Matlab预定义函数.ppt

1,Matlab与科学计算,计算机学院 刘咏梅 Email:,2,第四章 MATLAB编程（预定义函数）,Introduction to MATLAB MATLAB Basics of Numerical Computing MATLAB Programming(branching and Loops) MATLAB Programming(Predefined Functions) MATLAB Graphic and Image Processing Scientific Computing using MATLAB,3,本章学习的目标：,Introduction to Matlab Functions built in functions and user defined functions Optional Arguments Sharing Data Using Global Memory Preserving Data Between Calls to a Function Function Functions Subfunctions,4,Functions,Functions are more complex than scripts Functions have their own local variables Functions return output as specified, and can accept input as specified,5,Why we use functions?,Independent Testing of Sub-Tasks: Each task is an independent unit that can be tested separately (unit testing). Reusable Code: Within the same program (the code is not repeated). It can be used in another program. Isolation from unintended side effects: Isolation of function variables from the main program variables. The input and the output variables are specified clearly.,6,Syntax of Matlab Functions,User defined functions behave just like built in functions. All functions have a similar syntax, whether they are built-in functions or user-defined functions. Name Input Output,A=cos(x),7,How to call functions?,The functions can be called directly in the command window, or by any other program or function. Very important: if the input variables are changed in the functions they will not change in the main program (PASS-BY-VALUE SCHEME),8,Built in Functions,Built in functions allow us to reuse computer code for calculations that are performed frequently. For example, suppose there were no built in sine function in MATLAB and you will do a lot of trigonometric calculations involving the sine of an angle. Weve already become familiar with a number of MATLAB built in functions like sin (x) or plot (x,y) for example.,9,Some examples of Built in Functions,Exponential(指数) exp(x) exponential of x (ex) sqrt(x) square root of x Logarithmic(对数) log(x) natural logarithm( ln x ) log10(x) log2(x),10,Some examples of Built in Functions,Numeric(数值) fix(x) round to nearest integer towards 0 round(x) round to nearest integer sign(x) +1, 0 or -1 rem(x,y) Finds remainder of x/y Complex(复数) abs(x) absolute value angle(x) phase angle in complex plane conj(x) conjugate of x imag(x) imaginary part of x real(x) real part of x,11,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 larger value from corresponding positions in x and y max(3 5 2,6 4 8) ans= 6 5 8 same type of functions are available for min,12,Builtin Functions for vectors,sort(x) sort in ascending or descending order mean(x) average or mean value median(x) median value sum(x) sum of elements of x prod(x) product of elements of x cumsum(x) returns vector of same size with cumulative sum of x i.e. x=4,2,3 returns 4,6,9 cumprod(x) returns vector of same size with cumulative products in vector of same size i.e. x=4,2,3 returns 4,8,24,13,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,14,Builtin functions applied to matrices,sum(0 1 2;3 4 5) ans= 3 5 7 prod(0 1 2;3 4 5) ans= 0 4 10 cumsum(0 1 2;3 4 5) ans= 0 1 2 3 5 7,cumprod(0 1 2;3 4 5) ans= 0 1 2 0 4 10 sort(9 1 2;3 2 4) ans= 3 1 2 9 2 4,15,User-defined Functions,You can use user defined functions in your programs just as you would use MATLABs built in functions. User defined functions help you write more compact programs and write complex programs into shorter ones that are easier to debug and get running.,16,User-defined Functions,User-defined functions must start with a function definition line. The definition line contains The word function A variable(variables) that defines the function output A function name A variable(variables) used for the input argument,function output = poly(x),The above line of codes defines a function named poly.,17,A simple example of user-defined functions,18,You can use your user defined functions from the Command Window or from a M-file program.,19,When x is a vector,Consider the following, A = 1, 2, 5; % A is a 3-element row vector y = 2 * poly(A) y = 14 82 982 In the statement y = 2* poly(A) above, the user defined function poly is called which evaluates the polynomial at each point in the input row vector. Then, each value is multiplied by 2, resulting in the row vector called y having the values 14, 82, 982.,20,Comments for Functions,The comment lines immediately after the first line are returned when you query the help function,21,22,User defined functions may,Have more than one input variable, function s = f (x, y, z). This function has three input variables. Have more than one output variable, function out1, out2 = f (x) is a function with one input variable and two output variables. Input and output variables can be scalars, vectors or matrices. Within the body of the function, there needs to be one assignment statement for each output variable.,23,Local Variables,Any variables used within a function are called local variables. These variables do not appear in the Workspace Window and are not available for the main program to access. The output variable names used in the function statement and in the body of the function are also local variables. The input variables are local variables also.,24,Local Variables,Variables defined in an M-file function, only have meaning inside that program The only way to communicate between functions and the workspace, is through the function input and output arguments,25,x, y, a, and output are local variables to the g function,When the g function is executed, the only variable created is determined in the command window (or script M-file used to execute a program),ans is the only variable created,26,Optional Arguments,For example: plot function x=0:pi/100:2*pi; y1=sin(2*x); y2=2*cos(2*x); plot(x,y1,x,y2);,x=0:pi/100:2*pi; y1=sin(2*x); y2=2*cos(2*x); plot(x,y1); hold on; plot(x,y2);,27,Optional Arguments,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 larger value from corresponding positions in x and y same type of functions are available for min,28,Optional Arguments(Input and Output),Optional output,Optional input,29,Determine the number of input and output variables,Two built in functions let you determine the number of input and output variables in any function, for function s = f (x) nargin (f) returns in our case, ans =1 since f has one input argument, and nargout(f) also returns ans = 1 in our case because f has only one output variable.,nargin:determines the number of input arguments nargout:determines the number of output arguments,30,Global Variables,Remember variable names used within a function are local variables, they do not appear in the Workspace window of the main program. It is possible to define a Global Variable that is then common to both the main program and the function. It is recommended not to do this. Although it is possible to define global variables, it is a bad idea!,31,Sharing Data Using Global Memory,Global memory is a special memory that can be accessed from any workspace. Syntax: global var1 var2 var3 Remark: Each global variable must be declared to be global before it is used for the first time in a function. Better to be the first statement in the function after the initial comments.,32,Preserving Data Between Calls to a Function,Each time the function is finished, data in the workspace is destroyed. To make some variables persistent for the next function calls, use the persist command. Special type of memory that can be accessed only from the same function. Syntax: persistent var1 var2 var3 ,33,Preserving Data Between Calls to a Function,Exercise: running averages and standard deviations. User must enter the number of values in data set, and then enter value by v