From dd90513eb36ca261d8eacc8e6f4686221816f1cf Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 8 Dec 2017 11:32:08 +0100 Subject: [PATCH] Update on r codes --- .../html/._How2ReadData-bs000.html | 2 +- .../html/._How2ReadData-bs007.html | 9 +- .../html/._How2ReadData-bs025.html | 34 +- .../html/._How2ReadData-bs026.html | 32 +- .../How2ReadData/html/How2ReadData-bs.html | 2 +- .../html/How2ReadData-reveal.html | 69 +- .../html/How2ReadData-solarized.html | 69 +- doc/pub/How2ReadData/html/How2ReadData.html | 77 +- .../Untitled-checkpoint.ipynb | 6 + .../Untitled1-checkpoint.ipynb | 6 + .../Untitled2-checkpoint.ipynb | 6 + doc/pub/How2ReadData/ipynb/How2ReadData.ipynb | 125 +- doc/pub/How2ReadData/ipynb/How2ReadData.tex | 1121 +++++++++++++++++ .../How2ReadData_files/How2ReadData_18_1.png | Bin 0 -> 29262 bytes .../How2ReadData_files/How2ReadData_1_1.png | Bin 0 -> 22055 bytes .../How2ReadData_files/How2ReadData_20_0.png | Bin 0 -> 17767 bytes .../How2ReadData_files/How2ReadData_3_1.png | Bin 0 -> 14941 bytes .../How2ReadData_files/How2ReadData_5_0.png | Bin 0 -> 21986 bytes .../How2ReadData/ipynb/Hudson_Bay_data.pdf | Bin 0 -> 15705 bytes .../How2ReadData/ipynb/Hudson_Bay_data.png | Bin 0 -> 26300 bytes doc/pub/How2ReadData/ipynb/Hudson_Bay_sim.pdf | Bin 0 -> 17812 bytes doc/pub/How2ReadData/ipynb/Hudson_Bay_sim.png | Bin 0 -> 33287 bytes .../ipynb/ipynb-How2ReadData-src.tar.gz | Bin 113365 -> 113365 bytes .../pdf/How2ReadData-beamer-handouts2x3.pdf | Bin 300770 -> 300762 bytes .../How2ReadData/pdf/How2ReadData-beamer.pdf | Bin 273693 -> 273599 bytes .../How2ReadData/pdf/How2ReadData-minted.pdf | Bin 333619 -> 333812 bytes doc/src/How2ReadData/How2ReadData.do.txt | 10 +- doc/src/How2ReadData/knn.py | 38 + doc/src/How2ReadData/panda.py | 10 + doc/src/How2ReadData/test.py | 21 +- 30 files changed, 1431 insertions(+), 206 deletions(-) create mode 100644 doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled-checkpoint.ipynb create mode 100644 doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled1-checkpoint.ipynb create mode 100644 doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled2-checkpoint.ipynb create mode 100644 doc/pub/How2ReadData/ipynb/How2ReadData.tex create mode 100644 doc/pub/How2ReadData/ipynb/How2ReadData_files/How2ReadData_18_1.png create mode 100644 doc/pub/How2ReadData/ipynb/How2ReadData_files/How2ReadData_1_1.png create mode 100644 doc/pub/How2ReadData/ipynb/How2ReadData_files/How2ReadData_20_0.png create mode 100644 doc/pub/How2ReadData/ipynb/How2ReadData_files/How2ReadData_3_1.png create mode 100644 doc/pub/How2ReadData/ipynb/How2ReadData_files/How2ReadData_5_0.png create mode 100644 doc/pub/How2ReadData/ipynb/Hudson_Bay_data.pdf create mode 100644 doc/pub/How2ReadData/ipynb/Hudson_Bay_data.png create mode 100644 doc/pub/How2ReadData/ipynb/Hudson_Bay_sim.pdf create mode 100644 doc/pub/How2ReadData/ipynb/Hudson_Bay_sim.png create mode 100644 doc/src/How2ReadData/knn.py create mode 100644 doc/src/How2ReadData/panda.py diff --git a/doc/pub/How2ReadData/html/._How2ReadData-bs000.html b/doc/pub/How2ReadData/html/._How2ReadData-bs000.html index 1e3353733..01f883d0e 100644 --- a/doc/pub/How2ReadData/html/._How2ReadData-bs000.html +++ b/doc/pub/How2ReadData/html/._How2ReadData-bs000.html @@ -176,7 +176,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 6, 2017

+

Dec 8, 2017


diff --git a/doc/pub/How2ReadData/html/._How2ReadData-bs007.html b/doc/pub/How2ReadData/html/._How2ReadData-bs007.html index 415fb75d9..f3c958006 100644 --- a/doc/pub/How2ReadData/html/._How2ReadData-bs007.html +++ b/doc/pub/How2ReadData/html/._How2ReadData-bs007.html @@ -168,10 +168,13 @@ either Python or C++ as programming languages. To add more entropy, cython can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook -can easily be converted into a nicely rendered PDF file or a Latex file for further processing. - +can easily be converted into a nicely rendered PDF file or a Latex file for further processing. For example, convert to latex as +

+ + +

jupyter nbconvert filename.ipynb --to latex
+

-This never ends. If you use the light mark-up language doconce you can convert a standard ascii text file into various HTML formats, ipython notebooks, latex files, pdf files etc. diff --git a/doc/pub/How2ReadData/html/._How2ReadData-bs025.html b/doc/pub/How2ReadData/html/._How2ReadData-bs025.html index d6b8cf5bb..39f98e7d7 100644 --- a/doc/pub/How2ReadData/html/._How2ReadData-bs025.html +++ b/doc/pub/How2ReadData/html/._How2ReadData-bs025.html @@ -163,26 +163,26 @@ MathJax.Hub.Config({

- -

HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
+
+
HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
 fix(HudsonBay)
-dim(HudsonBay)
-names(HudsonBay)
-plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
-attach(HudsonBay)
-plot(Year, Hares..x1000.)
-plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
-summary(HudsonBay)
-summary(Hares..x1000.)
-library(MASS)
-library(ISLR)
-scatter.smooth(x=Year, y = Hares..x1000.)
-linearMod = lm(Hares..x1000. ~ Year)
-print(linearMod)
-summary(linearMod)
+dim(HudsonBay)
+names(HudsonBay)
+plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
+attach(HudsonBay)
+plot(Year, Hares..x1000.)
+plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
+summary(HudsonBay)
+summary(Hares..x1000.)
+library(MASS)
+library(ISLR)
+scatter.smooth(x=Year, y = Hares..x1000.)
+linearMod = lm(Hares..x1000. ~ Year)
+print(linearMod)
+summary(linearMod)
 plot(linearMod)
 confint(linearMod)
-predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
+predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
 

diff --git a/doc/pub/How2ReadData/html/._How2ReadData-bs026.html b/doc/pub/How2ReadData/html/._How2ReadData-bs026.html index 5b0df88f8..87e4867b9 100644 --- a/doc/pub/How2ReadData/html/._How2ReadData-bs026.html +++ b/doc/pub/How2ReadData/html/._How2ReadData-bs026.html @@ -163,26 +163,26 @@ MathJax.Hub.Config({

- -

set.seed(1485)
-len = 24
-x = runif(len)
-y = x^3+rnorm(len, 0,0.06)
-ds = data.frame(x = x, y = y)
-str(ds)
+
+
set.seed(1485)
+len = 24
+x = runif(len)
+y = x^3+rnorm(len, 0,0.06)
+ds = data.frame(x = x, y = y)
+str(ds)
 plot( y ~ x, main ="Known cubic with noise")
-s  = seq(0,1,length =100)
+s  = seq(0,1,length =100)
 lines(s, s^3, lty =2, col ="green")
-m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
-class(m)
-summary(m)
-power = round(summary(m)$coefficients[1], 3)
-power.se = round(summary(m)$coefficients[2], 3)
+m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
+class(m)
+summary(m)
+power = round(summary(m)$coefficients[1], 3)
+power.se = round(summary(m)$coefficients[2], 3)
 plot(y ~ x, main = "Fitted power model", sub = "Blue: fit; green: known")
-s = seq(0, 1, length = 100)
+s = seq(0, 1, length = 100)
 lines(s, s^3, lty = 2, col = "green")
-lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
-text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
+lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
+text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
 

diff --git a/doc/pub/How2ReadData/html/How2ReadData-bs.html b/doc/pub/How2ReadData/html/How2ReadData-bs.html index 1e3353733..01f883d0e 100644 --- a/doc/pub/How2ReadData/html/How2ReadData-bs.html +++ b/doc/pub/How2ReadData/html/How2ReadData-bs.html @@ -176,7 +176,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 6, 2017

