Changes made for Goa workshop .

6 files changed, 238 insertions, 123 deletions

diff --git a/day1/data/interpolate.png b/day1/data/interpolate.png
new file mode 100644
index 0000000..dd91788
--- /dev/null
+++ b/day1/data/interpolate.png
diff --git a/day1/session2.tex b/day1/session2.tex
index 150a1a3..493942b 100644
--- a/day1/session2.tex
+++ b/day1/session2.tex
@@ -260,6 +260,7 @@ Out[]: [2, 3]
 \end{lstlisting}
 \end{frame}
 
+%% more on list slicing
 \begin{frame}[fragile]
 \frametitle{List operations}
 \begin{lstlisting}
diff --git a/day1/session3.tex b/day1/session3.tex
index 7019a7c..bda7d8d 100644
--- a/day1/session3.tex
+++ b/day1/session3.tex
@@ -581,6 +581,7 @@ In []: TSq = T*T
 \end{itemize}
 \end{frame}
 
+%%making vander without vander, simple matrix
 \subsection{Van der Monde matrix generation}
 \begin{frame}[fragile]
 \frametitle{Van der Monde Matrix}
diff --git a/day1/session4.tex b/day1/session4.tex
index 4c0e913..7981771 100644
--- a/day1/session4.tex
+++ b/day1/session4.tex
@@ -128,45 +128,68 @@
 
 \begin{frame}
 \frametitle{Matrices: Introduction}
-We looked at the Van der Monde matrix in the previous session,\\ 
-let us now look at matrices in a little more detail.
+Let us now look at matrices in detail.\\
+\alert{All matrix operations are done using \kwrd{arrays}}
 \end{frame}
 
 \subsection{Initializing}
 \begin{frame}[fragile]
 \frametitle{Matrices: Initializing}
 \begin{lstlisting}
-In []: A = matrix([[ 1,  1,  2, -1],
-                   [ 2,  5, -1, -9],
-                   [ 2,  1, -1,  3],
-                   [ 1, -3,  2,  7]])
+In []: A = array([[ 1,  1,  2, -1],
+                  [ 2,  5, -1, -9],
+                  [ 2,  1, -1,  3],
+                  [ 1, -3,  2,  7]])
 In []: A
 Out[]: 
-matrix([[ 1,  1,  2, -1],
-        [ 2,  5, -1, -9],
-        [ 2,  1, -1,  3],
-        [ 1, -3,  2,  7]])
+array([[ 1,  1,  2, -1],
+       [ 2,  5, -1, -9],
+       [ 2,  1, -1,  3],
+       [ 1, -3,  2,  7]])
 \end{lstlisting}
 \end{frame}
 
+\begin{frame}[fragile]
+  \frametitle{Accessing elements of matrices}
+\begin{small}
+  \begin{lstlisting}
+In []: C = array([[1,1,2],
+                  [2,4,1],
+                  [-1,3,7]])
+In []: C[1,2]
+Out[]: 1
+
+In []: C[1]
+Out[]: array([2, 4, 1])
+
+In []: C[1,1] = -2
+In []: C
+Out[]: 
+array([[ 1,  1,  2],
+       [ 2, -2,  1],
+       [-1,  3,  7]])
+  \end{lstlisting}
+\end{small}
+\end{frame}
+
 \subsection{Basic Operations}
 
