Lecture 3 Creating M - files

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Programming tools: Input/output (assign/graph-&-display) Repetition (for) Decision (if) Arrays List of numbers in brackets A comma or space separates numbers (columns) A semicolon separates row Zeros and ones Matrices: zeros() ones() Indexing (row,column) Colon Operator: Range of Data first:last or first:increment:last Manipulating Arrays & Matrices Transpose

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Lecture 3 Lecture 3 Creating Mfiles Programming tools: Input/output (assign/graph&display) Repetition (for) Decision (if) © 2007 Daniel Valentine. All rights reserved. Published by Elsevier.
Review Review Arrays  – List of numbers in brackets  A comma or space separates numbers (columns)  A semicolon separates row – Zeros and ones Matrices: zeros()  ones()  – Indexing  (row,column) – Colon Operator:  Range of Data first:last or first:increment:last – Manipulating Arrays & Matrices  Transpose
Input Input  Examples of input to arrays: – Single number array & scalar: 1×1 >> a = 2 >> – Row array & row vector: 1×n >> b = [1 3 2 5] >> [1 – Column array & column vector: nx1 >> b = b’ % This an application of the transpose. >> This – Array of n rows x m columns & Matrix: n × m >> c = [1 2 3; 4 5 6; 7 6 9] % This example is 3 x 3. >> This
Basic elements of a program Basic elements of a program  Input – Initialize, define or assign numerical values to variables.  Set of command expressions – Operations applied to input variables that lead to the desired result.  Output – Display (graphically or numerically) result.
An example of technical computing An example of technical computing  Let us consider using the hyperbolic tangent to model a downhill section of a snowboard or snow ski facility.  Let us first examine the hyperbolic tangent function by executing the command: >> ezplot( ‘tanh(x)’ ) We get the following graph:
Ezplot(‘tanh(x)’) Ezplot(‘tanh(x)’)
Hyperbolic tangent: tanh(X) Hyperbolic tangent: tanh(X)  Properties (as illustrated in the figure): – As X approaches –Inf, tanh(X) approaches 1. – As X approaches Inf, tanh(X) approaches +1. – X = 0, tanh(X) = 0. – Transition from 1 to 1 is smooth and most rapid (roughly speaking) in the range 2
Problem background Problem background  Let us consider the design of a slope that is to be modeled by tanh(X). Consider the range 3
Formula for snow hill shape Formula for snow hill shape
Problem statement Problem statement  Find the altitude of the hill at 0.5 meter intervals from 5 meters to 5 meters using the shape described and illustrated in the previous two slides.  Tabulate the results.
Structure plan Structure plan  Structure plan – Initialize the range of X in 0.5 meter intervals. – Compute y, the altitude, with the formula: y = 1 – tanh(3*X/5). – Display the results in a table.  Implementation of the structure plan – Open the editor by typing edit in the command window. – Translate plan into the Mfile language.
SOLUTION TO IN-CLASS EXERCISE C o m m a n d w i n d o w OUTPUT This is from editor: It is X Y lec3.m 5.0000 1.9951 % 4.5000 1.9910 % Ski slope offsets for the 4.0000 1.9837 % HYPERBOLIC TANGENT DESIGN 3.5000 1.9705 % by D.T. Valentine...January 2007 3.0000 1.9468 % 2.5000 1.9051 % Points at which the function 2.0000 1.8337 % is to be evaluated: 1.5000 1.7163 1.0000 1.5370 % Step 1: Input x 0.5000 1.2913 x = 5:0.5:5; 0 1.0000 % Step 2: Compute the y offset, 0.5000 0.7087 % that is, the altitude: 1.0000 0.4630 y = 1 tanh(3.*x./5); 1.5000 0.2837 % 2.0000 0.1663 % Step 3: Display results in a table 2.5000 0.0949 % 3.0000 0.0532 3.5000 0.0295 disp(' ') % Skips a line 4.0000 0.0163 disp(' X Y') 4.5000 0.0090 disp([x' y']) 5.0000 0.0049
Use of repetition (‘for’) Use of repetition (‘for’)  Repetition: In the previous example, the fastest way to compute y was used. An alternative way is as follows: Replace: y = 1 tanh(3.*x./5); % This is “vectorized” approach. With: for n=1:21 y(n) = 1 tanh(3*x(n)/5); end Remark: Of course, the output is the same.
SOLUTION TO IN-CLASS EXERCISE C o m m a n d w i n d o w OUTPUT This is from editor: It is X Y lec3_2.m 5.0000 1.9951 % 4.5000 1.9910 % Ski slope offsets for the 4.0000 1.9837 % HYPERBOLIC TANGENT DESIGN 3.5000 1.9705 % by D.T. Valentine...January 2007 3.0000 1.9468 % 2.5000 1.9051 % Points at which the function 2.0000 1.8337 % is to be evaluated: 1.5000 1.7163 1.0000 1.5370 % Step 1: Input x 0.5000 1.2913 x = 5:0.5:5; 0 1.0000 % Step 2: Compute the y offset 0.5000 0.7087 for n=1:21 1.0000 0.4630 y(n) = 1 tanh(3*x(n)/5); 1.5000 0.2837 end 2.0000 0.1663 % 2.5000 0.0949 % Step 3: Display results in a table 3.0000 0.0532 3.5000 0.0295 disp(' ') % Skips a line 4.0000 0.0163 disp(' X Y') 4.5000 0.0090 disp([x' y']) 5.0000 0.0049
Decision: Application of ‘if’ Decision: Application of ‘if’  Temperature conversion problem: – Convert C to F or F to C.
Decision: Application of ‘if’ Temperature conversion problem:  – Convert C to F or F to C. – SOLUTION: % % Temperature conversion from C to F % or F to C as requested by the user % Dec = input(' Which way?: 1 => C to F? 0 => F to C: '); Temp = input(' What is the temperature you want to convert? '); % % Note the logical equals sgn (==) if Dec == 1 TF = (9/5)*Temp + 32; disp(' Temperature in F: ') disp(TF) else TC = (5/9)*(Temp-32); disp(' Temperature in C: ') disp(TC) end
Summary Summary  Introduced, by an example, the structure plan approach to design approaches to solve technical problems.  Input: Assignment with and without ‘input’ utility.  Output: Graphical & tabular were shown.  Illustrated array dotoperation, repetition (for) and decision (if) programming tools.