+

Dec 8, 2017


diff --git a/doc/pub/How2ReadData/html/How2ReadData-reveal.html b/doc/pub/How2ReadData/html/How2ReadData-reveal.html index 1b24cedfa..a881d6243 100644 --- a/doc/pub/How2ReadData/html/How2ReadData-reveal.html +++ b/doc/pub/How2ReadData/html/How2ReadData-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

 
-

Dec 6, 2017

+

Dec 8, 2017


@@ -305,10 +305,13 @@ either Python or C++ as programming languages. To add more entropy, cython can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook -can easily be converted into a nicely rendered PDF file or a Latex file for further processing. - +can easily be converted into a nicely rendered PDF file or a Latex file for further processing. For example, convert to latex as +

+ + +

jupyter nbconvert filename.ipynb --to latex
+

-This never ends. If you use the light mark-up language doconce you can convert a standard ascii text file into various HTML formats, ipython notebooks, latex files, pdf files etc. @@ -806,26 +809,26 @@ plt.show()

- -

HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
+
+
HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
 fix(HudsonBay)
-dim(HudsonBay)
-names(HudsonBay)
-plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
-attach(HudsonBay)
+dim(HudsonBay)
+names(HudsonBay)
+plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
+attach(HudsonBay)
 plot(Year, Hares..x1000.)
-plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
-summary(HudsonBay)
-summary(Hares..x1000.)
-library(MASS)
-library(ISLR)
+plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
+summary(HudsonBay)
+summary(Hares..x1000.)
+library(MASS)
+library(ISLR)
 scatter.smooth(x=Year, y = Hares..x1000.)
 linearMod = lm(Hares..x1000. ~ Year)
 print(linearMod)
-summary(linearMod)
+summary(linearMod)
 plot(linearMod)
 confint(linearMod)
-predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
+predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
 
@@ -838,26 +841,26 @@ predict(linearMod,data.frame(Year=c(1910,

- -

set.seed(1485)
-len = 24
-x = runif(len)
-y = x^3+rnorm(len, 0,0.06)
-ds = data.frame(x = x, y = y)
-str(ds)
+
+
set.seed(1485)
+len = 24
+x = runif(len)
+y = x^3+rnorm(len, 0,0.06)
+ds = data.frame(x = x, y = y)
+str(ds)
 plot( y ~ x, main ="Known cubic with noise")
-s  = seq(0,1,length =100)
+s  = seq(0,1,length =100)
 lines(s, s^3, lty =2, col ="green")
-m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
-class(m)
-summary(m)
-power = round(summary(m)$coefficients[1], 3)
-power.se = round(summary(m)$coefficients[2], 3)
+m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
+class(m)
+summary(m)
+power = round(summary(m)$coefficients[1], 3)
+power.se = round(summary(m)$coefficients[2], 3)
 plot(y ~ x, main = "Fitted power model", sub = "Blue: fit; green: known")
-s = seq(0, 1, length = 100)
+s = seq(0, 1, length = 100)
 lines(s, s^3, lty = 2, col = "green")
-lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
-text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
+lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
+text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
 
diff --git a/doc/pub/How2ReadData/html/How2ReadData-solarized.html b/doc/pub/How2ReadData/html/How2ReadData-solarized.html index 1abe49b41..9002542fa 100644 --- a/doc/pub/How2ReadData/html/How2ReadData-solarized.html +++ b/doc/pub/How2ReadData/html/How2ReadData-solarized.html @@ -140,7 +140,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 6, 2017

+

Dec 8, 2017












@@ -282,10 +282,13 @@ either Python or C++ as programming languages. To add more entropy, cython can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook -can easily be converted into a nicely rendered PDF file or a Latex file for further processing. - +can easily be converted into a nicely rendered PDF file or a Latex file for further processing. For example, convert to latex as +

+ + +

jupyter nbconvert filename.ipynb --to latex
+

-This never ends. If you use the light mark-up language doconce you can convert a standard ascii text file into various HTML formats, ipython notebooks, latex files, pdf files etc. @@ -799,26 +802,26 @@ plt.show()

- -

HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
+
+
HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
 fix(HudsonBay)
-dim(HudsonBay)
-names(HudsonBay)
-plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
-attach(HudsonBay)
+dim(HudsonBay)
+names(HudsonBay)
+plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
+attach(HudsonBay)
 plot(Year, Hares..x1000.)
-plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
-summary(HudsonBay)
-summary(Hares..x1000.)
-library(MASS)
-library(ISLR)
+plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
+summary(HudsonBay)
+summary(Hares..x1000.)
+library(MASS)
+library(ISLR)
 scatter.smooth(x=Year, y = Hares..x1000.)
 linearMod = lm(Hares..x1000. ~ Year)
 print(linearMod)
-summary(linearMod)
+summary(linearMod)
 plot(linearMod)
 confint(linearMod)
-predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
+predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
 
@@ -833,26 +836,26 @@ predict(linearMod,data.frame(Year=c(1910,

- -

set.seed(1485)
-len = 24
-x = runif(len)
-y = x^3+rnorm(len, 0,0.06)
-ds = data.frame(x = x, y = y)
-str(ds)
+
+
set.seed(1485)
+len = 24
+x = runif(len)
+y = x^3+rnorm(len, 0,0.06)
+ds = data.frame(x = x, y = y)
+str(ds)
 plot( y ~ x, main ="Known cubic with noise")
-s  = seq(0,1,length =100)
+s  = seq(0,1,length =100)
 lines(s, s^3, lty =2, col ="green")
-m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
-class(m)
-summary(m)
-power = round(summary(m)$coefficients[1], 3)
-power.se = round(summary(m)$coefficients[2], 3)
+m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
+class(m)
+summary(m)
+power = round(summary(m)$coefficients[1], 3)
+power.se = round(summary(m)$coefficients[2], 3)
 plot(y ~ x, main = "Fitted power model", sub = "Blue: fit; green: known")
-s = seq(0, 1, length = 100)
+s = seq(0, 1, length = 100)
 lines(s, s^3, lty = 2, col = "green")
-lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
-text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
+lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
+text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
 
diff --git a/doc/pub/How2ReadData/html/How2ReadData.html b/doc/pub/How2ReadData/html/How2ReadData.html index 4586bf651..ea28bf50a 100644 --- a/doc/pub/How2ReadData/html/How2ReadData.html +++ b/doc/pub/How2ReadData/html/How2ReadData.html @@ -145,7 +145,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 6, 2017

+

Dec 8, 2017












@@ -287,10 +287,13 @@ either Python or C++ as programming languages. To add more entropy, cython can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook -can easily be converted into a nicely rendered PDF file or a Latex file for further processing. - +can easily be converted into a nicely rendered PDF file or a Latex file for further processing. For example, convert to latex as +

+ + +

jupyter nbconvert filename.ipynb --to latex
+

-This never ends. If you use the light mark-up language doconce you can convert a standard ascii text file into various HTML formats, ipython notebooks, latex files, pdf files etc. @@ -804,26 +807,26 @@ plt.show()

- -

HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
+
+
HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
 fix(HudsonBay)
-dim(HudsonBay)
-names(HudsonBay)
-plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
-attach(HudsonBay)
-plot(Year, Hares..x1000.)
-plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
-summary(HudsonBay)
-summary(Hares..x1000.)
-library(MASS)
-library(ISLR)
-scatter.smooth(x=Year, y = Hares..x1000.)
-linearMod = lm(Hares..x1000. ~ Year)
-print(linearMod)
-summary(linearMod)
+dim(HudsonBay)
+names(HudsonBay)
+plot(HudsonBay$Year, HudsonBay$Hares..x1000.)
+attach(HudsonBay)
+plot(Year, Hares..x1000.)
+plot(Year, Hares..x1000., col="red", varwidth=T, xlab="Years", ylab="Haresx 1000")
+summary(HudsonBay)
+summary(Hares..x1000.)
+library(MASS)
+library(ISLR)
+scatter.smooth(x=Year, y = Hares..x1000.)
+linearMod = lm(Hares..x1000. ~ Year)
+print(linearMod)
+summary(linearMod)
 plot(linearMod)
 confint(linearMod)
-predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
+predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence")
 
