 'center'
+#sx, sy, angle = 1., 1., 2.5
+
+name= 'spiral'
+sx, sy, angle = 0.95, 0.95, 2.5
+
+theta = angle * pi/180.
+
+
+S = matrix([[sx, 0],
+ [0, sy]])
+
+R = matrix([[cos(theta), -sin(theta)],
+ [sin(theta), cos(theta)],])
+
+M = S*R # rotate then stretch
+
+# 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 X by the matrix
+X2 = M*X1
+
+# plot the original x,y as green dots and the transformed x, y as red
+# dots
+fig = figure()
+ax = fig.add_subplot(111)
+
+x1 = X1[0].flat
+y1 = X1[1].flat
+x2 = X2[0].flat
+y2 = X2[1].flat
+
+ax = fig.add_subplot(111)
+line1, line2 = ax.plot(x1, y1, 'go', x2, y2, 'ro', markersize=2)
+ax.set_title(name)
+
+
+fig.savefig('glass_dots1.png', dpi=100)
+fig.savefig('glass_dots1.eps', dpi=100)
+show()
Added: trunk/py4science/examples/skel/glass_dots_skel.py
===================================================================
--- trunk/py4science/examples/skel/glass_dots_skel.py (rev 0)
+++ trunk/py4science/examples/skel/glass_dots_skel.py 2007-10-21 20:57:54 UTC (rev 3977)
@@ -0,0 +1,77 @@
+"""
+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).
+"""
+from numpy import cos, sin, pi, matrix
+import numpy as npy
+import numpy.linalg as linalg
+from pylab import figure, show
+
+def csqrt(x):
+ """
+ sqrt func that handles returns sqrt(x)j for x<0
+ """
+ XXX
+
+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)
+
+ """
+ XXX
+ return lambda1, lambda2
+
+# 2000 random x,y points in the interval[-0.5 ... 0.5]
+X1 = XXX
+
+name = 'saddle'
+#sx, sy, angle = XXX
+
+#name = 'focus'
+#sx, sy, angle = XXX
+
+#name = 'center'
+#sx, sy, angle = XXX
+
+name= 'spiral'
+sx, sy, angle = XXX
+
+theta = angle * pi/180. # the rotation in radians
+
+
+# the scaling matrix
+# | sx 0 |
+# | 0 sy |
+S = XXX
+
+# the rotation matrix
+# | cos(theta) -sin(theta) |
+# | sin(theta) cos(theta) |
+R = XXX
+
+# the transformation is the matrix product of the scaling and rotation
+M = XXX
+
+# compute the eigenvalues using numpy linear algebra
+vals, vecs = XXX
+print 'numpy eigenvalues', vals
+
+# compare with the analytic values from myeig
+avals = myeig(M)
+print 'analytic eigenvalues', avals
+
+# transform X1 by the matrix M
+X2 = XXX
+
+# plot the original x,y as green dots and the transformed x, y as red
+# dots
+show()
Added: trunk/py4science/workbook/fig/glass_dots1.eps
===================================================================
--- trunk/py4science/workbook/fig/glass_dots1.eps (rev 0)
+++ trunk/py4science/workbook/fig/glass_dots1.eps 2007-10-21 20:57:54 UTC (rev 3977)
@@ -0,0 +1,4719 @@
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