CS122 Engineering Computation Lab Lab 3 Bruce Char Department of Computer Science Drexel University Winter 2012

Major Lab 2 concepts to remember Review of Lab 2 Cycle Major Lab 2 concepts to remember Use of “while” versus “for” loops – when each is appropriate “if” statement enables program to choose between execution paths Troubleshooting / debugging Review the “purple” error messages to understand nature of error (sometimes clear, other times not) Syntax errors – check to see where cursor is blinking within the code edit region

Administrative Notes Please contact your individual instructors with questions and problems CLC (room 147 UC) will be staffed from Monday through Friday (odd – quiz - weeks) – 9 AM to 5 PM In order to be eligible for a lab completion session, please see you instructor at the end of the lab period In order to be eligible for a makeup lab session, you must contact your instructor for permission as soon as you miss your regularly scheduled lab

Lab 3 Overview Based on materials from Chapter 13 and 14 readings More on user defined functions as represented by Maple proc We define them and then invoke them to draw things. We chain functions together to get more complicated drawings. Using Maple tables to store a collection of data How to initialize them How to get a program to enter values into a table How to use all the values you’ve put into a table in a plot Multiple assignment Return multiple proc results as a sequence of variables Revisit / introduce key plotting concepts line plots display feature to enable multiple plots on same grid Plotting data collected / stored in Maple tables Plot options – titles, labels, colors

Lab 3 Overview – Part 0 Part 0.1 – plotting (line and display), proc function Part 0.2 – introduction to Maple tables and multiple assignments, more on proc usage Part 0.3 – more on plotting (plot options), procs

Lab 3 Overview – Part 1 Part 1 – User defined functions that draw things (boxes) A. - proc to draw rectangular boxes anchored at origin B. - expand proc from part A. to specify line color and an anchor point other than origin C. – use of proc developed in B. to draw multiple boxes on same grid Will be using proc from part B. in Lab 4 as starting point for simulation of a particle bouncing around in a box

Lab 3 Overview – Part 2 Use a loop and tables to simulate a “time staged” chemical reaction involving 4 chemicals 2.1 – Calculate the levels of the 4 chemicals as they change over time. Plot the levels of one of the chemicals as it changes over time Utilizes a proc to encapsulate the simulation code and to pass in the number of time steps as an input parameter 2.2 – Extend the proc of 2.1 to : calculate and plot the levels of all 4 chemicals on the same graph Pass in initial concentration of all 4 reaction components as input parameters 2.3 – conduct analysis of simulation results from 2.1, 2.2

Lab 3 programming concepts More about procs The Maple proc is a user defined function in which: You can pass parameters into the proc You can include multiple statements You can (optionally) return a computed value or series of values Example Quadratic := proc(a,b,c) local x1, x2; X1 := (-b + sqrt(b^2-4*a*c)) / (2*a); X2 := (-b - sqrt(b^2-4*a*c)) / (2*a); return X1, X2; # returns a sequence of numeric results end proc; X1solution, X2solution := Quadratic(1, 1, -12); Note that this example contains a multiple assignment of results

Lab 3 programming concepts Working with Maple Tables While a Maple list can hold a series of values, it is not ideal for storing information that is being created dynamically within a loop Maple tables contain values that all have the same variable name and are differentiated by subscripts Tables are especially useful in conjunction with loops, where the loop counter variable can be used to represent the subscripts Working with tables usually requires: Declaration of the table Storage of data in the table within a loop Possible conversion of the table to an equivalent list for use in processes (such as plots) which require lists as input The example on the next slide illustrates using a table to collect points for subsequent plotting – as in Part 2 of today’s lab

Using Maple Tables to collect data for plotting chemical reaction compositions # Set up initial concentrations A := A0; B := B0; X := X0; Y := Y0; # declare tables indexTab := table(); Atab := table(); for i from 1 to numTimeSteps do newA := A - k1*A*X; … A := newA; indexTab[i] := i; Atab[i] := A; end do: # within Fplot, indexTab and Atab tables are converted to lists display([Fplot(indexTab,Atab,"Green")], title="graph of A", labels=["time", "concentration"]);

Lab 3 programming concepts A word about time staged simulations We introduce time staged simulations in the chemical reaction exercise in today’s lab – Part 2 In a time staged simulation, the loop steps represent time slices Each iteration of the loop calculates the next generation of values based on correlations using the present generation In today’s chemical reaction, the concentrations the of 4 reaction components are computed for the next generation (step) from their current values and other coefficients newA := fn(previousA, B, X, Y) newB := fn(previousA, B, X, Y) newX := ………….. newY := …………..

Lab 3 programming concepts And finally, some Maple plot features we’ll be using today Line plotting Requires with(plottools); Format  line( [x1, y1], [x2, y2] ) Display multiple plots on same grid Requires with(plots); Format  display( [line([x1,y1], [x2,y2]) , line([x3,y3],[x4,y4])], color=red); Plot points contained in X and Y coordinate lists xList := [1, 2, 3, 4, 5]; yList := [2, 4, 6, 8, 10]; Plot(xList, yList, style = point, title=“sometitle”, labels=[“x-axis”, “y-axis”]); Converting tables to lists (plot commands require Maple lists) xList := convert(xTab, list); yList := convert(yTab, list);

Course activities for Quiz week (2/20-2/24) Quiz 3 will be released on Friday (2/17) at 6 PM Deadline: Thursday (2/23) at 4:30 PM Makeup quiz – from Friday (2/24) at 9 AM through Sunday (2/26) at 11:00 PM 30% penalty Pre-lab 3 quizlet From Thursday (2/23 – noon) through Monday (2/27 – 8 AM) Be sure to visit the CLC for quiz assistance