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weka511 · Jun 2, 2022 · 1895b66 · 1895b66
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diff --git a/book/binomialconvolution.py b/book/binomialconvolution.py
@@ -1,34 +1,34 @@
-# binomialconvolution.py
-
-# Copyright (C) 2015,2018 Greenweaves Software Pty Ltd
-
-# This 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 software 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 GNU Emacs.  If not, see <http://www.gnu.org/licenses/>
-
-import math,matplotlib.pyplot as plt
-
-# Algorithm 1.25 from Krauth
-def binomial_convolution(theta,pi):
-    def calculate_row(pi):
-        return [theta*x + (1-theta)*y for (x,y) in zip(pi[:-1],pi[1:])]
-    return calculate_row([0]+pi+[0])
-
-
-if __name__=="__main__":
-    pi=[1]
-    theta=math.pi/4
-    for i in range(8):
-        pi=binomial_convolution(theta,pi)
-        plt.plot(pi)
-    plt.show()
+# binomialconvolution.py
+
+# Copyright (C) 2015,2018 Greenweaves Software Pty Ltd
+
+# This 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 software 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 GNU Emacs.  If not, see <http://www.gnu.org/licenses/>
+
+import math,matplotlib.pyplot as plt
+
+# Algorithm 1.25 from Krauth
+def binomial_convolution(theta,pi):
+    def calculate_row(pi):
+        return [theta*x + (1-theta)*y for (x,y) in zip(pi[:-1],pi[1:])]
+    return calculate_row([0]+pi+[0])
+
+
+if __name__=="__main__":
+    pi=[1]
+    theta=math.pi/4
+    for i in range(8):
+        pi=binomial_convolution(theta,pi)
+        plt.plot(pi)
+    plt.show()
 
diff --git a/book/boxmuller.py b/book/boxmuller.py
@@ -1,31 +1,31 @@
-# Copyright (C) 2015-2012 Greenweaves Software Limited
-
-# This 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 software 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 GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.
-
-''' Test for Box Muller algorithm'''
-
-from matplotlib.pyplot import hist, show, title, xlabel, ylabel
-from smac              import BoxMuller
-
-if __name__=="__main__":
-
-    gauss = BoxMuller()
-
-    hist([gauss.gauss() for _ in range(1000000)],
-         bins    = 200,
-         density = True)
-    title("Gaussian Histogram")
-    xlabel("Value")
-    ylabel("Frequency")
-    show()
+# Copyright (C) 2015-2012 Greenweaves Software Limited
+
+# This 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 software 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 GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.
+
+''' Test for Box Muller algorithm'''
+
+from matplotlib.pyplot import hist, show, title, xlabel, ylabel
+from smac              import BoxMuller
+
+if __name__=="__main__":
+
+    gauss = BoxMuller()
+
+    hist([gauss.gauss() for _ in range(1000000)],
+         bins    = 200,
+         density = True)
+    title("Gaussian Histogram")
+    xlabel("Value")
+    ylabel("Frequency")
+    show()
diff --git a/book/direct-gamma-zeta.py b/book/direct-gamma-zeta.py
@@ -1,36 +1,36 @@
-# Copyright (C) 2015 Greenweaves Software Pty Ltd
-
-# This 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# 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 GNU Emacs.  If not, see <http://www.gnu.org/licenses/>
-
-import random,math
-
-def direct_gamma_zeta(gamma,zeta,n):
-    sigma=0
-    sigma2=0
-    for i in range(n):
-        x=0
-        while x==0:
-            x=random.random()
-        x1=x**(1/(1+zeta))
-        x2=x1**(gamma-zeta)
-        sigma+=x2
-        sigma2+=(x2*x2)
-    mean=sigma/n
-    return (mean,math.sqrt(sigma2/n-mean*mean)/math.sqrt(n))
-
-def run(zeta,n):
-    print(zeta)
-    for gamma in [2.0,1.0,0.0,-0.1,-0.4,-0.8]:
-        (s,t)=direct_gamma_zeta(gamma,zeta,n)
-        print (gamma, s-t,s+t, (zeta+1)/(gamma+1))
-
-if __name__=="__main__":
-    for zeta in [0.0, -0.1, -0.7]:
+# Copyright (C) 2015 Greenweaves Software Pty Ltd
+
+# This 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# 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 GNU Emacs.  If not, see <http://www.gnu.org/licenses/>
+
+import random,math
+
+def direct_gamma_zeta(gamma,zeta,n):
+    sigma=0
+    sigma2=0
+    for i in range(n):
+        x=0
+        while x==0:
+            x=random.random()
+        x1=x**(1/(1+zeta))
+        x2=x1**(gamma-zeta)
+        sigma+=x2
+        sigma2+=(x2*x2)
+    mean=sigma/n
+    return (mean,math.sqrt(sigma2/n-mean*mean)/math.sqrt(n))
+
+def run(zeta,n):
+    print(zeta)
+    for gamma in [2.0,1.0,0.0,-0.1,-0.4,-0.8]:
+        (s,t)=direct_gamma_zeta(gamma,zeta,n)
+        print (gamma, s-t,s+t, (zeta+1)/(gamma+1))
+
+if __name__=="__main__":
+    for zeta in [0.0, -0.1, -0.7]:
         run(zeta,1000)
diff --git a/book/direct-gamma.py b/book/direct-gamma.py
@@ -1,63 +1,63 @@
-# MIT License
-# 
-# Copyright (c) 2018 Simon Crase
-# 
-# Permission is hereby granted, free of charge, to any person obtaining a copy
-# of this software and associated documentation files (the "Software"), to deal
-# in the Software without restriction, including without limitation the rights
-# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-# copies of the Software, and to permit persons to whom the Software is
-# furnished to do so, subject to the following conditions:
-#   
-#   The above copyright notice and this permission notice shall be included in all
-# copies or substantial portions of the Software.
