Functions in Matlab Builtin and user defined functions.

Functions in Matlab

Builtin and

user defined functions

Builtin Functions

Exponential exp(x) sqrt(x)

Logarithmic log(x) natural logarithm ln log10(x) log2(x)

Builtin continued numeric

ceil(x) round to nearest integer towards + fix(x) round to nearest integer towards 0 floor(x) round to nearest integer towards - round(x) round to nearest integer sign(x) +1, 0 or -1 rem(x,y) Finds remainder of x/y

complex abs(x) absolute value angle(x) in complex plane conj(x) imag(x) real(x)

Builtin continued Trigonometric and their inverse

cos(x) acos(x) sin(x) asin(x) tan(x) atan(x) cot(x) acot(x) csc(x) acsc(x) sec(x) asec(x) atan2(x,y)

Builtin Functions continued

Hyperbolic and their inverse cosh(x) acosh(x) coth(x) acoth(x) csch(x) acsch(x) sech(x) asech(x) sinh(x) asinh(x) tanh(x) atanh(x)

Remarks All trigonometric functions require the use of

radians and not degrees All buitlin functions can also be used with

complex numbers. To understand the meaning with complex

numbers need to go back to basic definitions: exp(i x) = cos(x) + i sin(x) sin(x) =(exp(i x) - exp(-i x) )/(2 i) sinh(x) = (exp(x) – exp(-x) )/2

Basic example exp( a + i b) = exp(a) exp(i b) = exp(a) (cos(x) + i

sin(x))

Remarks continued Since a trigonometric function is periodic

each value has many inverse values Matlab will return only one value, the so

called 'principle value' For engineering applications it is important

to check that this is the correct value. Plotting a complex valued function z

=f(x+iy) is not possible. It requires a four dimensional space (x,y,u,v) since z = u+iv

Builtin Functions for vectors max(x)

returns largest value in vector x [a,b] = max(x)

returns largest value in a and index where found in b

max(x,y) x and y arrays of same size, returns vector of

same length with lager value from corresponding positions in x and y

same type of functions are available for min

Builtin functions for vectors sort(x) mean(x) median(x) sum(x) prod(x) cumsum(x)

returns vector of same size with cummulative sum of x i.e. x=[4,2,3] returns [4,5,9]

cumprod(x) returns cummulative products in vector of same size

Builtin functions applied to matrices

Matrices (arrays) are stored in column major form

When builtin functions for vectors are applied to a matrix function operates on columns and returns a row vector

User defined functions Similar to script files except that

temporary variables remain local function use standardized input and output

parameters Script files good for quick and dirty jobs Functions can be used over and over

again with no side effects Similar to subroutine, function or

procedure in other programming languages like Fortran, PL/I, Pascal, C, C++

Example f(x,y) = 3*x +6*y^2 Questions to be answered first: Are x and y

allowed to be arrays? Since Matlab treats everything as an array

it is best to allow all parameters to be an array

If x and y are arrays they have to be of the same size and f(x,y) is returned as an array of the same size

In above example x or y could be scalar (i.e. a constant) and function still makes sense

Matlab code placed in file fun.m function z = fun(x,y) u=3*x; z = u + 6*y.^2 ;

Note operator .^ to allow for an array Here the operator * does not require the array operator

.* since it is a multiplication with a constant + alays operates on the elements of an array thus .+ is

not defined u is a local variable in will not be available after the

function is executed u is used in the example for demonstration only. It

would be better to write z = 3*x+6*y.^2;

Remarks Check that function name fun does not

yet exist via: exist fun The input parameters x, y and the

output parameter z are local fun(3,4) does not create a variable z instead

it returns the value in ans q = fun(x0,y0) gives anwser to q, assuming

x0 and y0 are defined fun([2:5],[7:10]) works since arrays are of

the same length

Parameters for functions

Input parameters: 0 or more parameter list enclosed by ( ) if there are no parameters can omit ()

function show_date today = date

Example with three input parameters function volume = box(height, width,

depth) volume = height.*width.*depth;

Parameters for user defined functions Output parameter 0 or more

parameter list enclosed by [ ] 0 or 1 output parameter, can omit [ ] 2 or more parameters separated by

commas first output parameter ist set to ans, if

function is called without output parameters Examples:

function [areaC, cirumC] = circle(radius); function areaSquare = square(sides) ;

Remarks Why pass constants like g Earth's gravitation to a

function? g varies with units and forces user to select the proper unit a better choice is to let the user select at the very

beginning, which units are to be used in this case need to state in function

global g and in main progra

global g g = 9.81

Input parameters are local even if they are change in the function the original value

remains unchanged if the value in the calling program needs to be changed

have to return value as an output parameter

Function handle Useful as parameter to other functions Can be considered as an alternate name for a

function – but with more capabilities Example:

sine_handle = @sin sine_handle(x) same values as sin(x) for all x x = [0 : 0.01 : 2*pi] ; y = sin( x ); plot(x,y) plot( x, sin(x) ) plot( [0 : 0.01 : 2*pi] , sin( [0 : 0.01 : 2*pi] )) ;

Function handle continued In last example everything is on one line It requires writing the interval twice It would be more convient to write

gen_plot( function_handle, interval ) The first parameter has to be a function

handle and not just the name of a function gen_plot( sin, [0 : 0.01 : 2*pi ] ) does not

make sense to Matlab, but the following does gen_plot( sine_handle, [0 : 0.01 : 2*pi] )

Using a function handle function [] = gen_plot( func_handle, interval ) ; plot( interval, func_handle(interval) ) ;

When plotting lots of functions it may be useful to have gen_plot available

The example shows how to pass functions as parameters. Another use is anonymous functions Assume the user needs to work temporaily with the

function x3+3*x – 1 Instead of writing the function

function y = mypoly(x) ; y = x.^3+3*x-1

and storing it as mypoly.m in subdirectory work we can use an anonymous function with the function handle mypoly

mypoly = @(x) x.^3+3*x-1

Using anonymous functions With a function handle an anonymous

function can be used like any other gen_plot( mypoly, [-10 : 0.01 : 10] ) fzero( mypoly, 0.0 ) roots( [1, 0, 3, -1] )

Without the function handle the anonymous function can be inserted directly as the parameter gen_plot( @(x) x.^3+3*x-1, [-10 : 0.01 : 10] )

More examples f1 = @(x) x + 2* exp(-x) -3 fzero( f1, 0 ) fzero( f1, 1 )

Assume f1 had been defined as a function and kept in f1.m then

fzero( f1, 0 ) would be in error Besides function handle Matlab provides the

the following alternate method fzero( 'f1', 0 ) fzero( 'sin', 0 ) fzero( 'x.^3', 0 ) need to use default variable name