Added Cheatsheets for day1.

4 files changed, 196 insertions, 0 deletions

diff --git a/day1/cheatsheet2.tex b/day1/cheatsheet2.tex
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+\documentclass[12pt]{article}
+%\title{Plotting Data}
+%\author{FOSSEE}
+\begin{document}
+\date{}
+\vspace{-1in}
+\begin{center}
+\LARGE{Plotting Data}\\
+\large{FOSSEE}
+\end{center}
+\section{Scripts}
+IPython History
+\begin{verbatim}
+In [1]: %hist
+In [2]: %hist -n
+\end{verbatim}
+
+Running a Script
+\begin{verbatim}
+In [3]:  %run script_name.py
+\end{verbatim}
+
+\section{Plotting from Data files}
+\begin{verbatim}
+In [1]: L = [] #Empty List
+In [2]: T = []
+In [3]: for line in open('pendulum.txt'): # Opening & Reading files
+  ....:     points = line.split() # Splitting a string
+  ....:     L.append(float(points[0])) # Appending to a list
+  ....:     T.append(float(points[1]))
+In [4]: TSq = []
+In [5]: for t in T:  #Iterating through lists
+ ....:     TSq.append(t*t)
+In [6]: plot(L, TSq, '.') # Plotting points
+\end{verbatim}
+\end{document}
+
diff --git a/day1/cheatsheet3.tex b/day1/cheatsheet3.tex
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+\documentclass[12pt]{article}
+\title{Interactive Plotting}
+\author{FOSSEE}
+\begin{document}
+\date{}
+\vspace{-1in}
+\begin{center}
+\LARGE{Statistics and Least square fit}\\
+\large{FOSSEE}
+\end{center}
+\section{Statistics}
+Dictionary
+\begin{verbatim}
+In [1]: d = {"Hitchhiker's guide" : 42, 
+  ....:      "Terminator" : "I'll be back"} #Creation
+In [2]: d["Hitchhiker's guide"] # Accessing a value with key
+In [3]: "Hitchhiker's guide" in d #Checking for a key
+In [4]: d.keys() # Obtaining List of Keys
+In [5]: d.values() # Obtaining List of Values
+\end{verbatim}
+Iterating through List indices
+\begin{verbatim}
+In [1]: names = ["Guido","Alex", "Tim"]
+In [2]: for i, name in enumerate(names):
+   ...:     print i, name
+\end{verbatim}
+
+\begin{verbatim}
+In [1]: score = int(score_str) if score_str != 'AA' else 0
+\end{verbatim}
+Drawing Pie Charts
+\begin{verbatim}
+In [1]: pie(science.values(), labels=science.keys())
+\end{verbatim}
+sum() and len() functions
+\begin{verbatim}
+In [1]: mean = sum(math_scores) / len(math_scores)
+\end{verbatim}
+Numpy Arrays
+\begin{verbatim}
+In [1]: a = array([1, 2, 3]) #Creating
+In [2]: b = array([4, 5, 6])
+In [3]: a + b #Sum; Element-wise
+\end{verbatim}
+Numpy statistical operations 
+\begin{verbatim}
+In [1]: mean(math_scores)
+In [2]: median(math_scores)
+In [3]: stats.mode(math_scores)
+In [4]: std(math_scores)
+\end{verbatim}
+Generating Van der Monde matrix
+\begin{verbatim}
+In [1]: A = vander(L, 2)
+\end{verbatim}
+Getting a Least Squares Fit curve
+\begin{verbatim}
+In [1]: coef, res, r, s = lstsq(A,TSq)
+In [2]: Tline = coef[0]*L + coef[1]
+In [3]: plot(L, Tline)
+\end{verbatim}
+\end{document}
+
diff --git a/day1/cheatsheet4.tex b/day1/cheatsheet4.tex
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+\documentclass[12pt]{article}
+\title{Matrices and Solution of Equations}
+\author{FOSSEE}
+\begin{document}
+\date{}
+\vspace{-1in}
+\begin{center}
+\LARGE{Matrices and Solution of Equations}\\
+\large{FOSSEE}
+\end{center}
+\section{Matrices}
+Inputting a Matrix
+\begin{verbatim}
+In [1]: A = matrix([[1, 2, 3],[4, 5, 6]])
+\end{verbatim}
+Matrix Operations
+\begin{verbatim}
+In [1]: A.T # Transpose
+In [2]: sum(A) # Sum of all elements
+In [3]: A+B # Addition
+In [1]: A*B # Product
+In [1]: inv(A) # Inverse
+In [1]: det(A) # Determinant
+\end{verbatim}
+
+Eigen Values and Eigen Vectors
+\begin{verbatim}
+In [1]: eig(A) #Eigen Values and Vectors
+In [2]: eigvals(A) #Eigen Values 
+\end{verbatim}
+Norm
+\begin{verbatim}
+In [1]: norm(A)
+\end{verbatim}
+Single Value Decomposition
+\begin{verbatim}
+In [1]: svd(A)
+\end{verbatim}
+Solving a set of equations
+\begin{verbatim}
+In [1]: A = matrix([...]) # Input Equation Coefficient Matrix   
+In [2]: b = matrix([...]) # Equation Target Values
+In [3]: x = solve(A, b)
+In [4]: Ax = A*x
+\end{verbatim}
+\end{document}
+
diff --git a/day1/cheatsheet5.tex b/day1/cheatsheet5.tex
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+\documentclass[12pt]{article}
+\title{Matrices and Solution of Equations}
+\author{FOSSEE}
+\begin{document}
+\date{}
+\vspace{-1in}
+\begin{center}
+\LARGE{Interpolation, Differentiation and Integration}\\
+\large{FOSSEE}
+\end{center}
+\section{}
+Loading a data file
+\begin{verbatim}
+In [2]: x, y = loadtxt('points.txt', unpack = True)
+#load data file directly into Arrays.
+\end{verbatim}
+\section{}
+Interploate
+\begin{verbatim}
+In []: from scipy.interpolate import splrep
+In []: tck = splrep(x,y) #get spline curve representation for x,y.
+In []: from scipy.interpolate import splev
+#To evaluate spline and it's derivatives.
+In []: Xnew = arange(0.01,3,0.02)
+#missing set of points
+In []: Ynew = splev(Xnew, tck)
+#Value of function at Xnew
+In []: plot(Xnew, Ynew)
+\end{verbatim}
+
+\section{Differentiation}
+Taylor series - finite difference approximations
+$f(x+h)=f(x)+hf^{'}(x)$ Forward
+\begin{verbatim}
+In []: x = linspace(0, 2*pi, 100)
+In []: y = sin(x)
+In []: deltax = x[1] - x[0]
+In []: fD = (y[1:] - y[:-1]) / deltax 
+#fD is the required forward difference
+\end{verbatim}
+
+\section{Quadrature}
+$\int_0^1(sin(x) + x^2)$ 
+In []: def f(x):
+           return sin(x)+x**2
+In []: from scipy.integrate import quad
+In []: quad(f, 0, 1)
+\end{document}
+