 \begin{frame}[fragile]
 \frametitle{Transpose of a Matrix}
 \begin{lstlisting}
-In []: linalg.transpose(A)
+In []: A.T
 Out[]:
-matrix([[ 1,  2,  2,  1],
-        [ 1,  5,  1, -3],
-        [ 2, -1, -1,  2],
-        [-1, -9,  3,  7]])
+array([[ 1,  2,  2,  1],
+       [ 1,  5,  1, -3],
+       [ 2, -1, -1,  2],
+       [-1, -9,  3,  7]])
 \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
   \frametitle{Sum of all elements}
   \begin{lstlisting}
-In []: linalg.sum(A)
+In []: sum(A)
 Out[]: 12
   \end{lstlisting}
 \end{frame}
@@ -174,41 +197,56 @@ Out[]: 12
 \begin{frame}[fragile]
   \frametitle{Matrix Addition}
   \begin{lstlisting}
-In []: B = matrix([[3,2,-1,5],
-                   [2,-2,4,9],
-                   [-1,0.5,-1,-7],
-                   [9,-5,7,3]])
-In []: linalg.add(A,B)
+In []: B = array([[3,2,-1,5],
+                  [2,-2,4,9],
+                  [-1,0.5,-1,-7],
+                  [9,-5,7,3]])
+In []: A + B
 Out[]: 
-matrix([[  4. ,   3. ,   1. ,   4. ],
-        [  4. ,   3. ,   3. ,   0. ],
-        [  1. ,   1.5,  -2. ,  -4. ],
-        [ 10. ,  -8. ,   9. ,  10. ]])
+array([[  4. ,   3. ,   1. ,   4. ],
+       [  4. ,   3. ,   3. ,   0. ],
+       [  1. ,   1.5,  -2. ,  -4. ],
+       [ 10. ,  -8. ,   9. ,  10. ]])
   \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
+\frametitle{Elementwise Multiplication}
+\begin{lstlisting}
+In []: A*B
+Out[]: 
+array([[  3. ,   2. ,  -2. ,  -5. ],
+       [  4. , -10. ,  -4. , -81. ],
+       [ -2. ,   0.5,   1. , -21. ],
+       [  9. ,  15. ,  14. ,  21. ]])
+
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
 \frametitle{Matrix Multiplication}
 \begin{lstlisting}
-In []: linalg.multiply(A, B)
+In []: dot(A,B)
 Out[]: 
-matrix([[  3. ,   2. ,  -2. ,  -5. ],
-        [  4. , -10. ,  -4. , -81. ],
-        [ -2. ,   0.5,   1. , -21. ],
-        [  9. ,  15. ,  14. ,  21. ]])
+array([[ -6. ,   6. ,  -6. ,  -3. ],
+       [-64. ,  38.5, -44. ,  35. ],
+       [ 36. , -13.5,  24. ,  35. ],
+       [ 58. , -26. ,  34. , -15. ]])
 \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
 \frametitle{Inverse of a Matrix}
+\begin{lstlisting}
+In []: inv(A)
+\end{lstlisting}
 \begin{small}
 \begin{lstlisting}
-In []: linalg.inv(A)
 Out[]: 
-matrix([[-0.5 ,  0.55, -0.15,  0.7 ],
-        [ 0.75, -0.5 ,  0.5 , -0.75],
-        [ 0.5 , -0.15, -0.05, -0.1 ],
-        [ 0.25, -0.25,  0.25, -0.25]])
+array([[-0.5 ,  0.55, -0.15,  0.7 ],
+       [ 0.75, -0.5 ,  0.5 , -0.75],
+       [ 0.5 , -0.15, -0.05, -0.1 ],
+       [ 0.25, -0.25,  0.25, -0.25]])
 \end{lstlisting}
 \end{small}
 \end{frame}
@@ -217,24 +255,25 @@ matrix([[-0.5 ,  0.55, -0.15,  0.7 ],
 \frametitle{Determinant}
 \begin{lstlisting}
 In []: det(A)
-Out[66]: 80.0
+Out[]: 80.0
 \end{lstlisting}
 \end{frame}
 
+%%use S=array(X,Y)
 \begin{frame}[fragile]
-\frametitle{Eigen Values and Eigen Matrix}
+\frametitle{Eigenvalues and Eigen Vectors}
 \begin{small}
 \begin{lstlisting}
-In []: E = matrix([[3,2,4],[2,0,2],[4,2,3]])
+In []: E = array([[3,2,4],[2,0,2],[4,2,3]])
 
-In []: linalg.eig(E)
+In []: eig(E)
 Out[]: 
 (array([-1.,  8., -1.]),
- matrix([[-0.74535599,  0.66666667, -0.1931126 ],
+ array([[-0.74535599,  0.66666667, -0.1931126 ],
         [ 0.2981424 ,  0.33333333, -0.78664085],
         [ 0.59628479,  0.66666667,  0.58643303]]))
 
