Lab 4: Structured Programming I

Transcription

1 4.1 Introduction Lab 4: Structured Programming I Lab this week is going to focus on selective structures and functions. 4.2 Resources The additional resources required for this assignment include: 0 Books: Punch & Enbody 0 Pratt Pundit Pages: Python:Logical Masks, Python:Plotting 0 Lab Manual Appendices: None 4.3 Getting Started 1. Log into one of the PCs in the lab using your NetId. Be sure it is set to log on to WIN. 2. In Windows: (a) Mount your CIFS drive. For instructions, start a browser and point it to: To Get Work Done Then click the link for File Access under Your Own Windows Computer. Note the comments on Pundit modifying what the OIT page instructions say. (b) Start a terminal with graphics. For instructions, point a browser to Check out the Using the PCs to Run Unix Programs Remotely section for how to get connected and make sure the connection is working. (c) Start Spyder. In the Windows menu, there is a group for Anaconda3; Spyder is in that group. If the PC asks for network permissions, click cancel. If the PC asks about updating, do not update. 3. In the terminal window (i.e. in UNIX; note the represents a space): (a) Change into your folder for EGR 103L, create a lab4 folder inside it, then switch into that folder: cd /EGR103 mkdir lab4 cd lab4 (b) Copy the tar file from Dr. G s space into your lab4 folder and expand the tar file: wget people.duke.edu/ mrg/egr103public/lab4files.tar tar -kxvf Lab4Files.tar (c) Make a personal copy of the lab report skeleton: cp -i Lab4Sample S19.tex lab4.tex 4 1

2 4.4 Ungraded You should look at, and if possible work on, 0 P&E Chapter 2 Exercises 1, 2, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16 (very similar to hms), 17 (perfect square means square root is an integer), 20, 22 (heh heh), 24, 25, 26, 28, 35, and 40. For these ungraded problems, you can compare answers and processes with classmates. Do not share answers outside of those people currently taking the course. 4.5 Assignment Sinusoidal Functions A sinusoid is an oscillating function of some independent variable that can generally be written with three parameters - an amplitude, an angular frequency, and a phase shift. For purposes of this problem, the sinusoid you will be working with is a generic cosine: y(t A ω φ) = A cos (ωt + φ) where t is the independent variable, A is the amplitude, ω is the angular frequency in radians per second, and φ is the phase shift in radians. You should start by defining a function called y(t, A, omega, phi) that will return values based on the calculation above. Because you will eventually want the function to return an array of values, you will need to use NumPy s version of the cos function. Your goal is to examine how each of the parameters changes the sinusoid by putting four different sinusoids on one graph. Each will have its own line color and style as well as marker shape, edge color, and face color. You will need to include a legend. The following table gives all the details you need about each sinusoid: y(t A ω φ) line style line color marker marker edge marker face y(t 1 1 0) solid blue triangle up red magenta y(t 2 1 0) dashed yellow square red magenta y(t 1 2 0) dotted blue pentagon cyan magenta y(t 1 1 π/4) dash-dot blue hexagon (1) red green Graph the lines using 101 values between 2π and 2π. You already know the plot commands to make this part work. For the markers, you are going to tell the plot command to only mark every tenth data point; you can do this by putting markevery=10 in the plot command. There is information on the Python:Plotting page on Pundit about this. Furthermore, there are some other adjustments to be made: 0 Information on the different keyword arguments you need to make these adjustments is at: https :// matplotlib. org / api / _as_gen / matplotlib. pyplot. plot. html 0 The marker size will be The edge color and the face color will be different - to accomplish this, you can give one of the two colors in the format string and then assign the other using a keyword argument. For example, if you wanted black diamonds filled with cyan, and assuming you already created a set of axes called ax you could use either of the following two codes: ax. p l o t ( x, y, kd, m a r k e r f a c e c o l o r= c ) ax. p l o t ( x, y, cd, markeredgecolor= k ) Furthermore, as given on the HTML page referenced above, there are shortcut names such as: ax. p l o t ( x, y, kd, mfc= c ) The legend entries will be associated with the point styles and should look like y(t, 1, 1, 0) - note that you can get Spyder to put LaTeX-like symbols in legends by surrounding the appropriate LaTeX command with dollar signs. Your legend will likely end up being on top of part of your lines - that is fine for this week. You do not need labels or a title. In the body of the lab report, discuss how you think A, ω, and φ changed each curve. 4 2