@@ -838,26 +841,26 @@ predict(linearMod,data.frame(Year

- -

set.seed(1485)
-len = 24
-x = runif(len)
-y = x^3+rnorm(len, 0,0.06)
-ds = data.frame(x = x, y = y)
-str(ds)
+
+
set.seed(1485)
+len = 24
+x = runif(len)
+y = x^3+rnorm(len, 0,0.06)
+ds = data.frame(x = x, y = y)
+str(ds)
 plot( y ~ x, main ="Known cubic with noise")
-s  = seq(0,1,length =100)
+s  = seq(0,1,length =100)
 lines(s, s^3, lty =2, col ="green")
-m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
-class(m)
-summary(m)
-power = round(summary(m)$coefficients[1], 3)
-power.se = round(summary(m)$coefficients[2], 3)
+m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)
+class(m)
+summary(m)
+power = round(summary(m)$coefficients[1], 3)
+power.se = round(summary(m)$coefficients[2], 3)
 plot(y ~ x, main = "Fitted power model", sub = "Blue: fit; green: known")
-s = seq(0, 1, length = 100)
+s = seq(0, 1, length = 100)
 lines(s, s^3, lty = 2, col = "green")
-lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
-text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
+lines(s, predict(m, list(x = s)), lty = 1, col = "blue")
+text(0, 0.5, paste("y =x^ (", power, " +/- ", power.se, ")", sep = ""), pos = 4)
 
