Python/Homework 0

Background

This page comes from an assignment Dr. G would give out to classes that have EGR 103 as a pre-requisite to give an idea of what kinds of computational abilities might come into play over the course of the semester. The assignment was not graded, but students were expected to complete it and ask questions about any topics they were unsure of. Given that, it might as well live on Pundit! Both MATLAB and Python solutions are available, though starting in Fall of 2021 the last of the MATLAB EGR 103 students will have generally graduated and so most people will be using Python. If you did not take EGR 103 or CS 101 (i.e. you have never seen Python), there will be some Pundit pages that should help out.

Problems

Linear fit

Many systems you will be learning about have some kind of linear relationship between an applied field and a measured response. This problem explores that for a circuit and the relationship between the voltage across an element and the current through it. There is a link below to data sets for ten experimental runs where a particular voltage was applied to an element and the current through it was measured. Write code that automates the process of

• Loading data from a file,
• Determining the line of best fit for the current as a function of the voltage, and
• Storing the slope and intercept of the fit into arrays called slope and intercept, respectively.

Once all data files are processed, print a table with results of all 10 runs to the screen using scientific notation for all the numbers and making sure the numbers line up under each other. Note that the slopes will generally be positive but the intercepts may be negative.

References

• Python:Iterative Structures - loops in Python
• Python:Flexible Programming - a couple ways to look for files in a folder and load them
• Python:Fitting - how to do curve fits in Python; for this problem, you only need Python:Fitting#Polynomial_Fitting
• https://peps.python.org/pep-3101/#format-strings and https://peps.python.org/pep-3101/#standard-format-specifiers for formatting strings

Answers

Your code should end up displaying the following:

     Slope  Intercept
 5.787e+00  1.440e-01
 4.640e+00  3.912e-02
 5.934e+00  1.174e-01
 5.234e+00  9.758e-02
 4.898e+00  1.168e-01
 5.923e+00  1.745e-01
 4.179e+00 -9.780e-02
 5.296e+00  8.575e-02
 5.206e+00  1.369e-01
 5.205e+00  4.678e-02

Solutions

Python

MATLAB

%% Initialize workspace
clear; format short e

%% First line of table
fprintf('%10s %10s\n', 'Slope', 'Intercept')

%% Initialize variables
N = 10;
slope = zeros(N, 1);
intercept = zeros(N, 1);

%% Loop to find, store, and print slope and intercept
for k=1:10
    eval(sprintf('data = load(''file%02.0f.dat'');', k));
    v = data(:, 1);
    i = data(:, 2);
    p = polyfit(v, i, 1);
    slope(k) = p(1);
    intercept(k) = p(2);
    fprintf('%10.3e %10.3e\n', slope(k), intercept(k))
end

Nonlinear Fit

Some of the elements you will be learning about have nonlinear relationships. In this case, you will once again be looking at the relationship between the voltage across an element and the current through it, but this time,. the element is nonlinear. There will be a link to a file below containing measurements from a circuit with an independent voltage source connected to a 1 k$$\Omega$$ resistor and an LED in series. The file has three columns. The first is total voltage across the resistor and LED; it turns out you won't need to do anything with this one. The second is the voltage over the resistor; you will divide this by 1000 to get the LED current. The third is the voltage across the LED; you will use this as the LED voltage. Given a model of: $$ \begin{align*} i&=Ae^{Bv}+C \end{align*} $$ use nonlinear regression to determine values for $$A$$, $$B$$, and $$C$$. Good initial values for the three coefficients are 1e-15, 20, and 0, respectively. Make sure the values are displayed onscreen. Once you have calculated the values, make a plot of the current through the LED as a function of the voltage across the LED that has a curve for the original data as a solid black line and the model as a dashed green line. Label the axes, include a legend, and turn on the grid.

References

Answers

Solutions

Python

MATLAB