ENGR-25_Programming-3.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Chp4 MATLAB Programming-3

ENGR-25_Programming-3.ppt 2 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Learning Goals  Write MATLAB Programs That can MAKE “Logical” Decisions that Affect Program Output  Write Programs that Employ LOOPing Processes For → No. Loops know a priori while → Loop Terminates based on Logic Criteria

ENGR-25_Programming-3.ppt 3 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods if Decision Statement  The if Statement Basic Form if logical expression statements end  Every if statement must have an accompanying end statement. The end statement marks the terminous of the statements that are to be executed if the logical expression is true. Start if Logical Expression Statements end Statements True False

ENGR-25_Programming-3.ppt 4 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods else Decision Statement  else Statement Basic Form if logical expression Statement Group-1 else Statement Group-2 end Start if Logical Expression Statements-1 end Statements True False Statements-2

ENGR-25_Programming-3.ppt 5 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Logical Expression on Arrays  When the test, if logical expression, is performed, where the logical expression may be an ARRAY, the test returns a value of true only if ALL the elements of the logical expression evaluated as true “Logic Gate” equivalent statement (“and”) –ALL High → Output High –ELSE Output Low

ENGR-25_Programming-3.ppt 6 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Logical Array Example  For example, if we fail to recognize how the test works, the following statements may not perform as expected x = [4,-9,25]; if x < 0 disp(’Some elements of x are negative.’) else y = sqrt(x) end  Because the test if x < 0 is false, when this program is run it gives the result y = i

ENGR-25_Programming-3.ppt 7 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Logical Array Example cont  Now Fine-Tune to Test for Positive x x = [4,-9,25]; if x >= 0 y = sqrt(x) else disp('Some elements of x are negative.') end  This File Produces Only the Message Some elements of x are negative.  The test if x = 0 also returns a false value because x >= 0 returns the vector [1,0,1]. ENTIRE Statement is FALSE since ONE element is False

ENGR-25_Programming-3.ppt 8 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Combine Decisions & Logicals  The following statements if logical expression 1 if logical expression 2 statements end end  Can be written more Concisely with if logical expression 1 & logical expression 2 statements end

ENGR-25_Programming-3.ppt 9 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Example: Decisions & Logicals  The Code r = 7; s = -11; % Double if if r < 13 if s > -17 t = log(abs(r)+abs(s)) end end % if-n-& if (r < 13)&(s > -17) q = log(abs(r)+abs(s)) end  The OutPut t = q =

ENGR-25_Programming-3.ppt 10 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods The elseif Statement  The elseif Statement Basic Form if logical expression 1 statement group 1 elseif logical expression 2 statement group 2 else statement group 3 end The else statement must come AFTER the elseif statement to since the else yields the DEFAULT result Default

ENGR-25_Programming-3.ppt 11 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods elseif FlowChart Start if Logical Expression Statements-1 end Statements elseif Logical Expr True else Statements-2 True Statements-3 else

ENGR-25_Programming-3.ppt 12 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods elseif Example  Given y = log(x) for x > 10 y = sqrt(x) for 0 <= x <= 10, y = exp(x) - 1 for x < 0  The Following finds y for given user input for x x = input('enter scalar: x = ') if x > 10; z = log(x); elseif x >= 0 z = sqrt(x); else z = exp(x) - 1; end % output to user y = z  The InPut & OutPut x = y =

ENGR-25_Programming-3.ppt 13 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Nested if FlowChart Start x < 13? y = sinh(x) Yes y, z out y > 43? y = 7.3x z = -19x + 29 y  17? z = √yz = y 1.89 z = 0 No Yes  Nesting if statements is a alternative to the elseif form

ENGR-25_Programming-3.ppt 14 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Strings  A STRING is a variable that contains Characters. Strings are useful for creating input prompts & messages, and for storing & operating on data such as names and addresses  To create a string variable, enclose the characters in single quotes. For example, Create string variable NYgiant : >> NYgiant = 'Mel Ott' NYgiant = Mel Ott

ENGR-25_Programming-3.ppt 15 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Strings cont  The following string, digits, is not the same as the variable number created by typing digits = 987. >> digits = '987' digits = 987 >> p = log(digits) ??? Function 'log' is not defined for values of class 'char'. No Indent for String

