Fondamenti di Informatica

Transcription

1 Fondamenti di Informatica Scripts and Functions lesson /04/12 Prof. Emiliano Casalicchio emiliano.casalicchio@uniroma2.it

2 Agenda n Matlab scripts examples n Matlab functions differences with script parameters examples 2

3 Programming Paradigms n Procedural programming the basic programs or subprograms are sequences of operations on data items. n Functional programming every programming operation is actually implemented as a function call with no side effects Maltab Script Maltab Function 1-3

4 Matlab script: definition n Sequence of MATLAB statements in file n A script file is an external file that contains a sequence of MATLAB statements. By typing the filename, you can obtain subsequent MATLAB input from the file. Script files have a filename extension of.m. 4

5 Matlab script: definition n Scripts are the simplest kind of MATLAB program. They are useful for automating blocks of MATLAB commands, such as computations you have to perform repeatedly from the command line. n Scripts can operate on existing data in the workspace, or they can create new data on which to operate. scripts do not return output arguments, any variables that they create remain in the workspace, so you can use them in further computations. scripts can produce graphical output using commands like plot. n Scripts can contain any series of MATLAB statements. They require no declarations or begin/end delimiters. n Like any MATLAB program, scripts can contain comments. Any text following a percent sign (%) on a given line is comment text. Comments can appear on lines by themselves, or you can append them to the end of any executable line. 5

6 Script: some consideration n All variables are declared and initialized inside the script n Typically output is displayed inside the script 6

7 Objectives Chapter 5 discusses the nature, implementation, and behavior of userdefined functions in MATLAB: How to define a function How data are passed into a function How to return data including multiple results How to include other functions not needed except as helpers to your own function 1-7

8 5.1 Concept: Abstraction Procedural abstraction permits a code block that solves a particular sub-problem to be packaged and applied to different data inputs. analogous to the concept of data abstraction where individual data items are gathered to form a collection. We have already used a number of built-in procedural abstractions in the form of functions. They allow us to apply a code block about which we know nothing to data that we provide. 1-8

9 5.1 Concept: Encapsulation Encapsulation is the concept of putting a wrapper around a collection that you wish to protect from outside influence. Functions encapsulate the code they contain in two ways: the variables declared within the function are not visible from elsewhere, and the function s ability to change the values of variables (otherwise known as causing side effects) is restricted to its own code body. 1-9

10 An example function x = mynewton(f,f1,x0,n)! % Solves f(x) = 0 by doing n steps of Newton?s method starting at x0.! % Inputs: f -- the function, input as an inline! % f1 -- it?s derivative, input as an inline! % x0 -- starting guess, a number! % n -- the number of steps to do! % Output: x -- the approximate solution! format long % prints more digits! format compact % makes the output more compact! x = x0; % set x equal to the initial guess x0! for i = 1:n % Do n times! x = x - f(x)/f1(x) % Newton?s formula, prints x too! end! 10

11 An example function x = mynewton(f,f1,x0,n)! % Solves f(x) = 0 by doing n steps of Newton?s method starting at x0.! % Inputs: f -- the function, input as an inline! % f1 -- it?s derivative, input as an inline! % x0 -- starting guess, a number! % n -- the number of steps to do! % Output: x -- the approximate solution! format long % prints more digits! format compact % makes the output more compact! x = x0; % set x equal to the initial guess x0! for i = 1:n % Do n times! x = x - f(x)/f1(x) % Newton?s formula, prints x too! end! n create input variables 11

12 An example function x = mynewton(f,f1,x0,n)! % Solves f(x) = 0 by doing n steps of Newton?s method starting at x0.! % Inputs: f -- the function, input as an inline! % f1 -- it?s derivative, input as an inline! % x0 -- starting guess, a number! % n -- the number of steps to do! % Output: x -- the approximate solution! format long % prints more digits! format compact % makes the output more compact! x = x0; % set x equal to the initial guess x0! for i = 1:n % Do n times! x = x - f(x)/f1(x) % Newton?s formula, prints x too! end! n create input variables n execute mynewton x, i, f, f1, x0, n are not accessible The output is stored in ans 12

13 5.2 Black Box View of a Function n n <param 1...n> are the formal parameters the names given to the incoming data inside the function. <item 1...n> are the actual parameters provided to the function by its caller. They may have names different from the formal parameter names They are correlated to the formal parameter names by their position 1-13

14 5.3 MATLAB Implementation The template for defining a function is: function <return info> <function name> (<parameters>)! <documentation>! <code body> % must return the results! n The function code must be stored in a file whose name is the name of the function. n Functions return data to the caller by assigning values to the return variable(s) (i.e. <return info>) n MATLAB throws an error if a function does not make assignments to all the return variables. 1-14

15 Tip:different icons 15

16 5.4 Engineering Example Measuring a Solid Object n We need to compute the volume and wetted area of this object. n This requires one function that computes the volume and wetted area of a cylinder n We have a range of disk heights for which we require this information. 1-16