diff --git a/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled-checkpoint.ipynb b/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled-checkpoint.ipynb new file mode 100644 index 000000000..2fd64429b --- /dev/null +++ b/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled1-checkpoint.ipynb b/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled1-checkpoint.ipynb new file mode 100644 index 000000000..2fd64429b --- /dev/null +++ b/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled1-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled2-checkpoint.ipynb b/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled2-checkpoint.ipynb new file mode 100644 index 000000000..2fd64429b --- /dev/null +++ b/doc/pub/How2ReadData/ipynb/.ipynb_checkpoints/Untitled2-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb b/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb index 42ff97acd..cfcebcef2 100644 --- a/doc/pub/How2ReadData/ipynb/How2ReadData.ipynb +++ b/doc/pub/How2ReadData/ipynb/How2ReadData.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: **Dec 6, 2017**\n", + "Date: **Dec 8, 2017**\n", "\n", "Copyright 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -125,9 +125,24 @@ "To add more entropy, **cython** can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook \n", "setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, \n", "including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook \n", - "can easily be converted into a nicely rendered **PDF** file or a Latex file for further processing.\n", - "\n", - "This never ends.\n", + "can easily be converted into a nicely rendered **PDF** file or a Latex file for further processing. For example, convert to latex as" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "jupyter nbconvert filename.ipynb --to latex" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "If you use the light mark-up language **doconce** you can convert a standard ascii text file into various HTML \n", "formats, ipython notebooks, latex files, pdf files etc. \n", "\n", @@ -138,7 +153,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -173,7 +188,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -283,7 +298,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -540,7 +555,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -614,7 +629,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -648,32 +663,28 @@ ] }, { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "HudsonBay = read.csv(\"src/Hudson_Bay.csv\",header=T)\n", - "fix(HudsonBay)\n", - "dim(HudsonBay)\n", - "names(HudsonBay)\n", - "plot(HudsonBay$Year, HudsonBay$Hares..x1000.)\n", - "attach(HudsonBay)\n", - "plot(Year, Hares..x1000.)\n", - "plot(Year, Hares..x1000., col=\"red\", varwidth=T, xlab=\"Years\", ylab=\"Haresx 1000\")\n", - "summary(HudsonBay)\n", - "summary(Hares..x1000.)\n", - "library(MASS)\n", - "library(ISLR)\n", - "scatter.smooth(x=Year, y = Hares..x1000.)\n", - "linearMod = lm(Hares..x1000. ~ Year)\n", - "print(linearMod)\n", - "summary(linearMod)\n", - "plot(linearMod)\n", - "confint(linearMod)\n", - "predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval=\"confidence\")" + " HudsonBay = read.csv(\"src/Hudson_Bay.csv\",header=T)\n", + " fix(HudsonBay)\n", + " dim(HudsonBay)\n", + " names(HudsonBay)\n", + " plot(HudsonBay$Year, HudsonBay$Hares..x1000.)\n", + " attach(HudsonBay)\n", + " plot(Year, Hares..x1000.)\n", + " plot(Year, Hares..x1000., col=\"red\", varwidth=T, xlab=\"Years\", ylab=\"Haresx 1000\")\n", + " summary(HudsonBay)\n", + " summary(Hares..x1000.)\n", + " library(MASS)\n", + " library(ISLR)\n", + " scatter.smooth(x=Year, y = Hares..x1000.)\n", + " linearMod = lm(Hares..x1000. ~ Year)\n", + " print(linearMod)\n", + " summary(linearMod)\n", + " plot(linearMod)\n", + " confint(linearMod)\n", + " predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval=\"confidence\")\n" ] }, { @@ -684,32 +695,28 @@ ] }, { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "set.seed(1485)\n", - "len = 24\n", - "x = runif(len)\n", - "y = x^3+rnorm(len, 0,0.06)\n", - "ds = data.frame(x = x, y = y)\n", - "str(ds)\n", - "plot( y ~ x, main =\"Known cubic with noise\")\n", - "s = seq(0,1,length =100)\n", - "lines(s, s^3, lty =2, col =\"green\")\n", - "m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)\n", - "class(m)\n", - "summary(m)\n", - "power = round(summary(m)$coefficients[1], 3)\n", - "power.se = round(summary(m)$coefficients[2], 3)\n", - "plot(y ~ x, main = \"Fitted power model\", sub = \"Blue: fit; green: known\")\n", - "s = seq(0, 1, length = 100)\n", - "lines(s, s^3, lty = 2, col = \"green\")\n", - "lines(s, predict(m, list(x = s)), lty = 1, col = \"blue\")\n", - "text(0, 0.5, paste(\"y =x^ (\", power, \" +/- \", power.se, \")\", sep = \"\"), pos = 4)" + " set.seed(1485)\n", + " len = 24\n", + " x = runif(len)\n", + " y = x^3+rnorm(len, 0,0.06)\n", + " ds = data.frame(x = x, y = y)\n", + " str(ds)\n", + " plot( y ~ x, main =\"Known cubic with noise\")\n", + " s = seq(0,1,length =100)\n", + " lines(s, s^3, lty =2, col =\"green\")\n", + " m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)\n", + " class(m)\n", + " summary(m)\n", + " power = round(summary(m)$coefficients[1], 3)\n", + " power.se = round(summary(m)$coefficients[2], 3)\n", + " plot(y ~ x, main = \"Fitted power model\", sub = \"Blue: fit; green: known\")\n", + " s = seq(0, 1, length = 100)\n", + " lines(s, s^3, lty = 2, col = \"green\")\n", + " lines(s, predict(m, list(x = s)), lty = 1, col = \"blue\")\n", + " text(0, 0.5, paste(\"y =x^ (\", power, \" +/- \", power.se, \")\", sep = \"\"), pos = 4)\n" ] } ], diff --git a/doc/pub/How2ReadData/ipynb/How2ReadData.tex b/doc/pub/How2ReadData/ipynb/How2ReadData.tex new file mode 100644 index 000000000..5c395ee6a --- /dev/null +++ b/doc/pub/How2ReadData/ipynb/How2ReadData.tex @@ -0,0 +1,1121 @@ + +% Default to the notebook output style + + + + +% Inherit from the specified cell style. + + + + + +\documentclass[11pt]{article} + + + + \usepackage[T1]{fontenc} + % Nicer default font (+ math font) than Computer Modern for most use cases + \usepackage{mathpazo} + + % Basic figure setup, for now with no caption control since it's done + % automatically by Pandoc (which extracts ![](path) syntax from Markdown). + \usepackage{graphicx} + % We will generate all images so they have a width \maxwidth. This means + % that they will get their normal width if they fit onto the page, but + % are scaled down if they would overflow the margins. + \makeatletter + \def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth + \else\Gin@nat@width\fi} + \makeatother + \let\Oldincludegraphics\includegraphics + % Set max figure width to be 80% of text width, for now hardcoded. + \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} + % Ensure that by default, figures have no caption (until we provide a + % proper Figure object with a Caption API and a way to capture that + % in the conversion process - todo). + \usepackage{caption} + \DeclareCaptionLabelFormat{nolabel}{} + \captionsetup{labelformat=nolabel} + + \usepackage{adjustbox} % Used to constrain images to a maximum size + \usepackage{xcolor} % Allow colors to be defined + \usepackage{enumerate} % Needed for markdown enumerations to work + \usepackage{geometry} % Used to adjust the document margins + \usepackage{amsmath} % Equations + \usepackage{amssymb} % Equations + \usepackage{textcomp} % defines textquotesingle + % Hack from http://tex.stackexchange.com/a/47451/13684: + \AtBeginDocument{% + \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code + } + \usepackage{upquote} % Upright quotes for verbatim code + \usepackage{eurosym} % defines \euro + \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support + \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document + \usepackage{fancyvrb} % verbatim replacement that allows latex + \usepackage{grffile} % extends the file name processing of package graphics + % to support a larger range + % The hyperref package gives us a pdf with properly built + % internal navigation ('pdf bookmarks' for the table of contents, + % internal cross-reference links, web links for URLs, etc.) + \usepackage{hyperref} + \usepackage{longtable} % longtable support required by pandoc >1.10 + \usepackage{booktabs} % table support for pandoc > 1.12.2 + \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) + \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) + % normalem makes italics be italics, not underlines + + + + + % Colors for the hyperref package + \definecolor{urlcolor}{rgb}{0,.145,.698} + \definecolor{linkcolor}{rgb}{.71,0.21,0.01} + \definecolor{citecolor}{rgb}{.12,.54,.11} + + % ANSI colors + \definecolor{ansi-black}{HTML}{3E424D} + \definecolor{ansi-black-intense}{HTML}{282C36} + \definecolor{ansi-red}{HTML}{E75C58} + \definecolor{ansi-red-intense}{HTML}{B22B31} + \definecolor{ansi-green}{HTML}{00A250} + \definecolor{ansi-green-intense}{HTML}{007427} + \definecolor{ansi-yellow}{HTML}{DDB62B} + \definecolor{ansi-yellow-intense}{HTML}{B27D12} + \definecolor{ansi-blue}{HTML}{208FFB} + \definecolor{ansi-blue-intense}{HTML}{0065CA} + \definecolor{ansi-magenta}{HTML}{D160C4} + \definecolor{ansi-magenta-intense}{HTML}{A03196} + \definecolor{ansi-cyan}{HTML}{60C6C8} + \definecolor{ansi-cyan-intense}{HTML}{258F8F} + \definecolor{ansi-white}{HTML}{C5C1B4} + \definecolor{ansi-white-intense}{HTML}{A1A6B2} + + % commands and environments needed by pandoc snippets + % extracted from the output of `pandoc -s` + \providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} + \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} + % Add ',fontsize=\small' for more characters per line + \newenvironment{Shaded}{}{} + \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} + \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} + \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}} + \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}} + \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}} + \newcommand{\RegionMarkerTok}[1]{{#1}} + \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} + \newcommand{\NormalTok}[1]{{#1}} + + % Additional