Initial upload of work from monday.

students/one-pavelG/data/data.txt

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+ 3       -4.621424         
+ 3.25	 -5.804482    
+ 3.5	 -6.70809     
+ 3.75	 -7.398549    
+ 4	 -7.922563    
+ 4.25	 -8.316091    
+ 4.5	 -8.606262    
+ 4.75	 -8.813852    
+ 5	 -8.954821    
+ 5.25	 -9.042461    
+ 5.5	 -9.08705     
+ 5.75	 -9.0977	     
+ 6	 -9.07705     
+ 6.25	 -9.03505     
+ 6.5	 -8.9743	     
+ 6.75	 -8.8984	     
+ 7	 -8.8103	     
+ 7.25	 -8.7122     
+ 7.5	 -8.60665     
+ 7.75	 -8.4949	     
+ 8	 -8.3785	     
+ 8.25	 -8.2585	     
+ 8.5	 -8.1362	     
+ 8.75	 -8.0118	     
+ 9	 -7.88685     
+ 9.25	 -7.7615	     
+ 9.5	 -7.63665     
+ 9.75	 -7.51265     
+ 10	 -7.3898      
+

students/one-pavelG/data/data_p.txt

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+
+    v= [3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5, 5.25, 5.5, 5.75, 6, 6.25, 6.5, 6.75, 7, 7.25, 7.5, 7.75, 8, 8.25, 8.5, 8.75, 9, 9.25, 9.5, 9.75, 10]
+
+    e= [-4.621424, -5.804482, -6.70809, -7.398549, -7.922563, -8.316091, -8.606262, -8.813852, -8.954821, -9.042461, -9.08705, -9.0977, -9.07705, -9.03505, -8.9743, -8.8984, -8.8103, -8.7122, -8.60665, -8.4949, -8.3785, -8.2585, -8.1362, -8.0118, -7.88685, -7.7615, -7.63665, -7.51265, -7.3898]

students/one-pavelG/instructions.txt

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+
+Project One: a simple data analyiss program and using git.
+
+The goal of the first project is to write a complete program to read in x-y data from a file and calculate least squares regression to this data. We will first do a linear regression using a parabolic model. Later we will add a nonlinear regression using a solid state equation of state called the Murnaghan equation.
+
+While developing your program you are tracking your development using git.
+Commit your project apporixmately after you have achieved the following milestones.
+
+Before you start do these 2 steps.
+1- Initialize your name and email for git (see cheat sheet):
+
+git config --global user.name "[name]"
+git config --global user.email "[email address]"
+
+2- Copy the project directory projects/one into the student subdirectory with your initial added like
+
+cp -r projects/one students/one-gs
+
+Work and make changes in this directory only. 
+
+1 - Read the data from file and create x and y data.
+2 - Add a plot of your data.
+3 - Perform a linear regression to a parabolic function using for example
+    (numpy/polyfit)
+    Update your graph.
+    Extract the minimum and the curvature from your linear regression.
+
+4 - Observe the performance of your regression and think about the validity of  a quadratic approximation. Improve your linear regression by restricting your data to a few points (how many is reasonable?) around the minimum.
+
+Optional:
+
+5 - Perform a nonlinear regression to the Murnaghan equation of state
+    (wikipedia: https://en.wikipedia.org/wiki/Murnaghan_equation_of_state)
+    using for example (numpy/curvefit) Update your graph.
+
+
+

students/one-pavelG/script.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+data = np.loadtxt('data/data.txt')
+
+X = data[:,0]
+Y = data[:, 1]
+
+coef = np.polyfit(X, Y, 2)
+fit = np.poly1d(coef)
+fitted_data = fit(X)
+
+
+f, ax = plt.subplots()
+ax.scatter(X, Y, label = 'Real Data')
+ax.plot(X, fitted_data, label = 'Quadratic Fit')
+ax.set_title('Quadratic Fit Plot')
+ax.legend()
+plt.show()
+
+
+crit = fit.deriv().r
+
+print('If we complete the square on the equation we get the following formula:')
+print('0.226729 * (x − 6.74078)^2 − 9.14145')
+print('Which means the minimum point of the fitted parabola is at X =', crit)
+print('and the curvature is 0.226729')
+
+X_alt = X[5:16]
+Y_alt = Y[5:16]
+
+coef_alt = np.polyfit(X_alt, Y_alt, 2)
+fit_alt = np.poly1d(coef_alt)
+fitted_data_alt = fit_alt(X_alt)
+
+
+f, ax = plt.subplots()
+ax.scatter(X_alt, Y_alt, label = 'Real Data')
+ax.plot(X_alt, fitted_data_alt, label = 'Quadratic Fit')
+ax.set_title('Modified Quadratic Fit Plot')
+ax.legend()
+plt.show()
+
+print('Using a subsection of the data allows for a closer fit as')
+print('the data is much more quadratic on the left side of the mininum')