Computational Physics-Project 2 Bad Data Solved

Data processing is one of the most common activities that software is designed to perform. One of the largest data producers and consumers in the world is the US National Oceanic and Atmospheric Administration (NOAA). They collect data from a myriad of sensors all over the globe measuring temperature, barometric pressure, wind speed, tidal currents, and more to predict future weather patterns. However, sometimes sensors malfunction and either provide incorrect information, as seen by the temperature sensor that contributed to the Artemis I launch being scrubbed, or they fail to collect any information at all. In cases where no data is collected, interpolation can be used by selecting data that is in close proximity to the gap, taking the average of that data, and using the resulting value to fill the gap. Additionally, in order to verify that such methods are effective, if no real data is available, synthetic data can be generated that mimics the real data.

For this project, you will be creating a program that can generate and then interpolate synthetic temperature data. Your program will provide the user with a menu of options that include the ability to create a new synthetic temperature dataset of a desired size, the ability to interpolate holes in that dataset using the surrounding data or using the entire dataset, and the ability to compare the original dataset to the interpolated dataset.

Program Requirements 

•       As with all projects in this course, your program should have a comment at the top that includes your name, the date the program was created, and a brief description of the project, in your own words

•       Import any required libraries

•       All variables must be declared inside of functions, and no global variables are allowed

•       Define a new function named main that takes in no arguments o Create a variable to store a List representing the synthetic data and initialize it to the values  

▪ -1,391,408,403,389,-1,439,397,429,410,-1,-1,-1,435,-1,351,415,401,415,-1 o Create a variable to store a List representing the interpolated data and initialize it to an empty List

o Output an appropriate welcome message to the user o Declare a variable to store the user’s menu choice and initialize it to an appropriate value o Create a loop of your choice that allows the user to repeatedly choose menu options until the choose the option to quit the program

▪  Call the function to output the menu and store the result in an appropriate variable

▪  If the user enters 1, call the function to generate synthetic data and store the result in the appropriate List variable

▪  If the user enters 2, 3, or 4, call the function to interpolate the data, passing in the appropriate number of minutes on either side of incorrect data to interpolate across and the synthetic data List, and store the result in the appropriate List variable

▪  If the user enters 5, call the function to interpolate across all of the data, passing in the synthetic data List, and store the result in the appropriate List variable

▪  If the user enters 6, call the function to compare the data, passing in the synthetic data

List and the interpolated data List

▪  If the user enters 7, output an appropriate exit message

▪  If the user enters anything else, politely inform them of their mistake

•       Define a new function named menu that takes in no arguments o Provide the user with the following numbered menu options

▪  Generate a synthetic dataset

▪  Interpolate with 2 minutes

▪  Interpolate with 4 minutes

▪  Interpolate with 6 minutes

▪  Interpolate with all minutes

▪  Output data comparison

▪  Exit o Prompt the user for a choice o Return the user’s input

•       Define a new function named outputValues that takes in a List containing a series of values and a String representing the prefix for the line o Output the prefix o On the same line as the prefix, output each of the values

▪  Note, this function can be used to output multiple types of values such as minutes and temperatures, however the data should line up vertically, so make sure you take that into account when designing the output

▪  See example output for an example o Output an empty line

•       Define a new function named generateDataset that takes in no arguments o Prompt the user for a number of minutes (10 or more) to generate data for

▪ If the user enters a number less than 10, politely inform them of their mistake and repeatedly prompt them for a new value until they provide something 10 or greater

o   Declare an empty List to store the temperatures

o   Using the number of minutes the user entered, for each minute ▪ Generate an integer between 1 and 5

•       If the integer is 5, add a -1 to the List indicating that no data was collected for that minute

•       Otherwise, add a random integer between 350 and 450, inclusively, to the List of temperatures

o   Using the appropriate function, output each of the minutes on the same line with the prefix “Min:”

o   Using the appropriate function, output the generated temperature for each of the minutes in the List, on the same line, with the prefix "Temp:”

o   Return the List of temperatures

•       Define a new function named calcMean that takes in a List containing a series of temperatures o Calculate the mean across all of the temperatures  

