Chapter 3. built in functions help feature elementary math functions data analysis functions random number functions computational limits

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1 Chapter 3 built in functions help feature elementary math functions data analysis functions random number functions computational limits

2 I have used resources for instructors, available from the publisher of the text.

3 MATLAb uses built in functions consistent with most major programming language Examples pi sqrt(2.5) sin(pi/3) cos(pi/3) log(4.0) % log e 4.0 log10(100) 2 % log

4 Function input can be scalar or matrices

5 Predefined functions Functions consist of Name Input argument(s) Output

6 Some functions need multiple input Remainder function returns the remainder in a division problem >> rem(15,4) ans= 3 >> % 3 is the remainder when 15 is divided by 4. >> x=[11, 13, 17]; >> y= [2,5,6]; >> rem(x,y) ans= % One can take many remainder operations in one go.

7 Some functions return multiple results size functions determines the number of rows and columns

8 You can assign names to the return results

9 You can assign names to the return results The variable names are arbitrary choose something that makes sense in the context of your problem

10 MATLAB has extensive built in functions. Use help feature to find out what they are and how to use them. Can do so from the command window, or from the help menu.

11 From the command window

12 From the Help Menu

14 Elementary math functions We have already seen many: sqrt, sin, cos, tan, log, log10

15 Rounding functions round(x) % round it to the closest integer fix(x) % truncate the function floor(x) % integer value closest to ceil(x) % integer value closest to +

16 Example 1

17 Example 2

18 Discrete Mathematics factor(x) gcd(x,y) greatest common denominator lcm(x) lowest common multiple rats(x) represents x as a fraction factorial(x) primes(x) isprime(x)

19 Trigonometric functions sin(x) sine cos(x) cosine tan(x) tangent sind(x) sine with degree input cosd(x) cosine with degree input tand(x) tangent with degree input

20 Data Analysis (x is an array vector) max(x) % finds the maximum element of x min(x) % finds the minimum element of x mean(x) % finds the mean (average) of x median(x) % finds the middle element of x sum(x) % finds the sum of the elements of x prod(x) % finds the product of the elements of x sort(x) % sorts the elements of x.

21 When the max function is used with a vector (either a row or a column), it returns the maximum value in the vector

22 When the max function is used with a vector (either a row or a column), it returns the maximum value in the vector When x is a matrix, the max is found for each column

23 max value index number where the max value occurs The max function can also be used to determine where the maximum occurs

24 Vector of row numbers Vector of maximums

25 MATLAB is column dominant, so when sort is used with a 2 column matrix, each column is sorted in ascending order

26 The sortrows function allows you to sort entire rows, based on the value in a specified column. The default sorting column is #1

27 In this example the matrix is sorted in ascending order, based on the second column

28 To sort based on descending order, place a negative sign in front of the column number Notice that this is a different strategy than that used by the sort function!

29 Random Numbers rand(x) Returns an x by x matrix of random numbers between 0 and 1 rand(n,m) Returns an n by m matrix of random numbers These random numbers are evenly distributed

31 If you create a very large matrix of random numbers using the rand function, the average value will be 0.5 Notice that we created a 1 by 10 7 matrix, which required 2 inputs (rand (1,10e6)). If we had entered a single value (rand(10e6)) the result would have been a 1x10 7 by 1x10 7 matrix.

32 To generate random numbers between other bounds such as [a,b] We generate x as follows x = (b a)*rand(1) + a or x = (b a)*rand + 1 [a,b] is the interval (a and b are the lower and upper bounds); rand(1) or rand generates one random value between 0 and 1.

33 Computational Limitations MATLAB s computational range on most computers is: When you divide by 0, the computer returns Inf

34 Check the limits on your computer with these commands realmax realmin intmax intmin

36 When using very large or very small numbers the result may depend on the order of operation

37 Special Values and Functions pi i,j Inf NaN clock date eps ans Hint: The function i is the most common of these functions to be unintentionally renamed by MATLAB users.

38 Summary MATLAB contains a wide array of predefined functions Elementary Math Functions Trigonometric Functions Data Analysis Functions Random Numbers Complex Numbers Computational Limits Special Values and Functions

What is a Function? EF102 - Spring, A&S Lecture 4 Matlab Functions

What is a Function? EF102 - Spring, 2002 A&S Lecture 4 Matlab Functions What is a M-file? Matlab Building Blocks Matlab commands Built-in commands (if, for, ) Built-in functions sin, cos, max, min Matlab