-In []: linalg.eigvals(E)
+In []: eigvals(E)
 Out[]: array([-1.,  8., -1.])
 \end{lstlisting}
 \end{small}
@@ -243,23 +282,23 @@ Out[]: array([-1.,  8., -1.])
 \begin{frame}[fragile]
 \frametitle{Computing Norms}
 \begin{lstlisting}
-In []: linalg.norm(E)
+In []: norm(E)
 Out[]: 8.1240384046359608
 \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
-  \frametitle{Single Value Decomposition}
+  \frametitle{Singular Value Decomposition}
   \begin{small}
   \begin{lstlisting}
-In [76]: linalg.svd(E)
-Out[76]: 
-(matrix(
+In []: svd(E)
+Out[]: 
+(array(
 [[ -6.66666667e-01,  -1.23702565e-16,   7.45355992e-01],
  [ -3.33333333e-01,  -8.94427191e-01,  -2.98142397e-01],
  [ -6.66666667e-01,   4.47213595e-01,  -5.96284794e-01]]),
  array([ 8.,  1.,  1.]),
- matrix([[-0.66666667, -0.33333333, -0.66666667],
+ array([[-0.66666667, -0.33333333, -0.66666667],
         [-0.        ,  0.89442719, -0.4472136 ],
         [-0.74535599,  0.2981424 ,  0.59628479]]))
   \end{lstlisting}
@@ -289,12 +328,12 @@ Solution:
 \frametitle{Solving using Matrices}
 Let us now look at how to solve this using \kwrd{matrices}
   \begin{lstlisting}
-    In []: A = matrix([[3,2,-1],
-                       [2,-2,4],
-                       [-1, 0.5, -1]])
-    In []: b = matrix([[1], [-2], [0]])
-    In []: x = linalg.solve(A, b)
-    In []: Ax = dot(A, x)
+    In []: A = array([[3,2,-1],
+                      [2,-2,4],                   
+                      [-1, 0.5, -1]])
+    In []: b = array([[1], [-2], [0]])
+    In []: x = solve(A, b)
+    In []: Ax = dot(A,x)
   \end{lstlisting}
 \end{frame}
 
@@ -314,9 +353,9 @@ array([[ 1.],
 \begin{lstlisting}
 In []: Ax
 Out[]: 
-matrix([[  1.00000000e+00],
-        [ -2.00000000e+00],
-        [  2.22044605e-16]])
+array([[  1.00000000e+00],
+       [ -2.00000000e+00],
+       [  2.22044605e-16]])
 \end{lstlisting}
 \begin{block}{}
 The last term in the matrix is actually \alert{0}!\\
@@ -332,7 +371,74 @@ Out[]: True
 \subsection{Exercises}
 
 \begin{frame}[fragile]
-\frametitle{Problem Set 4: Problem 4.1}
+\frametitle{Problem 1}
+Given the matrix:\\
+\begin{center}
+$\begin{bmatrix}
+-2 & 2 & 3\\
+ 2 & 1 & 6\\
+-1 &-2 & 0\\
+\end{bmatrix}$
+\end{center}
+Find:
+\begin{itemize}
+  \item[i] Transpose
+  \item[ii]Inverse
+  \item[iii]Determinant
+  \item[iv] Eigenvalues and Eigen vectors
+  \item[v] Singular Value decomposition
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Problem 2}
+Given 
+\begin{center}
+A = 
+$\begin{bmatrix}
+-3 & 1 & 5 \\
+1 & 0 & -2 \\
+5 & -2 & 4 \\
+\end{bmatrix}$
+, B = 
+$\begin{bmatrix}
+0 & 9 & -12 \\
+-9 & 0 & 20 \\
+12 & -20 & 0 \\
+\end{bmatrix}$
+\end{center}
+Find:
+\begin{itemize}
+  \item[i] Sum of A and B
+  \item[ii]Elementwise Product of A and B
+  \item[iii] Matrix product of A and B
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solution}
+Sum: 
+$\begin{bmatrix}
+-3 & 10 & 7 \\
+-8 & 0 & 18 \\
+17 & -22 & 4 \\
+\end{bmatrix}$
+,\\ Elementwise Product:
+$\begin{bmatrix}
+0 & 9 & -60 \\
+-9 & 0 & -40 \\
+60 & 40 & 0 \\
+\end{bmatrix}$
+,\\ Matrix product:
+$\begin{bmatrix}
+51 & -127 & 56 \\
+-24 & 49 & -12 \\
+66 & -35 & -100 \\
+\end{bmatrix}$
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Problem 3}
 Solve the set of equations:
 \begin{align*}
   x + y + 2z -w & = 3\\
@@ -345,37 +451,30 @@ Solve the set of equations:
 
