Lecture Creating M-files Programming tools: Input/output (assign/graph-&-display) Repetition (for) Decision (if) © 2007 Daniel Valentine All rights reserved Published by Elsevier 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 Examples of input to arrays: – Single number array & scalar: 1×1 >> a = – Row array & row vector: 1×n >> b = [1 5] – Column array & column vector: nx1 >> b = b’ % This an application of the transpose – Array of n rows x m columns & Matrix: n × m >> c = [1 3; 6; 9] % This example is x 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 Let us consider using the hyperbolic tangent to model a down-hill 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)’) 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) = Transition from -1 to is smooth and most rapid (roughly speaking) in the range -2