commands for more recent versions of Pandoc + \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}} + \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} + \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}} + \newcommand{\ImportTok}[1]{{#1}} + \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}} + \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}} + \newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} + \newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}} + \newcommand{\BuiltInTok}[1]{{#1}} + \newcommand{\ExtensionTok}[1]{{#1}} + \newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}} + \newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}} + \newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + \newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} + + + % Define a nice break command that doesn't care if a line doesn't already + % exist. + \def\br{\hspace*{\fill} \\* } + % Math Jax compatability definitions + \def\gt{>} + \def\lt{<} + % Document parameters + \title{How2ReadData} + + + + + % Pygments definitions + +\makeatletter +\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax% + \let\PY@ul=\relax \let\PY@tc=\relax% + \let\PY@bc=\relax \let\PY@ff=\relax} +\def\PY@tok#1{\csname PY@tok@#1\endcsname} +\def\PY@toks#1+{\ifx\relax#1\empty\else% + \PY@tok{#1}\expandafter\PY@toks\fi} +\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{% + \PY@it{\PY@bf{\PY@ff{#1}}}}}}} +\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}} + +\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}} +\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}} +\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} +\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}} 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+\expandafter\def\csname PY@tok@dl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}} +\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}} +\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} +\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} + +\def\PYZbs{\char`\\} +\def\PYZus{\char`\_} +\def\PYZob{\char`\{} +\def\PYZcb{\char`\}} +\def\PYZca{\char`\^} +\def\PYZam{\char`\&} +\def\PYZlt{\char`\<} +\def\PYZgt{\char`\>} +\def\PYZsh{\char`\#} +\def\PYZpc{\char`\%} +\def\PYZdl{\char`\$} +\def\PYZhy{\char`\-} +\def\PYZsq{\char`\'} +\def\PYZdq{\char`\"} +\def\PYZti{\char`\~} +% for compatibility with earlier versions +\def\PYZat{@} +\def\PYZlb{[} +\def\PYZrb{]} +\makeatother + + + % Exact colors from NB + \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} + \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} + + + + + % Prevent overflowing lines due to hard-to-break entities + \sloppy + % Setup hyperref package + \hypersetup{ + breaklinks=true, % so long urls are correctly broken across lines + colorlinks=true, + urlcolor=urlcolor, + linkcolor=linkcolor, + citecolor=citecolor, + } + % Slightly bigger margins than the latex defaults + + \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} + + + + \begin{document} + + + \maketitle + + + + + \hypertarget{data-analysis-and-machine-learning-introduction-and-representing-data}{% +\section{Data Analysis and Machine Learning: Introduction and +Representing +data}\label{data-analysis-and-machine-learning-introduction-and-representing-data}} + +\textbf{Morten Hjorth-Jensen}, Department of Physics, University of Oslo +and Department of Physics and Astronomy and National Superconducting +Cyclotron Laboratory, Michigan State University + +Date: \textbf{Dec 6, 2017} + +Copyright 1999-2017, Morten Hjorth-Jensen. Released under CC +Attribution-NonCommercial 4.0 license + +\hypertarget{what-is-machine-learning}{% +\subsection{What is Machine Learning?}\label{what-is-machine-learning}} + +Machine learning is the science of giving computers the ability to learn +without being explicitly programmed. The idea is that there exist +generic algorithms which can be used to find patterns in a broad class +of data sets without having to write code specifically for each problem. +The algorithm will build its own logic based on the data. + +Machine learning is a subfield of computer science, and is closely +related to computational statistics. It evolved from the study of +pattern recognition in artificial intelligence (AI) research, and has +made contributions to AI tasks like computer vision, natural language +processing and speech recognition. It has also, especially in later +years, found applications in a wide variety of other areas, including +bioinformatics, economy, physics, finance and marketing. + +\hypertarget{types-of-machine-learning}{% +\subsection{Types of Machine Learning}\label{types-of-machine-learning}} + +The approaches to machine learning are many, but are often split into +two main categories. In \emph{supervised learning} we know the answer to +a problem, and let the computer deduce the logic behind it. On the other +hand, \emph{unsupervised learning} is a method for finding patterns and +relationship in data sets without any prior knowledge of the system. +Some authours also operate with a third category, namely +\emph{reinforcement learning}. This is a paradigm of learning inspired +by behavioural psychology, where learning is achieved by +trial-and-error, solely from rewards and punishment. + +Another way to categorize machine learning tasks is to consider the +desired output of a system. Some of the most common tasks are: + +\begin{itemize} +\item + Classification: Outputs are divided into two or more classes. The goal + is to produce a model that assigns inputs into one of these classes. + An example is to identify digits based on pictures of hand-written + ones. Classification is typically supervised learning. +\item + Regression: Finding a functional relationship between an input data + set and a reference data set. The goal is to construct a function that + maps input data to continuous output values. +\item + Clustering: Data are divided into groups with certain common traits, + without knowing the different groups beforehand. It is thus a form of + unsupervised learning. +\end{itemize} + +\hypertarget{different-algorithms}{% +\subsection{Different algorithms}\label{different-algorithms}} + +In this course we will build our machine learning approach on a +statistical foundation, with elements from data analysis, stochastic +processes etc before we proceed with the following machine learning +algorithms + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + Linear regression and its variants +\item + Decision tree algorithms, from simpler to more complex ones +\item + Nearest neighbors models +\item + Bayesian statistics +\item + Support vector machines and finally various variants of +\item + Artifical neural networks +\end{enumerate} + +Before we proceed however, there are several practicalities with data +analysis and software tools we would like to present. These tools will +help us in our understanding of various machine learning algorithms. + +Our emphasis here is on understanding the mathematical aspects of +different algorithms, however, where possible we will emphasize the +importance of using available software. + +\hypertarget{software-and-needed-installations}{% +\subsection{Software and needed +installations}\label{software-and-needed-installations}} + +We will make intensive use of python as programming language and the +myriad of available libraries. Furthermore, you will find +IPython/Jupyter notebooks invaluable in your work. You can run +\textbf{R} codes in the Jupyter/IPython notebooks, with the immediate +benefit of visualizing your data. + +If you have Python installed (we recommend Python3) and you feel pretty +familiar with installing different packages, we recommend that you +install the following Python packages via \textbf{pip} as 1. pip install +numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow + +For Python3, replace \textbf{pip} with \textbf{pip3}. + +For OSX users we recommend also, after having installed Xcode, to +install \textbf{brew}. Brew allows for a seamless installation of +additional software via for example 1. brew install python3 + +For Linux users, with its variety of distributions like for example the +widely popular Ubuntu distribution you can use \textbf{pip} as well and +simply install Python as 1. sudo apt-get install python3 (or python for +pyhton2.7) + +etc etc. + +\hypertarget{python-installers}{% +\subsection{Python installers}\label{python-installers}} + +If you don't want to perform these operations separately, we recommend +two widely used distrubutions which set up all relevant dependencies for +Python, namely 1. \href{https://docs.anaconda.com/}{Anaconda} Anaconda +is an open source distribution of the Python and R programming languages +for large-scale data processing, predictive analytics, and scientific +computing, that aims to simplify package management and deployment. +Package versions are managed by the package management system +\textbf{conda} + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\setcounter{enumi}{1} +\tightlist +\item + \href{https://www.enthought.com/product/canopy/}{Enthought canopy} is + a Python distribution for scientific and analytic computing + distribution and analysis environment, available for free and under a + commercial license. +\end{enumerate} + +\hypertarget{installing-r-c-cython-or-julia}{% +\subsection{Installing R, C++, cython or +Julia}\label{installing-r-c-cython-or-julia}} + +You will also find it convenient to utilize R. Jupyter/Ipython notebook +allows you run \textbf{R} code interactively in your browser. The +software library \textbf{R} is tuned to statistically analysis and +allows for an easy usage of the tools we will discuss in these texts. + +To install \textbf{R} with Jupyter notebook +\href{https://mpacer.org/maths/r-kernel-for-ipython-notebook}{following +the link