 \begin{frame}[fragile]
 \frametitle{Solution}
-Solution:
-\begin{lstlisting}
+Use \kwrd{solve()}
 \begin{align*}
   x & = -5\\
   y & = 2\\
   z & = 3\\
   w & = 0\\
 \end{align*}
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Problem 4.2}
-
 \end{frame}
 
 \section{Summary}
 \begin{frame}
-  \frametitle{Summary}
-So what did we learn??
+  \frametitle{What did we learn??}
   \begin{itemize}
   \item Matrices
     \begin{itemize}
+      \item Accessing elements
       \item Transpose
       \item Addition
       \item Multiplication
       \item Inverse of a matrix
       \item Determinant
-      \item Eigen values and Eigen matrix
+      \item Eigenvalues and Eigen vector
       \item Norms
-      \item Single Value Decomposition
+      \item Singular Value Decomposition
     \end{itemize}
   \item Solving linear equations
   \end{itemize}
diff --git a/day1/session5.tex b/day1/session5.tex
index 24b1282..af0848c 100644
--- a/day1/session5.tex
+++ b/day1/session5.tex
@@ -124,18 +124,36 @@
 %% %  \pausesections
 %% \end{frame}
 
-
 \section{\typ{loadtxt}}
 
 \begin{frame}[fragile]
+  \frametitle{Array slicing}
+  \begin{lstlisting}
+In []: A = array([[ 1,  1,  2, -1],
+                  [ 2,  5, -1, -9],
+                  [ 2,  1, -1,  3],
+                  [ 1, -3,  2,  7]])
+
+In []: A[:,0]
+Out[]: array([ 1,  2,  2, 1])
+
+In []: A[1:3,1:3]
+Out[]: 
+array([[ 5, -1],
+       [ 1, -1]])
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
   \frametitle{\typ{loadtxt}}
   \begin{itemize}
   \item Load data from a text file.
   \item Each row must have same number of values.
   \end{itemize}
 \begin{lstlisting}
-In []: L, T = loadtxt('pendulum.txt', 
-                       unpack = True)
+In []: data = loadtxt('pendulum.txt')
+In []: x = data[:, 0]
+In []: y = data[:, 1]
 \end{lstlisting}
 \end{frame}
 
@@ -151,6 +169,7 @@ In []: L, T = loadtxt('pendulum.txt',
   \item It contains x,y position of particle.
   \item Plot the given points.
 %%  \item Interpolate the missing region.
+%%  load txt the unpack part.
 \end{itemize}
 \begin{lstlisting}
 In []: x, y = loadtxt('points.txt',
@@ -195,6 +214,8 @@ In []: plot(x, y, '.')
 %% \end{lstlisting}
 %% \end{frame}
 
+%%better example, maybe parabola
+
 \begin{frame}[fragile]
 \frametitle{Spline Interpolation}
 \begin{small}
@@ -223,22 +244,29 @@ In []: tck = splrep(x, y)
 
 \begin{frame}[fragile]
 \frametitle{\typ{splev}}
-To Evaluate a B-spline and it's derivatives
+To Evaluate a spline and it's derivatives
 \begin{lstlisting}
-In []: Xnew = arange(0.01,3,0.02)
+In []: Xnew = linspace(0.01,3,100)
 In []: Ynew = splev(Xnew, tck)
 