17 Solution n The function stored in cylinder.m function [area, volume] = cylinder(height, radius)! % function to compute the area and volume of a cylinder! % usage: [area, volume] = cylinder(height, radius)! base = pi.* radius.^2;! volume = base.* height;! area = 2 * pi * radius.* height + 2 * base;! n The test script clear! clc! h = 1:5; % set a range of disk thicknesses! R = 25;! r = 3;! [Area Vol] = cylinder(h, R) % dimensions of large disk! [area vol] = cylinder(h, r) % dimensions of the hole! % compute remaining volume! Vol = Vol - 8*vol! Area = Area + 8*(area - 2*2*pi*r.^2)! 1-17

18 Variable scoping in Matlab n The base workspace stores variables that you create at the command line. This includes any variables that scripts create, assuming that you run the script from the command line or from the Editor. Variables in the base workspace exist until you clear them or end your MATLAB session. the base workspace is called also Global Scope n Variable in the base workspace can be accessed by every script executed from the base workspace 18

19 Variable scoping in Matlab n Functions do not use the base workspace. Every function has its own function workspace. Each function workspace is separate from the base workspace and all other workspaces to protect the integrity of the data. Variables specific to a function workspace are called local variables. Typically, local variables do not remain in memory from one function call to the next. 19

20 Variable scoping in Matlab n When you call a script from a function, the script uses the function workspace. n Like local functions, nested functions have their own workspaces. However, these workspaces are unique in two significant ways: Nested functions can access and modify variables in the workspaces of the functions that contain them. All of the variables in nested functions or the functions that contain them must be explicitly defined. That is, you cannot call a function or script that assigns values to variables unless those variables already exist in the function workspace. 20

21 Global Scope and Local Scope function x = mynewton(f,f1,x0,n)! % Solves f(x) = 0 by doing n steps of Newton?s method starting at x0.! % Inputs: f -- the function, input as an inline! % f1 -- it?s derivative, input as an inline! % x0 -- starting guess, a number! % n -- the number of steps to do! % Output: x -- the approximate solution! format long % prints more digits! format compact % makes the output more compact! x = x0; % set x equal to the initial guess x0! for i = 1:n % Do n times! x = x - f(x)/f1(x) % Newton?s formula, prints x too! end! n The workspace Base Workspace or global scope 21

22 Global Scope and Local Scope Local scope, that is the local workspace containing local variables 22

23 Global Variables from: n Global variables are variables that you can access from functions or from the command line. They have their own workspace, which is separate from the base and function workspaces. n However, global variables carry notable risks. For example: Any function can access and update a global variable. Other functions that use the variable might return unexpected results. If you unintentionally give a "new" global variable the same name as an existing global variable, one function can overwrite the values expected by another. This error is difficult to diagnose. n Use global variables sparingly, if at all. n If you use global variables, declare them using the global keyword before you access them within any particular location (function or command line). 23

24 Global Variables: an example n For example, create a function in a file called falling.m: function h = falling(t)! global GRAVITY! h = 1/2*GRAVITY*t.^2;! n Then, enter these commands at the prompt: global GRAVITY! GRAVITY = 32; % m/s 2 (approx ft/s 2 )! y = falling((0:.1:5)');! n The two global statements make the value assigned to GRAVITY at the command prompt available inside the function. 24

25 Global Variables: an example n However, as a more robust alternative, redefine the function to accept the value as an input: function h = falling(t,gravity)! h = 1/2*gravity*t.^2;! n Then, enter these commands at the prompt: GRAVITY = 32;! y = falling((0:.1:5)',gravity);! 25

26 Find a value in a matrix: script A = [ ;! ];! thevalue=9;! n=size(a,1);! m=size(a,2);! exit=false;! for i = 1:n! for j = 1:m! if A(i,j) == thevalue! exit=true;! break;! end! end! if exit! break;! end! end! fprintf('the value %d is at place (%d,%d) in A \n', thevalue, i, j); 26

27 function [idx1 idx2]=find_a_value_in_m(a,thevalue)! % Find the value thevalue in matrix A and return the index of! % the element of A containing thevalue! %Input: A -- the matrix! % thevalue -- the value to be searched! %Output: [idx1 idx2] -- are the index of A such that! %A(idx1,idx2)==theValue. If thevalue is not in a idx1=idx2=0.! %! n=size(a,1);! m=size(a,2);! exit=false;! idx1=0;! idx2=0;! for i = 1:n! for j = 1:m! if A(i,j) == thevalue! exit=true;! idx1=i;! idx2=j;! break;! end! end! if exit! break;! end! end! 27

28 How to use the new function n let us create a script findavaluescript.m clear;! clc;! B = [ ;! v=9;! ];! [r(1) r(2)]=find_a_value_in_m(b,v);! if r(1) == 0! else! fprintf('value not found');! fprintf('the value %d is at place (%d,%d) in A \n', B(r(1),r(2)), r(1), r(2));! end! 28

29 Homework n scrivere le funzioni per il massimo di un vettore/matrice n scriver la funzione per la somma comulativa degli elementi di un vettore 29