\documentclass[12pt]{article}

\title{Matrices and Least Square Fit}

\author{FOSSEE}

\usepackage{listings}

\lstset{language=Python,

    basicstyle=\ttfamily,

  commentstyle=\itshape\bfseries,

  showstringspaces=false,

}

\newcommand{\typ}[1]{\lstinline{#1}}

\usepackage[english]{babel}

\usepackage[latin1]{inputenc}

\usepackage{times}

\usepackage[T1]{fontenc}

\usepackage{ae,aecompl}

\usepackage{mathpazo,courier,euler}

\usepackage[scaled=.95]{helvet}

\begin{document}

\date{}

\vspace{-1in}

\begin{center}

\LARGE{Matrices and Least Square Fit}\\

\large{FOSSEE}

\end{center}

\section{Matrices}

Inputting a Matrix

\begin{lstlisting}

In []: C = array([[1,1,2],

                  [2,4,1],

                  [-1,3,7]])

In []: B = ones_like(C)

In []: A = ones((3,2))

In []: I = identity(3)

\end{lstlisting}

Accessing Elements

\begin{lstlisting}

In []: C[1,2]

Out[]: 1

In []: C[1]

Out[]: array([2, 4, 1])

\end{lstlisting}

Changing elements

\begin{lstlisting}

In []: C[1,1] = -2

In []: C

Out[]: 

array([[ 1,  1,  2],

       [ 2, -2,  1],

       [-1,  3,  7]])

In []: C[1] = [0,0,0]

In []: C

Out[]: 

array([[ 1,  1,  2],

       [ 0,  0,  0],

       [-1,  3,  7]])

\end{lstlisting}

Slicing

\begin{lstlisting}

In []: C[:,1]

Out[]: array([1, 0, 3])

In []: C[1,:]

Out[]: array([0, 0, 0])

In []: C[0:2,:]

Out[]: 

array([[1, 1, 2],

       [0, 0, 0]])

In []: C[1:3,:]

Out[]: 

array([[ 0,  0,  0],

       [-1,  3,  7]])

In []: C[:2,:]

Out[]: 

array([[1, 1, 2],

       [0, 0, 0]])

In []: C[1:,:]

Out[]: 

array([[ 0,  0,  0],

       [-1,  3,  7]])

In []: C[1:,:2]

Out[]: 

array([[ 0,  0],

       [-1,  3]])

\end{lstlisting}

Striding

\begin{lstlisting}

In []: C[::2,:]

Out[]: 

array([[ 1,  1,  2],

       [-1,  3,  7]])

In []: C[:,::2]

Out[]: 

xarray([[ 1,  2],

       [ 0,  0],

       [-1,  7]])

In []: C[::2,::2]

Out[]: 

array([[ 1,  2],

       [-1,  7]])

\end{lstlisting}

Matrix Operations

\begin{lstlisting}

In []: A.T # Transpose

In []: sum(A) # Sum of all elements

In []: A+B # Addition

In []: A*B # Product

In []: inv(A) # Inverse

In []: det(A) # Determinant

\end{lstlisting}

Eigen Values and Eigen Vectors

\begin{lstlisting}

In []: eig(A) #Eigen Values and Vectors

In []: eigvals(A) #Eigen Values 

\end{lstlisting}

%% Norm

%% \begin{lstlisting}

%% In []: norm(A)

%% \end{lstlisting}

%% Single Value Decomposition

%% \begin{lstlisting}

%% In []: svd(A)

%% \end{lstlisting}

Least Square Fit Line

\begin{lstlisting}

In []: A = array([L, ones_like(L)])

In []: A = A.T

In []: result = lstsq(A,TSq)

In []: coef = result[0]

In []: Tline = coef[0]*L + coef[1]

In []: plot(L, Tline)

\end{lstlisting}

\end{document}