ENGR-25_Programming-3.ppt 16 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Strings & the input Statement  The prompt program on the next slide uses the isempty(x) function, which returns a 1 if the array x is empty and 0 otherwise  The Program also uses the input function, with syntax  This function displays the string prompt on the screen, waits for input from the keyboard, and returns the entered value in the string variable x. The function returns an empty matrix if you press the Enter key without typing anything. x = input(’prompt’, ’string’)

ENGR-25_Programming-3.ppt 17 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Strings and Decisions  The following prompt program is a script file that allows the user to answer Yes by typing either Y or y or by pressing the Enter key. Any other response is treated as the answer No. response = input('Want to continue? Y/N:','s') if (isempty(response))|(response==’Y’)| response==’y’) response = ’Y’ else response = ’N’ end

ENGR-25_Programming-3.ppt 18 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Display Str&Double on SAME Line >> disp(['the SqRt of "e" is ', num2str(exp(1/2), 7), '; a nice result ;-)']) the SqRt of "e" is ; a nice result ;-) >> Eto3_7_Ltrs = num2str(exp(3.7), 11) Eto3_7_Ltrs = >> disp(['e to 3.7 pwr = ', Eto3_7_Ltrs]) e to 3.7 pwr =

ENGR-25_Programming-3.ppt 19 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Example: Prob 4-20  Given Spring- Loaded Platform  In This Case the ENGR36 Force- Balance Model  In ENGR36 we Learn that the Spring Force Where –k  the “Spring Constant” in N/m –x  the Compression Distance in m

ENGR-25_Programming-3.ppt 20 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Problem 4-20 cont  Find or Create a.A Function to find x given W, k 1, k 2, and d b.A Plot of x vs. W for 0  W  3000 N given –k 1 = 10 kN/m = 10 N/mm –k 2 = 15 kN/m = 15 N/mm –d = 100 mm  Solve Force-Balance Eqns for x

ENGR-25_Programming-3.ppt 21 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods The Prob 4-20 Plots  Before Brk-Pt  After Brk-Pt

ENGR-25_Programming-3.ppt 22 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods All Done for Today A Nice Spring Platform

ENGR-25_Programming-3.ppt 23 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Appendix

ENGR-25_Programming-3.ppt 24 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob 4-20: spring_plat.m

ENGR-25_Programming-3.ppt 25 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Prob-20 Test Session  Case-1 → W = 500N >> spring_plat(500,10e3,15e3,0.1) The Compression distance in m, x =  Case-2 → W = 2 kN >> spring_plat(2e3,10e3,15e3,0.1) The Compression distance in m, x =

ENGR-25_Programming-3.ppt 26 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods.m-file = Prob4_20_plot.m  Documentation & Inputs % Bruce Mayer, PE * 26Sep11 % ENGR25 * Problem 4-20 % file = Prob4_20_plot.m % Plot Displacement vs. Wt for Spring Platform % % INPUT SECTION Wmax = input('Max Weight in N = '); k1 = input('Main-Spring Const in N/m = '); k2 = input('Secondary-Spring Const in N/m = '); d = input('distance to 2nd Springs in m = ');

ENGR-25_Programming-3.ppt 27 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods.m-file = Prob4_20_plot.m cont %CALCULATION SECTION % calc Critical-Load for Curve Break-Point Wcrit = k1*d % Plot 3 pts for PieceWise Linear range if Wcrit <= Wmax % All 3 springs engaged W=[0, Wcrit, Wmax]; % 3element row vector % make corresponding 3-pt output vector x = [spring_plat(W(1),k1,k2,d),spring_plat(W(2),k1,k2,d),... spring_plat(W(3),k1,k2,d)]; plot(W,1000*x,'-s'), xlabel('Wt (N)'), ylabel('Compression (mm)'),... title('Above-Critical Load') % Plot 2pts for one Spring Linear Range else W = [0,Wmax] x = [spring_plat(W(1),k1,k2,d), spring_plat(W(2),k1,k2,d)]; plot(W,1000*x,'-s'), xlabel('Wt (N)'), ylabel('Compression (mm)'),... title('Below-Critical Load') end