3 4.5.2 Based on P&E 4.48 Instead of what is asked for in the problem, write a function called mult_table that takes up two two inputs - a number of rows and a number of columns to use in making a multiplication table. You may assume that the values given will be integers between 1 and 30 for each. The default values for each should be 12. The table should have a column header and row labels. Regardless of how many rows and columns, your program should leave two spaces for the row index and then four spaces for each value in the table. For example: In [ 1 ] : m u l t t a b l e ( 3, 7 ) will produce the following (where represents a space): When done, run the test_table.py script. This program will run three tests and produce outputs on the screen and then it will run the same three tests but will redirect the results to a text file. That text file should be imported to your lab document P&E 2.32 In addition to what is stated in the problem, assume that neither A nor C will be equal to 0. There is no requirement that A, B, or C be unique, however. There are more and less efficient ways of solving this problem. One quick thing to think about is the following: can you narrow down the possibilities for B in advance of writing the code? For each set of A and B values your program finds that work, your script should end by printing out a line such as: AB **2 is CAB but with your numbers in the place of the A, B, and C. For example, if your code (incorrectly) decided that A=7 and B=6 work, your code would print out: 76** 2 is 5776 You should indicate the values of A, B, and C in the body of your lab report. Note: the reason the example above does not work is that the resulting square is not a three-digit number as specified in the problem While it is possible for you to solve this without a computer - that is not the point. Your code needs to be written such that it scans through all - or a reasonable subset of - the possible combinations of A and B and checks to see which work P&E 2.38 You will be writing a function called digit_sum() which will take a single non-negative integer as an input and will return the single-digit sum described in the book. After thinking about how you the human would do this problem, you next need to think about how Python deals with numbers. One hint is that the // and % operations might come in very handy when thinking about how to isolate and all all the digits in a number together. One critical thing to note here is that the program may need to act recursively - that is, in cases where the result of adding all the digits together is still a number greater than 10, the function should then run on that new number. Try to get your function to first provide the initial sum of digits - for example, get to the point where digit_sum(827) returns 17. Then consider efficient ways to have to code continue calculating if need be or report out a value if done. There is a tester code to generate a diary of results - include those results in your lab report Based on Chapra Problem 3.10 This problem comes from Civil Engineering, and the methods used to solve it are used in classes taken by all engineers. It primarily relates to the Grand Challenge of restoring and improving urban infrastructure because it demonstrates a means of finding the amount of deflection experienced by a structural beam - something it is critical to understand before pursuing studies in this field. Though used on a beam in this problem, singularity functions show up at some point in every engineer s field of study. This problem is therefore an introduction to a mathematical and computational method that engineers have used to simplify the solution and analysis of many different problems - part of engineering the tools of scientific discovery. To solve this problem, you will use a function called Singularity to take an input array x, the shift value a, and the power n and return the result of the singularity function. 4 3

4 The function includes a logical mask - see the Pratt Pundit page for more information and for examples of logical masks. You can see how this function works with a linearly spaced array of points and several different values of the shift a and power n. The test_singularity.py code will be used to demonstrate this function. Note that for the lab you will not be including this example code or graph as a part of the document since it is purely an example - the graph and the code to make it are also on the shown below: Figure 4.1: Plots of y =< x a > n for different values of a and n 1 import numpy as np 2 import m a t p l o t l i b. pyplot as p l t 3 4 def s i n g u l a r i t y ( x, a, n ) : 5 return ( x > a ) 1 ( ( x a ) 1 1n ) 6 7 i f name == m a i n : 8 x = np. l i n s p a c e ( 2, 5, 500 ) 9 f i g, ax = p l t. s u b p l o t s (num=1 ) 10 f i g. c l f ( ) 11 f i g, ax = p l t. s u b p l o t s (num=1 ) ax. p l o t ( x, s i n g u l a r i t y ( x, 1, 0 ), k, 14 x, s i n g u l a r i t y ( x, 0, 1 ), r, 15 x, s i n g u l a r i t y ( x, 1, 1 ), g., 16 x, s i n g u l a r i t y ( x, 3, 2 ), b : ) 17 ax. legend ( l a b e l s =[ 2<x+1>ˆ02, 2<x>ˆ12, 18 2<x 1>ˆ12, 2<x 3>ˆ22 ], l o c= b est ) 19 ax. s e t t i t l e ( Four D i f f e r e n t Values o f 2y=<x a>ˆn2 ( NetID ) ) 20 ax. s e t x l a b e l ( x ) 21 ax. s e t y l a b e l ( y ) 22 ax. g r i d ( True ) 23 f i g. t i g h t l a y o u t ( ) 24 f i g. s a v e f i g ( S i n g P l o t s. eps ) 25 f i g. s a v e f i g ( S i n g P l o t s. pdf ) Table 4.1: test singularity.py code to generate graph in Figure

5 Next, write a script that uses the function to calculate the deflection u of a beam with nearly the same loading diagram in the book, except the torque being applied is 325 kip-ft instead of 150 kip-ft. This changes the equation to: u y x) = 5 6 x 0 4 x x x x x You will need to copy the singularity function from the test_singularity.py to your new code. Be sure that the plot has a proper title (with NetID) and axis labels. With respect to the original figure, a kip is equal to a kilo-pound, or 1000 lbs. 1 The x-axis of your plot will be measured in feet while the y-axis will not have units since units are not specified in the book. For the lab report, you must include your script which has all the code to analyze the beam, as well as the plot of the beam s deflection. In the body of the lab report, you will report what the maximum positive (up) and maximum negative (down) displacements are and approximately where along the beam those values can be found. Be sure to include units for the locations of the largest displacements; again, you will not need units for the displacements themselves since the book does not provide them. You should use 100 points for the x coordinates of the plot and 10 6 points to determine and locate the extreme displacements. For information on how (and why) to do this, see the Pratt Pundit page on Python:Plotting, specifically the section called Using Different Scales. less. As opposed to Kip, who is the Electrical and Computer Engineering Department Laboratory Manager and weighs significantly 4 5