here} + +\hypertarget{installing-r-c-cython-or-julia-1}{% +\subsection{Installing R, C++, cython or +Julia}\label{installing-r-c-cython-or-julia-1}} + +For the C++ affecianodas, Jupyter/IPython notebook allows you also to +install C++ and run codes written in this language interactively in the +browser. Since we will emphasize writing many of the algorithms +yourself, you can thus opt for either Python or C++ as programming +languages. + +To add more entropy, \textbf{cython} can also be used when running your +notebooks. It means that Python with the Jupyter/IPython notebook setup +allows you to integrate widely popular softwares and tools for +scientific computing. With its versatility, including symbolic +operations, Python offers a unique computational environment. Your +Jupyter/IPython notebook can easily be converted into a nicely rendered +\textbf{PDF} file or a Latex file for further processing. + +This never ends. If you use the light mark-up language \textbf{doconce} +you can convert a standard ascii text file into various HTML formats, +ipython notebooks, latex files, pdf files etc. + +\hypertarget{introduction-to-jupyter-notebook-and-available-tools}{% +\subsection{Introduction to Jupyter notebook and available +tools}\label{introduction-to-jupyter-notebook-and-available-tools}} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}1}]:} \PY{o}{\PYZpc{}}\PY{k}{matplotlib} inline + + \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} + \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} + \PY{k+kn}{from} \PY{n+nn}{scipy} \PY{k}{import} \PY{n}{sparse} + \PY{k+kn}{import} \PY{n+nn}{pandas} \PY{k}{as} \PY{n+nn}{pd} + \PY{k+kn}{from} \PY{n+nn}{IPython}\PY{n+nn}{.}\PY{n+nn}{display} \PY{k}{import} \PY{n}{display} + \PY{n}{eye} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{eye}\PY{p}{(}\PY{l+m+mi}{4}\PY{p}{)} + \PY{n+nb}{print}\PY{p}{(}\PY{n}{eye}\PY{p}{)} + \PY{n}{sparse\PYZus{}mtx} \PY{o}{=} \PY{n}{sparse}\PY{o}{.}\PY{n}{csr\PYZus{}matrix}\PY{p}{(}\PY{n}{eye}\PY{p}{)} + \PY{n+nb}{print}\PY{p}{(}\PY{n}{sparse\PYZus{}mtx}\PY{p}{)} + \PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{100}\PY{p}{)} + \PY{n}{y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sin}\PY{p}{(}\PY{n}{x}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{y}\PY{p}{,}\PY{n}{marker}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{x}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} + \PY{n}{data} \PY{o}{=} \PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Name}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{John}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Anna}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Peter}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Linda}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Location}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{p}{[}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Nairobi}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Napoli}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{London}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Buenos Aires}\PY{l+s+s2}{\PYZdq{}}\PY{p}{]}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Age}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:}\PY{p}{[}\PY{l+m+mi}{51}\PY{p}{,} \PY{l+m+mi}{21}\PY{p}{,} \PY{l+m+mi}{34}\PY{p}{,} \PY{l+m+mi}{45}\PY{p}{]}\PY{p}{\PYZcb{}} + \PY{n}{data\PYZus{}pandas} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{DataFrame}\PY{p}{(}\PY{n}{data}\PY{p}{)} + \PY{n}{display}\PY{p}{(}\PY{n}{data\PYZus{}pandas}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +[[ 1. 0. 0. 0.] + [ 0. 1. 0. 0.] + [ 0. 0. 1. 0.] + [ 0. 0. 0. 1.]] + (0, 0) 1.0 + (1, 1) 1.0 + (2, 2) 1.0 + (3, 3) 1.0 + + \end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{How2ReadData_files/How2ReadData_1_1.png} + \end{center} + { \hspace*{\fill} \\} + + + \begin{verbatim} + Age Location Name +0 51 Nairobi John +1 21 Napoli Anna +2 34 London Peter +3 45 Buenos Aires Linda + \end{verbatim} + + + \hypertarget{representing-data-more-examples}{% +\subsection{Representing data, more +examples}\label{representing-data-more-examples}} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}2}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} + \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} + \PY{k+kn}{from} \PY{n+nn}{scipy} \PY{k}{import} \PY{n}{sparse} + \PY{k+kn}{import} \PY{n+nn}{pandas} \PY{k}{as} \PY{n+nn}{pd} + \PY{k+kn}{from} \PY{n+nn}{IPython}\PY{n+nn}{.}\PY{n+nn}{display} \PY{k}{import} \PY{n}{display} + \PY{k+kn}{import} \PY{n+nn}{mglearn} + \PY{k+kn}{import} \PY{n+nn}{sklearn} + \PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{linear\PYZus{}model} \PY{k}{import} \PY{n}{LinearRegression} + \PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{tree} \PY{k}{import} \PY{n}{DecisionTreeRegressor} + \PY{n}{x}\PY{p}{,} \PY{n}{y} \PY{o}{=} \PY{n}{mglearn}\PY{o}{.}\PY{n}{datasets}\PY{o}{.}\PY{n}{make\PYZus{}wave}\PY{p}{(}\PY{n}{n\PYZus{}samples}\PY{o}{=}\PY{l+m+mi}{100}\PY{p}{)} + \PY{n}{line} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{3}\PY{p}{,}\PY{l+m+mi}{1000}\PY{p}{,}\PY{n}{endpoint}\PY{o}{=}\PY{k+kc}{False}\PY{p}{)}\PY{o}{.}\PY{n}{reshape}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)} + \PY{n}{reg} \PY{o}{=} \PY{n}{DecisionTreeRegressor}\PY{p}{(}\PY{n}{min\PYZus{}samples\PYZus{}split}\PY{o}{=}\PY{l+m+mi}{3}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{y}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{line}\PY{p}{,} \PY{n}{reg}\PY{o}{.}\PY{n}{predict}\PY{p}{(}\PY{n}{line}\PY{p}{)}\PY{p}{,} \PY{n}{label}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{decision tree}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} + \PY{n}{regline} \PY{o}{=} \PY{n}{LinearRegression}\PY{p}{(}\PY{p}{)}\PY{o}{.}\PY{n}{fit}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{y}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{line}\PY{p}{,} \PY{n}{regline}\PY{o}{.}\PY{n}{predict}\PY{p}{(}\PY{n}{line}\PY{p}{)}\PY{p}{,} \PY{n}{label}\PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Linear Rgression}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +/usr/local/lib/python3.6/site-packages/scipy/linalg/basic.py:1226: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver. + warnings.warn(mesg, RuntimeWarning) + + \end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{How2ReadData_files/How2ReadData_3_1.png} + \end{center} + { \hspace*{\fill} \\} + + \hypertarget{predator-prey-model-from-ecology}{% +\subsection{Predator-Prey model from +ecology}\label{predator-prey-model-from-ecology}} + +The population dynamics of a simple predator-prey system is a classical +example shown in many biology textbooks when ecological systems are +discussed. The system contains all elements of the scientific method: + +\begin{itemize} +\item + The set up of a specific hypothesis combined with +\item + the experimental methods needed (one can study existing data or + perform experiments) +\item + analyzing and interpreting the data and performing further experiments + if needed +\item + trying to extract general behaviors and extract eventual laws or + patterns +\item + develop mathematical relations for the uncovered regularities/laws and + test these by per forming new experiments +\end{itemize} + +\hypertarget{case-study-from-hudson-bay}{% +\subsection{Case study from Hudson +bay}\label{case-study-from-hudson-bay}} + +Lots of data about populations of hares and lynx collected from furs in +Hudson Bay, Canada, are available. It is known that the populations +oscillate. Why? Here we start by + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\item + plotting the data +\item + derive a simple model for the population dynamics +\item + (fitting parameters in the model to the data) +\item + using the model predict the evolution other predator-pray systems +\end{enumerate} + +\hypertarget{hudson-bay-data}{% +\subsection{Hudson bay data}\label{hudson-bay-data}} + +Most mammalian predators rely on a variety of prey, which complicates +mathematical modeling; however, a few predators have become highly +specialized and seek almost exclusively a single prey species. An +example of this simplified predator-prey interaction is seen in Canadian +northern forests, where the populations of the lynx and the snowshoe +hare are intertwined in a life and death struggle. + +One reason that this particular system has been so extensively studied +is that the Hudson Bay company kept careful records of all furs from the +early 1800s into the 1900s. The records for the furs collected by the +Hudson Bay company showed distinct oscillations (approximately 12 year +periods), suggesting that these species caused almost periodic +fluctuations of each other's populations. The table here shows data from +1900 to 1920. + +Year + +Hares (x1000) + +Lynx (x1000) + +1900 + +30.0 + +4.0 + +1901 + +47.2 + +6.1 + +1902 + +70.2 + +9.8 + +1903 + +77.4 + +35.2 + +1904 + +36.3 + +59.4 + +1905 + +20.6 + +41.7 + +1906 + +18.1 + +19.0 + +1907 + +21.4 + +13.0 + +1908 + +22.0 + +8.3 + +1909 + +25.4 + +9.1 + +1910 + +27.1 + +7.4 + +1911 + +40.3 + +8.0 + +1912 + +57 + +12.3 + +1913 + +76.6 + +19.5 + +1914 + +52.3 + +45.7 + +1915 + +19.5 + +51.1 + +1916 + +11.2 + +29.7 + +1917 + +7.6 + +15.8 + +1918 + +14.6 + +9.7 + +1919 + +16.2 + +10.1 + +1920 + +24.7 + +8.6 + +\hypertarget{plotting-the-data}{% +\subsection{Plotting the data}\label{plotting-the-data}} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}3}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} + \PY{k+kn}{from} \PY{n+nn}{matplotlib} \PY{k}{import} \PY{n}{pyplot} \PY{k}{as} \PY{n}{plt} + + \PY{c+c1}{\PYZsh{} Load in data file} + \PY{n}{data} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{loadtxt}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{src/Hudson\PYZus{}Bay.