Lecture note Data visualization - Chapter 21

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The main contents of the chapter consist of the following: Script m-file, editor/debugger window, cell mode, using built-in functions, using the HELP feature , window HELP screen, elementary math functions, rounding functions, discrete mathematics, trigonometric function, data analysis function.

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Nội dung Text: Lecture note Data visualization - Chapter 21

Lecture 21
Recap Script Mfile Editor/Debugger Window Cell Mode Chapter 3 “Built in MATLAB Function” Using Builtin Functions Using the HELP Feature Window HELP Screen Elementary Math Functions Rounding Functions
Sums and Products
Sorting Values
Matrix Size
Variance and Standard Deviation
Normal Distribution
Random Numbers Random numbers are often used in engineering calculations to simulate measured data Measured data rarely behave exactly as predicted by mathematical models, so we can add small values of random numbers to our predictions to make a model behave more like a real system Random numbers are also used to model games of chance Two different types of random numbers can be generated in MATLAB: Uniform random numbers Gaussian random numbers
Uniform Random Numbers Uniform random numbers are generated with the rand function. These numbers are evenly distributed between 0 and 1 We can create a set of random numbers over other ranges by modifying the numbers created by the rand function For example: to create a set of 100 evenly distributed numbers between 0 and 5 first create a set over the default range with the command r = rand(100,1);
Example Continued…. If we want to change the range to 5 to 10, we can add 5 to every value in the array: r = r + 5; The result will be random numbers varying from 5 to 10. We can generalize these results with the equation x=(max min) . random_number_set + min
Gaussian Random Numbers
Continued…. If we need a data set with a different average or a different standard deviation, we start with the default set of random numbers and then modify it Since the default standard deviation is 1, we must multiply by the required standard deviation for the new data set Since the default mean is 0, we’ll need to add the new mean: x = standard_deviation . random_data_set + mean For example: to create a sequence of 500 Gaussian random variables with a standard deviation of 2.5 and a
Complex Numbers MATLAB includes several functions used primarily with complex numbers Complex numbers consist of two parts a real component an imaginary component For example: 5+3i is a complex number. The real component is 5, and the imaginary component is 3. Complex numbers can be entered into MATLAB in two ways: 
Continued…. As is standard in MATLAB, the input to the complex function can be either two scalars or two arrays of values Thus, if x and y are defined as x = 1:3; y = [1,5,12]; then the complex function can be used to define an array of complex numbers as follows: complex(x,y) ans =
real and imag Function The real and imag functions can be used to separate the real and imaginary components of complex numbers For example: for A = 5 + 3*i , we have real(A) ans = 5 imag(A) ans = 3
isreal Function The isreal function can be used to determine whether a variable is storing a complex number It returns a 1 if the variable is real and a 0 if it is complex Since A is a complex number, we get isreal(A) ans =0 Thus, the isreal function is false and returns a value of 0
Conjugate of Complex Number The complex conjugate of a complex number consists of the same real component, but an imaginary component of the opposite sign The conj function returns the complex conjugate: conj(A) ans = 5.0000 3.0000i The transpose operator also returns the complex conjugate of an array, in addition to converting rows to columns and columns to rows Thus, we have