 In []: y.shape
 Out[]: (40,)
 
 In []: Ynew.shape
-Out[]: (150,)
+Out[]: (100,)
  
-In []: plot(Xnew, Ynew)
+In []: plot(Xnew, Ynew, '+')
 \end{lstlisting}
 
 \end{frame}
 
+\begin{frame}
+  \frametitle{Interpolated data}
+  \begin{center}
+    \includegraphics[height=2in, interpolate=true]{data/interpolate}
+  \end{center}
+\end{frame}
+
 %% \begin{frame}[fragile]
 %% \frametitle{Interpolation \ldots}
 %% \begin{itemize}
@@ -257,8 +285,8 @@ In []: plot(Xnew, Ynew)
 \end{itemize}
 \begin{center}
 \begin{tabular}{l l}
-$f(x+h)=f(x)+h.f^{'}(x)$ &Forward \\
-$f(x-h)=f(x)-h.f^{'}(x)$ &Backward
+$f(x+h)=f(x)+hf^{'}(x)$ &Forward \\
+$f(x-h)=f(x)-hf^{'}(x)$ &Backward
 \end{tabular}
 \end{center}
 \end{frame}
@@ -277,7 +305,10 @@ Obtain the finite forward difference of y
 \frametitle{Forward Difference \ldots}
 \begin{lstlisting}
 In []: fD = (y[1:] - y[:-1]) / deltax
-In []: plot(x, y, x[:-1], fD)
+In []: print len(fD)
+Out[]: 99
+In []: plot(x, y) 
+In []: plot(x[:-1], fD)
 \end{lstlisting}
 \begin{center}
   \includegraphics[height=2in, interpolate=true]{data/fwdDiff}
@@ -310,27 +341,18 @@ $X$ & $Y$ \\ \hline
 \frametitle{Example \ldots}
 \begin{itemize}
 \item Read the file
-\item Obtain an array of x, y
+\item Obtain an array of X, Y(S)
 \item Obtain velocity and acceleration
 \item use \typ{deltaT = 0.05}
 \end{itemize}
 \begin{lstlisting}
-In []: X = []
-In []: Y = []
-In []: for line in open('location.txt'):
-  ....     points = line.split()
-  ....     X.append(float(points[0]))
-  ....     Y.append(float(points[1]))
-In []: S = array([X, Y])
+In []: S = loadtxt('location.txt')
 \end{lstlisting}
 \end{frame}
 
 
 \begin{frame}[fragile]
 \frametitle{Example \ldots}
-\begin{itemize}
-\item use \typ{deltaT = 0.05}
-\end{itemize}
 \begin{lstlisting}
 In []: deltaT = 0.05
 
@@ -345,18 +367,17 @@ Try Plotting the position, velocity \& acceleration.
 
 \begin{frame}[fragile]
 \frametitle{Quadrature}
-\begin{itemize}
-\item We wish to find area under a curve
-\item Area under $(sin(x) + x^2)$ in $(0,1)$
-\item scipy has functions to do that
-\end{itemize}
-\begin{small}
-  \typ{In []: from scipy.integrate import quad}
-\end{small}
+
+\emphbar{$\int_0^1(sin(x) + x^2)$}
+
+\typ{In []: from scipy.integrate import quad}
+
 \begin{itemize}
 \item Inputs - function to integrate, limits
 \end{itemize}
 \begin{lstlisting}
+%% In []: quad(sin(x)+x**2, 0, 1)
+%% NameError: name 'x' is not defined
 In []: x = 0
 In []: quad(sin(x)+x**2, 0, 1)
 \end{lstlisting}
@@ -406,8 +427,7 @@ In []: quad(f, 0, 1)
 \end{lstlisting}
 Returns the integral and an estimate of the absolute error in the result.
 \begin{itemize}
-\item Look at \typ{dblquad} for Double integrals
-\item Use \typ{tplquad} for Triple integrals
+\item \typ{dblquad}, \typ{tplquad} are available
 \end{itemize}
 \end{frame}
 