▪  Note if the temperature is -1, ignore it and do not include it in the calculation o If all of the temperatures in the List were -1, return a -1 o Otherwise, return the mean

•       Define a new function named calcVariance that takes in a List containing a series of temperatures, and a number representing the mean temperature o Calculate the variance across all of the temperatures  

▪  Note if the temperature is -1, ignore it and do not include it in the calculation

▪  Remember the equation to calculate variance is ∑ (𝑥− 𝑥̅)2 where:

𝑛−1

•       𝑥 is a temperature

•       𝑥̅ is the mean temperature • 𝑛 is the number of temperatures

o Return the variance

•       Define a new function named interpolateMinutes, that takes in an integer representing the number of minutes to use in interpolate and a List containing a series of temperatures o Output how many minutes are being used to interpolate with o Declare an empty List to store the interpolated data o For each temperature in the passed in List ▪ If the temperature is -1

•       Extract the values to the left and right of the temperature, based on the number of minutes specified, and create a new single List containing all of those values

•       Using the appropriate function, calculate the mean of those temperatures

•       Append the mean to the List of interpolated data

•       Note, if the -1 temperature is at the beginning or end of the List, only use the available temperatures to calculate the mean

▪ Otherwise, append the temperature to the List of interpolated data o Return the List of interpolated data

•       Define a new function named interpolateGlobal, that takes in a List containing a series of temperatures o Output that all minutes are being used for interpolation o Declare an empty List to store the interpolated data o Using the appropriate function calculate the mean of the List of temperatures and store it in an appropriate variable

o For each temperature in the passed in List ▪ If the temperature is -1

•       Append the mean to the List of interpolated data

▪ Otherwise, append the temperature to the List of interpolated data

o Return the List of interpolated data

•       Define a new function named compareData, that takes in a List containing the synthetic temperatures and a List containing the interpolated temperatures o If interpolation has not been performed yet, inform the user that they must use one of the interpolation functions first, and then return from this function

o   Using the appropriate function, output each of the minutes on the same line with the prefix

“Min:” o Using the appropriate function, output the temperature for each of the minutes in the synthetic

List, on the same line, with the prefix "Temp:” o Using the appropriate function, output the temperature for each of the minutes in the interpolated List, on the same line, with the prefix "Temp:”

o   Using the appropriate function, calculate the mean of the synthetic temperatures and then output it with two decimal points of precision and an appropriate message

o   Using the appropriate function, calculate the variance of the synthetic temperatures and then output it with two decimal points of precision and an appropriate message

o   Calculate the standard deviation of the synthetic temperatures and then output it with two decimal points of precision and an appropriate message

▪  Remember that standard deviation is the square root of the variance o Using the appropriate function, calculate the mean of the interpolated temperatures and then output it with two decimal points of precision and an appropriate message

o   Using the appropriate function, calculate the variance of the interpolated temperatures and then output it with two decimal points of precision and an appropriate message

o   Calculate the standard deviation of the interpolated temperatures and then output it with two decimal points of precision and an appropriate message

▪  Remember that standard deviation is the square root of the variance o Using matplotlib:

▪  Plot the synthetic temperatures in red using the marker o

▪  Plot the interpolated temperatures in blue using the marker o

▪  Set the title of the plot to “Synthetic Data vs Interpolated Data”, with a font size of 14

▪  Set the x label of the plot to “Minutes”, with a font size of 14

▪  Set the y label of the plot to “Temperature”, with a font size of 14

▪  Set the grid to True

▪  Show the plot

▪  Note that plots will appear in the Plots pane in Spyder

•       Call the main function

•       Your code should be well documented in terms of comments. For example, good comments in general consist of a header (with your name, date, and brief description), comments for each variable, docstrings describing each function, and commented blocks of code

•       Your program source code should be named TempSense.py