-
diff --git a/doc/pub/week37/html/._week37-bs035.html b/doc/pub/week37/html/._week37-bs035.html index e462a453f..e57db43f3 100644 --- a/doc/pub/week37/html/._week37-bs035.html +++ b/doc/pub/week37/html/._week37-bs035.html @@ -302,37 +302,32 @@ theorem.
-
from numpy import *
-from numpy.random import randint, randn
+import numpy as np
from time import time
-import matplotlib.mlab as mlab
+from scipy.stats import norm
import matplotlib.pyplot as plt
-# Returns mean of bootstrap samples # Alternatively, we can run it using Scikit-Learn's function resample # See the examples below
-
-def statistics(data):
- return mean(data)
-
-
+# Returns mean of bootstrap samples
# Bootstrap algorithm
-def bootstrap(data, statistic, R):
- t = zeros(R); n = len(data); inds = arange(n); t0 = time()
+def bootstrap(data, datapoints):
+ t = np.zeros(datapoints)
+ n = len(data)
# non-parametric bootstrap
- for i in range(R):
- t[i] = statistic(data[randint(0,n,n)])
-
+ for i in range(datapoints):
+ t[i] = np.mean(data[np.random.randint(0,n,n)])
# analysis
- print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :")
+ print("Bootstrap Statistics :")
print("original bias std. error")
- print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t)))
+ print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
return t
-
+# We set the mean value to 100 and the standard deviation to 15
mu, sigma = 100, 15
datapoints = 10000
-x = mu + sigma*random.randn(datapoints)
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
# bootstrap returns the data sample
-t = bootstrap(x, statistics, datapoints)
+t = bootstrap(x, datapoints)
We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
diff --git a/doc/pub/week37/html/._week37-bs036.html b/doc/pub/week37/html/._week37-bs036.html
index dc3ca707e..8fd1c6a99 100644
--- a/doc/pub/week37/html/._week37-bs036.html
+++ b/doc/pub/week37/html/._week37-bs036.html
@@ -287,17 +287,14 @@ MathJax.Hub.Config({
-
# the histogram of the bootstrapped data
-n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)
-
+# the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
# add a 'best fit' line
-y = mlab.normpdf( binsboot, mean(t), std(t))
-lt = plt.plot(binsboot, y, 'r--', linewidth=1)
-plt.xlabel('Smarts')
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
plt.ylabel('Probability')
-plt.axis([99.5, 100.6, 0, 3.0])
plt.grid(True)
-
plt.show()
diff --git a/doc/pub/week37/html/week37-bs.html b/doc/pub/week37/html/week37-bs.html
index a875d46ec..f984145ed 100644
--- a/doc/pub/week37/html/week37-bs.html
+++ b/doc/pub/week37/html/week37-bs.html
@@ -302,7 +302,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 16, 2021
Sep 17, 2021
diff --git a/doc/pub/week37/html/week37-reveal.html b/doc/pub/week37/html/week37-reveal.html
index f48a11faa..3000dce08 100644
--- a/doc/pub/week37/html/week37-reveal.html
+++ b/doc/pub/week37/html/week37-reveal.html
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 16, 2021
Sep 17, 2021
@@ -1225,37 +1225,32 @@ theorem.
-
from numpy import *
-from numpy.random import randint, randn
+import numpy as np
from time import time
-import matplotlib.mlab as mlab
+from scipy.stats import norm
import matplotlib.pyplot as plt
-# Returns mean of bootstrap samples # Alternatively, we can run it using Scikit-Learn's function resample # See the examples below
-
-def statistics(data):
- return mean(data)
-
-
+# Returns mean of bootstrap samples
# Bootstrap algorithm
-def bootstrap(data, statistic, R):
- t = zeros(R); n = len(data); inds = arange(n); t0 = time()
+def bootstrap(data, datapoints):
+ t = np.zeros(datapoints)
+ n = len(data)
# non-parametric bootstrap
- for i in range(R):
- t[i] = statistic(data[randint(0,n,n)])
-
+ for i in range(datapoints):
+ t[i] = np.mean(data[np.random.randint(0,n,n)])
# analysis
- print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :")
+ print("Bootstrap Statistics :")
print("original bias std. error")
- print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t)))
+ print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
return t
-
+# We set the mean value to 100 and the standard deviation to 15
mu, sigma = 100, 15
datapoints = 10000
-x = mu + sigma*random.randn(datapoints)
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
# bootstrap returns the data sample
-t = bootstrap(x, statistics, datapoints)
+t = bootstrap(x, datapoints)
We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
@@ -1267,17 +1262,14 @@ We see that our new variance and from that the standard deviation, agrees with t
-
# the histogram of the bootstrapped data
-n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)
-
+# the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
# add a 'best fit' line
-y = mlab.normpdf( binsboot, mean(t), std(t))
-lt = plt.plot(binsboot, y, 'r--', linewidth=1)
-plt.xlabel('Smarts')
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
plt.ylabel('Probability')
-plt.axis([99.5, 100.6, 0, 3.0])
plt.grid(True)
-
plt.show()
diff --git a/doc/pub/week37/html/week37-solarized.html b/doc/pub/week37/html/week37-solarized.html
index 2178da4cf..92297bafd 100644
--- a/doc/pub/week37/html/week37-solarized.html
+++ b/doc/pub/week37/html/week37-solarized.html
@@ -243,7 +243,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 16, 2021
Sep 17, 2021
@@ -1243,37 +1243,32 @@ theorem.