@@ -419,9 +439,7 @@ Returns the integral and an estimate of the absolute error in the result.
   \item Functions
     \begin{itemize}
     \item Definition
-    \item Calling
-    \item Default Arguments
-    \item Keyword Arguments
+    \item Calling    
     \end{itemize}
   \item Quadrature
   \end{itemize}
diff --git a/day1/session6.tex b/day1/session6.tex
index 0b5f681..2858a5e 100644
--- a/day1/session6.tex
+++ b/day1/session6.tex
@@ -123,6 +123,7 @@
 %%   % You might wish to add the option [pausesections]
 %% \end{frame}
 
+%%more exercise on plotting
 \section{ODEs}
 
 \begin{frame}[fragile]
@@ -138,7 +139,7 @@ We shall use the simple ODE of a simple pendulum.
 \dot{\theta} &= \omega \\
 \dot{\omega} &= -\frac{g}{L}sin(\theta) \\
  \text{At}\ t &= 0 : \nonumber \\
- \theta = \theta_0\quad & \&\quad  \omega = 0 \nonumber
+ \theta = \theta_0(10^o)\quad & \&\quad  \omega = 0\ (Initial\ values)\nonumber 
 \end{align}
 \end{frame}
 
@@ -149,9 +150,9 @@ We shall use the simple ODE of a simple pendulum.
 \item Define a function as below
 \end{itemize}
 \begin{lstlisting}
-In []: def pend_int(unknown, t, p):
-  ....     theta, omega = unknown
-  ....     g, L = p
+In []: def pend_int(initial, t):
+  ....     theta, omega = initial
+  ....     g, L = 9.81, 0.2
   ....     f=[omega, -(g/L)*sin(theta)]
   ....     return f
   ....
@@ -162,25 +163,22 @@ In []: def pend_int(unknown, t, p):
 \frametitle{Solving ODEs using SciPy \ldots}
 \begin{itemize}
 \item \typ{t} is the time variable \\ 
-\item \typ{p} has the constants \\
 \item \typ{initial} has the initial values
 \end{itemize}
 \begin{lstlisting}
 In []: t = linspace(0, 10, 101)
-In []: p=(-9.81, 0.2)
 In []: initial = [10*2*pi/360, 0]
-\end{lstlisting}
+\end{lstlisting} 
 \end{frame}
 
 \begin{frame}[fragile]
 \frametitle{Solving ODEs using SciPy \ldots}
-\begin{small}
-  \typ{In []: from scipy.integrate import odeint}
-\end{small}
+%%\begin{small}
+\typ{In []: from scipy.integrate import odeint}
+%%\end{small}
 \begin{lstlisting}
 In []: pend_sol = odeint(pend_int, 
-                         initial,t, 
-                         args=(p,))
+                         initial,t)
 \end{lstlisting}
 \end{frame}
 
@@ -308,14 +306,13 @@ In []: pend_sol = odeint(pend_int,
 \begin{frame}[fragile]
 \frametitle{Initial Estimates \ldots}
 \begin{lstlisting}
-  In []: def our_f(x):
-   ....:     return cos(x)-x**2
-   ....: 
-  In []: x = linspace(-pi/2, pi/2, 11)
+In []: def our_f(x):
+ ....:     return cos(x) - x*x
+ ....: 
+In []: x = linspace(-pi/2, pi/2, 11)
+In []: y = our_f(x)
 \end{lstlisting}
-\begin{itemize}
-\item Get the intervals of x, where sign changes occur
-\end{itemize}
+Get the intervals of x, where sign changes occur
 \end{frame}
 
 \begin{frame}[fragile]
@@ -335,7 +332,6 @@ Now use Newton-Raphson?
 \frametitle{Scipy Methods - \typ{roots}}
 \begin{itemize}
 \item Calculates the roots of polynomials
-\item Array of coefficients is the only parameter
 \end{itemize}
 \begin{lstlisting}
   In []: coeffs = [1, 6, 13]