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{delimiter}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{,}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{skiprows}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)} + \PY{c+c1}{\PYZsh{} Make arrays containing x\PYZhy{}axis and hares and lynx populations} + \PY{n}{year} \PY{o}{=} \PY{n}{data}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]} + \PY{n}{hares} \PY{o}{=} \PY{n}{data}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]} + \PY{n}{lynx} \PY{o}{=} \PY{n}{data}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]} + + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{year}\PY{p}{,} \PY{n}{hares} \PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b\PYZhy{}+}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{year}\PY{p}{,} \PY{n}{lynx}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r\PYZhy{}o}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{axis}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1900}\PY{p}{,}\PY{l+m+mi}{1920}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mf}{100.0}\PY{p}{]}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+sa}{r}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Year}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+sa}{r}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Numbers of hares and lynx }\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Hares}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Lynx}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{,} \PY{n}{loc}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{upper right}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+sa}{r}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Population of hares and lynx from 1900\PYZhy{}1920 (x1000)\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{savefig}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Hudson\PYZus{}Bay\PYZus{}data.pdf}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{savefig}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Hudson\PYZus{}Bay\PYZus{}data.png}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{How2ReadData_files/How2ReadData_5_0.png} + \end{center} + { \hspace*{\fill} \\} + + \hypertarget{hares-and-lynx-in-hudson-bay-from-1900-to-1920}{% +\subsection{Hares and lynx in Hudson bay from 1900 to +1920}\label{hares-and-lynx-in-hudson-bay-from-1900-to-1920}} + +\hypertarget{why-now-create-a-computer-model-for-the-hare-and-lynx-populations}{% +\subsection{Why now create a computer model for the hare and lynx +populations?}\label{why-now-create-a-computer-model-for-the-hare-and-lynx-populations}} + +We see from the plot that there are indeed fluctuations. We would like +to create a mathematical model that explains these population +fluctuations. Ecologists have predicted that in a simple predator-prey +system that a rise in prey population is followed (with a lag) by a rise +in the predator population. When the predator population is sufficiently +high, then the prey population begins dropping. After the prey +population falls, then the predator population falls, which allows the +prey population to recover and complete one cycle of this interaction. +Thus, we see that qualitatively oscillations occur. Can a mathematical +model predict this? What causes cycles to slow or speed up? What affects +the amplitude of the oscillation or do you expect to see the +oscillations damp to a stable equilibrium? The models tend to ignore +factors like climate and other complicating factors. How significant are +these? + +\begin{itemize} +\item + We see oscillations in the data +\item + What causes cycles to slow or speed up? +\item + What affects the amplitude of the oscillation or do you expect to see + the oscillations damp to a stable equilibrium? +\item + With a model we can better \emph{understand the data} +\item + More important: we can understand the ecology dynamics of + predator-pray populations +\end{itemize} + +\hypertarget{the-traditional-top-down-approach}{% +\subsection{The traditional (top-down) +approach}\label{the-traditional-top-down-approach}} + +The classical way (in all books) is to present the Lotka-Volterra +equations: + + \[ +\begin{align*} +\frac{dH}{dt} &= H(a - b L)\\ +\frac{dL}{dt} &= - L(d - c H) +\end{align*} +\] + + Here, + +\begin{itemize} +\item + \(H\) is the number of preys +\item + \(L\) the number of predators +\item + \(a\), \(b\), \(d\), \(c\) are parameters +\end{itemize} + +Most books quickly establish the model and then use considerable space +on discussing the qualitative properties of this \emph{nonlinear system +of ODEs} (which cannot be solved) + +\hypertarget{basic-mathematics-notation}{% +\subsection{Basic mathematics +notation}\label{basic-mathematics-notation}} + +\begin{itemize} +\item + Time points: \(t_0,t_1,\ldots,t_m\) +\item + Uniform distribution of time points: \(t_n=n\Delta t\) +\item + \(H^n\): population of hares at time \(t_n\) +\item + \(L^n\): population of lynx at time \(t_n\) +\item + We want to model the changes in populations, \(\Delta H=H^{n+1}-H^n\) + and \(\Delta L=L^{n+1}-L^n\) during a general time interval + \([t_{n+1},t_n]\) of length \(\Delta t=t_{n+1}-t_n\) +\end{itemize} + +\hypertarget{basic-dynamics-of-the-population-of-hares}{% +\subsection{Basic dynamics of the population of +hares}\label{basic-dynamics-of-the-population-of-hares}} + +The population of hares evolves due to births and deaths exactly as a +bacteria population: + + \[ +\Delta H = a \Delta t H^n +\] + + However, hares have an additional loss in the population because they +are eaten by lynx. All the hares and lynx can form \(H\cdot L\) pairs in +total. When such pairs meet during a time interval \(\Delta t\), there +is some small probablity that the lynx will eat the hare. So in fraction +\(b\Delta t HL\), the lynx eat hares. This loss of hares must be +accounted for. Subtracted in the equation for hares: + + \[ +\Delta H = a\Delta t H^n - b \Delta t H^nL^n +\] + + \hypertarget{basic-dynamics-of-the-population-of-lynx}{% +\subsection{Basic dynamics of the population of +lynx}\label{basic-dynamics-of-the-population-of-lynx}} + +We assume that the primary growth for the lynx population depends on +sufficient food for raising lynx kittens, which implies an adequate +source of nutrients from predation on hares. Thus, the growth of the +lynx population does not only depend of how many lynx there are, but on +how many hares they can eat. In a time interval \(\Delta t HL\) hares +and lynx can meet, and in a fraction \(b\Delta t HL\) the lynx eats the +hare. All of this does not contribute to the growth of lynx, again just +a fraction of \(b\Delta t HL\) that we write as \(d\Delta t HL\). In +addition, lynx die just as in the population dynamics with one isolated +animal population, leading to a loss \(-c\Delta t L\). + +The accounting of lynx then looks like + + \[ +\Delta L = d\Delta t H^nL^n - c\Delta t L^n +\] + + \hypertarget{evolution-equations}{% +\subsection{Evolution equations}\label{evolution-equations}} + +By writing up the definition of \(\Delta H\) and \(\Delta L\), and +putting all assumed known terms \(H^n\) and \(L^n\) on the right-hand +side, we have + + \[ +H^{n+1} = H^n + a\Delta t H^n - b\Delta t H^n L^n +\] + + \[ +L^{n+1} = L^n + d\Delta t H^nL^n - c\Delta t L^n +\] + + Note: + +\begin{itemize} +\item + These equations are ready to be implemented! +\item + But to start, we need \(H^0\) and \(L^0\) (which we can get from the + data) +\item + We also need values for \(a\), \(b\), \(d\), \(c\) +\end{itemize} + +\hypertarget{adapt-the-model-to-the-hudson-bay-case}{% +\subsection{Adapt the model to the Hudson Bay +case}\label{adapt-the-model-to-the-hudson-bay-case}} + +\begin{itemize} +\item + As always, models tend to be general - as here, applicable to ``all'' + predator-pray systems +\item + The critical issue is whether the \emph{interaction} between hares and + lynx is sufficiently well modeled by \(\hbox{const}HL\) +\item + The parameters \(a\), \(b\), \(d\), and \(c\) must be estimated from + data +\item + Measure time in years +\item + \(t_0=1900\), \(t_m=1920\) +\end{itemize} + +\hypertarget{the-program}{% +\subsection{The program}\label{the-program}} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}4}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} + \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} + + \PY{k}{def} \PY{n+nf}{solver}\PY{p}{(}\PY{n}{m}\PY{p}{,} \PY{n}{H0}\PY{p}{,} \PY{n}{L0}\PY{p}{,} \PY{n}{dt}\PY{p}{,} \PY{n}{a}\PY{p}{,} \PY{n}{b}\PY{p}{,} \PY{n}{c}\PY{p}{,} \PY{n}{d}\PY{p}{,} \PY{n}{t0}\PY{p}{)}\PY{p}{:} + \PY{l+s+sd}{\PYZdq{}\PYZdq{}\PYZdq{}Solve the difference equations for H and L over m years} + \PY{l+s+sd}{ with time step dt (measured in years.\PYZdq{}\PYZdq{}\PYZdq{}} + + \PY{n}{num\PYZus{}intervals} \PY{o}{=} \PY{n+nb}{int}\PY{p}{(}\PY{n}{m}\PY{o}{/}\PY{n+nb}{float}\PY{p}{(}\PY{n}{dt}\PY{p}{)}\PY{p}{)} + \PY{n}{t} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{n}{t0}\PY{p}{,} \PY{n}{t0} \PY{o}{+} \PY{n}{m}\PY{p}{,} \PY{n}{num\PYZus{}intervals}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)} + \PY{n}{H} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{t}\PY{o}{.}\PY{n}{size}\PY{p}{)} + \PY{n}{L} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{zeros}\PY{p}{(}\PY{n}{t}\PY{o}{.}\PY{n}{size}\PY{p}{)} + + \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Init:}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{H0}\PY{p}{,} \PY{n}{L0}\PY{p}{,} \PY{n}{dt}\PY{p}{)} + \PY{n}{H}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{=} \PY{n}{H0} + \PY{n}{L}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{=} \PY{n}{L0} + + \PY{k}{for} \PY{n}{n} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{n+nb}{len}\PY{p}{(}\PY{n}{t}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{:} + \PY{n}{H}\PY{p}{[}\PY{n}{n}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{H}\PY{p}{[}\PY{n}{n}\PY{p}{]} \PY{o}{+} \PY{n}{a}\PY{o}{*}\PY{n}{dt}\PY{o}{*}\PY{n}{H}\PY{p}{[}\PY{n}{n}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{b}\PY{o}{*}\PY{n}{dt}\PY{o}{*}\PY{n}{H}\PY{p}{[}\PY{n}{n}\PY{p}{]}\PY{o}{*}\PY{n}{L}\PY{p}{[}\PY{n}{n}\PY{p}{]} + \PY{n}{L}\PY{p}{[}\PY{n}{n}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{L}\PY{p}{[}\PY{n}{n}\PY{p}{]} \PY{o}{+} \PY{n}{d}\PY{o}{*}\PY{n}{dt}\PY{o}{*}\PY{n}{H}\PY{p}{[}\PY{n}{n}\PY{p}{]}\PY{o}{*}\PY{n}{L}\PY{p}{[}\PY{n}{n}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{c}\PY{o}{*}\PY{n}{dt}\PY{o}{*}\PY{n}{L}\PY{p}{[}\PY{n}{n}\PY{p}{]} + \PY{k}{return} \PY{n}{H}\PY{p}{,} \PY{n}{L}\PY{p}{,} \PY{n}{t} + + \PY{c+c1}{\PYZsh{} Load in data file} + \PY{n}{data} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{loadtxt}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{src/Hudson\PYZus{}Bay.