-
from numpy import *
-from numpy.random import randint, randn
+import numpy as np
from time import time
-import matplotlib.mlab as mlab
+from scipy.stats import norm
import matplotlib.pyplot as plt
-# Returns mean of bootstrap samples # Alternatively, we can run it using Scikit-Learn's function resample # See the examples below
-
-def statistics(data):
- return mean(data)
-
-
+# Returns mean of bootstrap samples
# Bootstrap algorithm
-def bootstrap(data, statistic, R):
- t = zeros(R); n = len(data); inds = arange(n); t0 = time()
+def bootstrap(data, datapoints):
+ t = np.zeros(datapoints)
+ n = len(data)
# non-parametric bootstrap
- for i in range(R):
- t[i] = statistic(data[randint(0,n,n)])
-
+ for i in range(datapoints):
+ t[i] = np.mean(data[np.random.randint(0,n,n)])
# analysis
- print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :")
+ print("Bootstrap Statistics :")
print("original bias std. error")
- print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t)))
+ print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
return t
-
+# We set the mean value to 100 and the standard deviation to 15
mu, sigma = 100, 15
datapoints = 10000
-x = mu + sigma*random.randn(datapoints)
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
# bootstrap returns the data sample
-t = bootstrap(x, statistics, datapoints)
+t = bootstrap(x, datapoints)
We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
@@ -1285,17 +1280,14 @@ We see that our new variance and from that the standard deviation, agrees with t
-
# the histogram of the bootstrapped data
-n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)
-
+# the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
# add a 'best fit' line
-y = mlab.normpdf( binsboot, mean(t), std(t))
-lt = plt.plot(binsboot, y, 'r--', linewidth=1)
-plt.xlabel('Smarts')
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
plt.ylabel('Probability')
-plt.axis([99.5, 100.6, 0, 3.0])
plt.grid(True)
-
plt.show()
diff --git a/doc/pub/week37/html/week37.html b/doc/pub/week37/html/week37.html
index 9c67887f6..5e7a20f6f 100644
--- a/doc/pub/week37/html/week37.html
+++ b/doc/pub/week37/html/week37.html
@@ -248,7 +248,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 16, 2021
Sep 17, 2021
@@ -1248,37 +1248,32 @@ theorem.
-
from numpy import *
-from numpy.random import randint, randn
+import numpy as np
from time import time
-import matplotlib.mlab as mlab
+from scipy.stats import norm
import matplotlib.pyplot as plt
-# Returns mean of bootstrap samples # Alternatively, we can run it using Scikit-Learn's function resample # See the examples below
-
-def statistics(data):
- return mean(data)
-
-
+# Returns mean of bootstrap samples
# Bootstrap algorithm
-def bootstrap(data, statistic, R):
- t = zeros(R); n = len(data); inds = arange(n); t0 = time()
+def bootstrap(data, datapoints):
+ t = np.zeros(datapoints)
+ n = len(data)
# non-parametric bootstrap
- for i in range(R):
- t[i] = statistic(data[randint(0,n,n)])
-
+ for i in range(datapoints):
+ t[i] = np.mean(data[np.random.randint(0,n,n)])
# analysis
- print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :")
+ print("Bootstrap Statistics :")
print("original bias std. error")
- print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t)))
+ print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
return t
-
+# We set the mean value to 100 and the standard deviation to 15
mu, sigma = 100, 15
datapoints = 10000
-x = mu + sigma*random.randn(datapoints)
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
# bootstrap returns the data sample
-t = bootstrap(x, statistics, datapoints)
+t = bootstrap(x, datapoints)
We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
@@ -1290,17 +1285,14 @@ We see that our new variance and from that the standard deviation, agrees with t
-
# the histogram of the bootstrapped data
-n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)
-
+# the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
# add a 'best fit' line
-y = mlab.normpdf( binsboot, mean(t), std(t))
-lt = plt.plot(binsboot, y, 'r--', linewidth=1)
-plt.xlabel('Smarts')
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
plt.ylabel('Probability')
-plt.axis([99.5, 100.6, 0, 3.0])
plt.grid(True)
-
plt.show()
diff --git a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz
index 5f1c144d1..9a14287c6 100644
Binary files a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz and b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz differ
diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb
index 65168ab5c..ea7af2c3b 100644
--- a/doc/pub/week37/ipynb/week37.ipynb
+++ b/doc/pub/week37/ipynb/week37.ipynb
@@ -10,7 +10,7 @@
" \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
- "Date: **Sep 16, 2021**\n",
