Basic Concepts in Matlab, by M. G. Kay

FUNCTIONS AND SCRIPTS1 2 3 4 5sum(a)(Array summation)ans =15cumsum(a)(Cumulative summation)ans =1 3 6 10 15By default, Matlab is column oriented; thus, for matrices,summation is performed along each column (the 1stdimension) unless summation along each row (the 2nddimension) is explicitly specified:AA =1 3 45 7 8sum(A)ans =6 10 12sum(A,2)(Sum along rows)ans =820sum(A,1)(Sum along columns)ans =6 10 12sum(sum(A))(Sum entire matrix)ans =28Forcing column summation: Even if the default columnsummation is desired, it is useful (in programming mode) toexplicitly specify this in case the matrix has only a singlerow, in which case it would be treated as a vector and sumto a single scalar value (an error):A = A(1,:) (Convert A to single-row matrix)A =1 3 4sum(A)(Incorrect)ans =8sum(A, 1)(Correct)ans =1 3 48. Functions and ScriptsFunctions and scripts in Matlab are just text files with a .mextension. User-defined functions can be used to extend thecapabilities of Matlab beyond its basic functions. A userdefinedfunction is treated just like any other function.Scripts are sequences of expressions that are automaticallyexecuted instead of being manually executed one at a time atthe command-line. A scripts uses variables in the (base)workspace, while each function has its own (local)workspace for its variables that is isolated from otherworkspaces. Functions communicate only through theirinput and output arguments. A function is distinguishedfrom a script by placing the keyword function as the firstterm of the first line in the file.Although developing a set of functions to solve a particularproblem is at the heart of using Matlab in the programmingmode, the easiest way to create a function is to do it in anincremental, calculator mode by writing each line at thecommand-line, executing it, and, if it works, copying it tothe function’s text file.Example: Given a 2-D point x and m other 2-D points inP, create a function mydist.m to determine the Euclidean(i.e., straight-line) distance d from x to each of the m pointsin P:⎡ p1,1 p1,2⎤x = [ x ] = ⎢ ⎥1 x2, P ⎢ ⎥⎣pm,1 pm,2⎦⎡2 2 ⎤⎢ ( x1− p1,1) + ( x2 − p1,2)⎥d = ⎢⎥⎢2 2 ⎥⎢⎣( x1 − pm,1) + ( x2 − pm,2)⎥⎦The best way to start is to create some example data forwhich you know the correct answer:6