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{delimiter}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{,}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{skiprows}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)} + \PY{c+c1}{\PYZsh{} Make arrays containing x\PYZhy{}axis and hares and lynx populations} + \PY{n}{t\PYZus{}e} \PY{o}{=} \PY{n}{data}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{]} + \PY{n}{H\PYZus{}e} \PY{o}{=} \PY{n}{data}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{]} + \PY{n}{L\PYZus{}e} \PY{o}{=} \PY{n}{data}\PY{p}{[}\PY{p}{:}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{]} + + \PY{c+c1}{\PYZsh{} Simulate using the model} + \PY{n}{H}\PY{p}{,} \PY{n}{L}\PY{p}{,} \PY{n}{t} \PY{o}{=} \PY{n}{solver}\PY{p}{(}\PY{n}{m}\PY{o}{=}\PY{l+m+mi}{20}\PY{p}{,} \PY{n}{H0}\PY{o}{=}\PY{l+m+mf}{34.91}\PY{p}{,} \PY{n}{L0}\PY{o}{=}\PY{l+m+mf}{3.857}\PY{p}{,} \PY{n}{dt}\PY{o}{=}\PY{l+m+mf}{0.1}\PY{p}{,} + \PY{n}{a}\PY{o}{=}\PY{l+m+mf}{0.4807}\PY{p}{,} \PY{n}{b}\PY{o}{=}\PY{l+m+mf}{0.02482}\PY{p}{,} \PY{n}{c}\PY{o}{=}\PY{l+m+mf}{0.9272}\PY{p}{,} \PY{n}{d}\PY{o}{=}\PY{l+m+mf}{0.02756}\PY{p}{,} + \PY{n}{t0}\PY{o}{=}\PY{l+m+mi}{1900}\PY{p}{)} + + \PY{c+c1}{\PYZsh{} Visualize simulations and data} + \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{t\PYZus{}e}\PY{p}{,} \PY{n}{H\PYZus{}e}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{b\PYZhy{}+}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{t\PYZus{}e}\PY{p}{,} \PY{n}{L\PYZus{}e}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r\PYZhy{}o}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{t}\PY{p}{,} \PY{n}{H}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{m\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{t}\PY{p}{,} \PY{n}{L}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{k\PYZhy{}\PYZhy{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Year}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Numbers of hares and lynx}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{axis}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{1900}\PY{p}{,} \PY{l+m+mi}{1920}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{140}\PY{p}{]}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+sa}{r}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Population of hares and lynx 1900\PYZhy{}1920 (x1000)}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{H\PYZus{}e}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{L\PYZus{}e}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{H}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{L}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{,} \PY{n}{loc}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{upper left}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{savefig}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Hudson\PYZus{}Bay\PYZus{}sim.pdf}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{savefig}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Hudson\PYZus{}Bay\PYZus{}sim.png}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} + \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} +\end{Verbatim} + + \begin{Verbatim}[commandchars=\\\{\}] +Init: 34.91 3.857 0.1 + + \end{Verbatim} + + \begin{center} + \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{How2ReadData_files/How2ReadData_18_1.png} + \end{center} + { \hspace*{\fill} \\} + + \hypertarget{the-plot}{% +\subsection{The plot}\label{the-plot}} + +If we perform a least-square fitting, we can find optimal values for the +parameters \(a\), \(b\), \(d\), \(c\). The optimal parameters are +\(a=0.4807\), \(b=0.02482\), \(d=0.9272\) and \(c=0.02756\). These +parameters result in a slightly modified initial conditions, namely +\(H(0) = 34.91\) and \(L(0)=3.857\). With these parameters we are now +ready to solve the equations and plot these data together with the +experimental values. + +\hypertarget{linear-regression-in-python}{% +\subsection{Linear regression in +Python}\label{linear-regression-in-python}} + + \begin{Verbatim}[commandchars=\\\{\}] +{\color{incolor}In [{\color{incolor}5}]:} \PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} + \PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt} + \PY{k+kn}{from} \PY{n+nn}{IPython}\PY{n+nn}{.}\PY{n+nn}{display} \PY{k}{import} \PY{n}{display} + \PY{k+kn}{import} \PY{n+nn}{sklearn} + \PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{linear\PYZus{}model} \PY{k}{import} \PY{n}{LinearRegression} + \PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{tree} \PY{k}{import} \PY{n}{DecisionTreeRegressor} + + + \PY{n}{data} \PY{o}{=} 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To add more entropy, _cython_ can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook -can easily be converted into a nicely rendered _PDF_ file or a Latex file for further processing. +can easily be converted into a nicely rendered _PDF_ file or a Latex file for further processing. For example, convert to latex as +!bc pycod +jupyter nbconvert filename.ipynb --to latex +!ec -This never ends. If you use the light mark-up language _doconce_ you can convert a standard ascii text file into various HTML formats, ipython notebooks, latex files, pdf files etc. @@ -445,7 +447,7 @@ plt.show() !split ===== Linear Least squares in R ===== !bblock -!bc pycod +!bc r HudsonBay = read.csv("src/Hudson_Bay.csv",header=T) fix(HudsonBay) dim(HudsonBay) @@ -471,7 +473,7 @@ predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval="confidence") !split ===== Non-Linear Least squares in R ===== !bblock -!bc pycod +!bc r set.seed(1485) len = 24 x = runif(len) diff --git a/doc/src/How2ReadData/knn.py b/doc/src/How2ReadData/knn.py new file mode 100644 index 000000000..77327baad --- /dev/null +++ b/doc/src/How2ReadData/knn.py @@ -0,0 +1,38 @@ +import numpy as np +import matplotlib.pyplot as plt +from IPython.display import display +import sklearn +from sklearn.linear_model import LinearRegression +from sklearn.tree import DecisionTreeRegressor +from sklearn.model_selection import train_test_split +import mglearn +X, y = mglearn.datasets.make_forge() +X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0) +from sklearn.neighbors import KNeighborsClassifier +clf = KNeighborsClassifier(n_neighbors=3) +clf.fit(X_train, y_train) +KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',metric_params=None, n_jobs=1, n_neighbors=3, p=2,weights='uniform') + +clf.predict(X_test) + +clf.score(X_test, y_test) +fig, axes = plt.subplots(1, 3, figsize=(10, 3)) +for n_neighbors, ax in zip([1, 3, 9], axes): + clf = KNeighborsClassifier(n_neighbors=n_neighbors).fit(X, y) + mglearn.plots.plot_2d_separator(clf, X, fill=True, eps=0.5, ax=ax, alpha=.4) + ax.scatter(X[:, 0], X[:, 1], c=y, s=60, cmap=mglearn.cm2) + ax.set_title("%d neighbor(s)" % n_neighbors) + + +data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1) +x = data[:,0] +y = data[:,1] +#x_train, y_train = train_test_split(x, y, random_state=0) +line = np.linspace(1900,1930,1000,endpoint=False).reshape(-1,1) +reg = DecisionTreeRegressor(min_samples_split=3).fit(x.reshape(-1,1),y.reshape(-1,1)) +plt.plot(line, reg.predict(line), label="decision tree") +regline = LinearRegression().fit(x.reshape(-1,1),y.reshape(-1,1)) +plt.plot(line, regline.predict(line), label= "Linear Regression") +plt.plot(x, y, label= "Linear Regression") +plt.show() + diff --git a/doc/src/How2ReadData/panda.py b/doc/src/How2ReadData/panda.py new file mode 100644 index 000000000..79a1a9a66 --- /dev/null +++ b/doc/src/How2ReadData/panda.py @@ -0,0 +1,10 @@ +import numpy as np +import matplotlib.pyplot as plt +from IPython.display import display +import pandas as pd + +data = pd.read_csv('src/Hudson_Bay.csv', delimiter=',', skiprows=1) + + +data_pandas = pd.DataFrame(data) +display(data_pandas) diff --git a/doc/src/How2ReadData/test.py b/doc/src/How2ReadData/test.py index be8ccd053..77327baad 100644 --- a/doc/src/How2ReadData/test.py +++ b/doc/src/How2ReadData/test.py @@ -5,12 +5,29 @@ import sklearn from sklearn.linear_model import LinearRegression from sklearn.tree import DecisionTreeRegressor from sklearn.model_selection import train_test_split -X_train, X_test, y_train, y_test = train_test_split(x, y, random_state=0) +import mglearn +X, y = mglearn.datasets.make_forge() +X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0) +from sklearn.neighbors import KNeighborsClassifier +clf = KNeighborsClassifier(n_neighbors=3) +clf.fit(X_train, y_train) +KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',metric_params=None, n_jobs=1, n_neighbors=3, p=2,weights='uniform') + +clf.predict(X_test) + +clf.score(X_test, y_test) +fig, axes = plt.subplots(1, 3, figsize=(10, 3)) +for n_neighbors, ax in zip([1, 3, 9], axes): + clf = KNeighborsClassifier(n_neighbors=n_neighbors).fit(X, y) + mglearn.plots.plot_2d_separator(clf, X, fill=True, eps=0.5, ax=ax, alpha=.4) + ax.scatter(X[:, 0], X[:, 1], c=y, s=60, cmap=mglearn.cm2) + ax.set_title("%d neighbor(s)" % n_neighbors) + data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1) x = data[:,0] y = data[:,1] -x_train, y_train = train_test_split(x, y, random_state=0) +#x_train, y_train = train_test_split(x, y, random_state=0) line = np.linspace(1900,1930,1000,endpoint=False).reshape(-1,1) reg = DecisionTreeRegressor(min_samples_split=3).fit(x.reshape(-1,1),y.reshape(-1,1)) plt.plot(line, reg.predict(line), label="decision tree")