+ "Date: **Sep 17, 2021**\n",
"\n",
"Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -1258,37 +1258,32 @@
},
"outputs": [],
"source": [
- "from numpy import *\n",
- "from numpy.random import randint, randn\n",
+ "import numpy as np\n",
"from time import time\n",
- "import matplotlib.mlab as mlab\n",
+ "from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
- "# Returns mean of bootstrap samples # Alternatively, we can run it using Scikit-Learn's function resample # See the examples below\n",
- "\n",
- "def statistics(data):\n",
- " return mean(data)\n",
- "\n",
- "\n",
+ "# Returns mean of bootstrap samples \n",
"# Bootstrap algorithm\n",
- "def bootstrap(data, statistic, R):\n",
- " t = zeros(R); n = len(data); inds = arange(n); t0 = time()\n",
+ "def bootstrap(data, datapoints):\n",
+ " t = np.zeros(datapoints)\n",
+ " n = len(data)\n",
" # non-parametric bootstrap \n",
- " for i in range(R):\n",
- " t[i] = statistic(data[randint(0,n,n)])\n",
- "\n",
+ " for i in range(datapoints):\n",
+ " t[i] = np.mean(data[np.random.randint(0,n,n)])\n",
" # analysis \n",
- " print(\"Runtime: %g sec\" % (time()-t0)); print(\"Bootstrap Statistics :\")\n",
+ " print(\"Bootstrap Statistics :\")\n",
" print(\"original bias std. error\")\n",
- " print(\"%8g %8g %14g %15g\" % (statistic(data), std(data),mean(t),std(t)))\n",
+ " print(\"%8g %8g %14g %15g\" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))\n",
" return t\n",
"\n",
- "\n",
+ "# We set the mean value to 100 and the standard deviation to 15\n",
"mu, sigma = 100, 15\n",
"datapoints = 10000\n",
- "x = mu + sigma*random.randn(datapoints)\n",
+ "# We generate random numbers according to the normal distribution\n",
+ "x = mu + sigma*np.random.randn(datapoints)\n",
"# bootstrap returns the data sample \n",
- "t = bootstrap(x, statistics, datapoints)"
+ "t = bootstrap(x, datapoints)"
]
},
{
@@ -1309,17 +1304,14 @@
},
"outputs": [],
"source": [
- "# the histogram of the bootstrapped data \n",
- "n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)\n",
- "\n",
+ "# the histogram of the bootstrapped data (normalized data if density = True)\n",
+ "n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n",
"# add a 'best fit' line \n",
- "y = mlab.normpdf( binsboot, mean(t), std(t))\n",
- "lt = plt.plot(binsboot, y, 'r--', linewidth=1)\n",
- "plt.xlabel('Smarts')\n",
+ "y = norm.pdf(binsboot, np.mean(t), np.std(t))\n",
+ "lt = plt.plot(binsboot, y, 'b', linewidth=1)\n",
+ "plt.xlabel('x')\n",
"plt.ylabel('Probability')\n",
- "plt.axis([99.5, 100.6, 0, 3.0])\n",
"plt.grid(True)\n",
- "\n",
"plt.show()"
]
},
diff --git a/doc/src/week37/week37.do.txt b/doc/src/week37/week37.do.txt
index ab8b7e895..e3b9e3bd1 100644
--- a/doc/src/week37/week37.do.txt
+++ b/doc/src/week37/week37.do.txt
@@ -910,56 +910,47 @@ theorem.
!bc pycod
-from numpy import *
-from numpy.random import randint, randn
+import numpy as np
from time import time
-import matplotlib.mlab as mlab
+from scipy.stats import norm
import matplotlib.pyplot as plt
-# Returns mean of bootstrap samples # Alternatively, we can run it using Scikit-Learn's function resample # See the examples below
-
-def statistics(data):
- return mean(data)
-
-
+# Returns mean of bootstrap samples
# Bootstrap algorithm
-def bootstrap(data, statistic, R):
- t = zeros(R); n = len(data); inds = arange(n); t0 = time()
+def bootstrap(data, datapoints):
+ t = np.zeros(datapoints)
+ n = len(data)
# non-parametric bootstrap
- for i in range(R):
- t[i] = statistic(data[randint(0,n,n)])
-
+ for i in range(datapoints):
+ t[i] = np.mean(data[np.random.randint(0,n,n)])
# analysis
- print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :")
+ print("Bootstrap Statistics :")
print("original bias std. error")
- print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t)))
+ print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
return t
-
+# We set the mean value to 100 and the standard deviation to 15
mu, sigma = 100, 15
datapoints = 10000
-x = mu + sigma*random.randn(datapoints)
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
# bootstrap returns the data sample
-t = bootstrap(x, statistics, datapoints)
+t = bootstrap(x, datapoints)
!ec
We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
!split
===== Plotting the Histogram =====
!bc pycod
-# the histogram of the bootstrapped data
-n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)
-
+# the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
# add a 'best fit' line
-y = mlab.normpdf( binsboot, mean(t), std(t))
-lt = plt.plot(binsboot, y, 'r--', linewidth=1)
-plt.xlabel('Smarts')
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
plt.ylabel('Probability')
-plt.axis([99.5, 100.6, 0, 3.0])
plt.grid(True)
-
plt.show()
-
!ec