-# 
-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-# SOFTWARE.
-
-# Implement Algorithm 1.29, subtract mean value for each sample, and generate
-# histograms of the average of N samples and the rescaled averages.
-
-import random,pylab,math,numpy as np
-from scipy.stats import gaussian_kde
-
-def direct_gamma(gamma,generator=False,K=10000,N=1000000):
-    sigma = 0
-    for i in range(N): 
-        sigma += random.random()**gamma
-    return sigma/N
-
-
-if __name__ == '__main__':
-    import argparse
-    parser = argparse.ArgumentParser(description='Evaluate integral from Krauth Section 1.4.')
-    parser.add_argument('steps', metavar='M', type=int, nargs=1,help='Number of steps for integral')
-    parser.add_argument('--N', metavar='N', type=int, nargs='+',default=[1,10,100,1000,10000],help='Number of steps for integral')
-    parser.add_argument('--gamma',metavar='gamma',type=float,nargs=1,default=-0.8,help='exponent')
-    args = parser.parse_args()
-    M = args.steps[0]
-    gamma = args.gamma
-    bins=[0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5,10,10.5,11,100000000000]
-
-    for N in args.N:
-        def scaled(n):
-            return (direct_gamma(gamma,N=n)-5)/(N**(-1-gamma))
-        data = [direct_gamma(gamma,N=N) for m in range(M)]
-        density = gaussian_kde(data)
-        y,binEdges=np.histogram(data,normed=True,bins=bins)
-        bincenters = 0.5*(binEdges[1:]+binEdges[:-1])
-        pylab.plot(bincenters,density(bincenters),label='N={0}'.format(N))        
-    pylab.xlim(1,10)
-    pylab.xlabel(r'$\Sigma/N$')
-    pylab.ylabel(r'$\pi(\Sigma/N$)')
-    pylab.title(r'$Average\ {0}\ iterations$'.format(M))
-    pylab.legend()
-    pylab.savefig('histogram.png')
-    pylab.show()
-
-
+# MIT License
+# 
+# Copyright (c) 2018 Simon Crase
+# 
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#   
+#   The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+# 
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+# Implement Algorithm 1.29, subtract mean value for each sample, and generate
+# histograms of the average of N samples and the rescaled averages.
+
+import random,pylab,math,numpy as np
+from scipy.stats import gaussian_kde
+
+def direct_gamma(gamma,generator=False,K=10000,N=1000000):
+    sigma = 0
+    for i in range(N): 
+        sigma += random.random()**gamma
+    return sigma/N
+
+
+if __name__ == '__main__':
+    import argparse
+    parser = argparse.ArgumentParser(description='Evaluate integral from Krauth Section 1.4.')
+    parser.add_argument('steps', metavar='M', type=int, nargs=1,help='Number of steps for integral')
+    parser.add_argument('--N', metavar='N', type=int, nargs='+',default=[1,10,100,1000,10000],help='Number of steps for integral')
+    parser.add_argument('--gamma',metavar='gamma',type=float,nargs=1,default=-0.8,help='exponent')
+    args = parser.parse_args()
+    M = args.steps[0]
+    gamma = args.gamma
+    bins=[0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5,10,10.5,11,100000000000]
+
+    for N in args.N:
+        def scaled(n):
+            return (direct_gamma(gamma,N=n)-5)/(N**(-1-gamma))
+        data = [direct_gamma(gamma,N=N) for m in range(M)]
+        density = gaussian_kde(data)
+        y,binEdges=np.histogram(data,normed=True,bins=bins)
+        bincenters = 0.5*(binEdges[1:]+binEdges[:-1])
+        pylab.plot(bincenters,density(bincenters),label='N={0}'.format(N))        
+    pylab.xlim(1,10)
+    pylab.xlabel(r'$\Sigma/N$')
+    pylab.ylabel(r'$\pi(\Sigma/N$)')
+    pylab.title(r'$Average\ {0}\ iterations$'.format(M))
+    pylab.legend()
+    pylab.savefig('histogram.png')
+    pylab.show()
+
+