Objectives of this lesson

Transcription

1 FONDAMENTI DI INFORMATICA Prof. Luigi Ingrosso

2 04/04/16 Computer Skills - Lesson 4 - L.Ingrosso 2 Objectives of this lesson We ll discuss Vector and matrix introduction How to create vectors How to refer to and modify elements of vectors Vector and matrix dimension

3 04/04/16 Computer Skills - Lesson 4 - L.Ingrosso 3 Concept: data collections We study two very common ways to group and store set of values of the same type: vectors and matrices. Data abstraction allows us to refer to groups of data collectively, e.g.,: all the temperature readings for September all the purchases from Walmart We can also perform mathematical or logical operations on these groups, e.g.: average, maximum, or minimum temperatures for a month A homogeneous collection is constrained to accept only items of the same data type In this case, they will all be numbers

4 4 Vectors Individual items in a vector are usually referred to as its elements. Vector elements have two separate and distinct attributes that make them unique in a specific vector: their numerical value and their position (index) in that vector. Example: the individual number 66 is the third element in this vector. Its value is 66 and its index is 3. There may be other items in the vector with the value of 66, but no other item will be located in this vector at position 3.

5 5 Matrices A matrix is a table of values. The dimensions of a matrix are m x n, where m is the number of rows and n is the number of columns.

6 04/04/16 Computer Skills - Lesson 4 - L.Ingrosso 6 Types of vectors Row vector Dimension: 1 x n Column vector Dimension: 1 x m Scalar (one element) Dimension: 1 x 1 Vectors and scalars are just special types of matrices In other programming languages: Vector: one-dimensional array Matrix: two-dimensional array

7 7 Vector manipulation We consider the following basic operations on vectors: Create a vector Determine the size (dimension) of a vector Extract data from a vector by indexing Shorten a vector Mathematical and logical operations on vectors

8 8 Creating a row vector: constant values Entering the values directly, e.g. >> A = [2, 5, 7, 1, 3]; >> A = [ ]; Entering the values automatically, e.g. range of numbers equally distributed in a linear space as random, zeros, ones

9 9 Creating a row vector: entering the values as a range B = [v 1, v 2,, v n ] = {v i v min <=v i <=v max, v i =v i-1 +K, v 1 =v min, i=2,,n} K is the step value (integer constant value) Example: K=3, v min =1 and v max =20 B=[1,4,7,10,13,16,19] Let s define an algorithm to create vector B

10 10 Flow diagram Start B = [v 1, v 2,, v n ] = {v i v min <=v i <=v max, v i =v i-1 +K, v 1 =v min, i=2,,n} read: v min, v max, K i 1, v i v min i i+1 No v i v i-1 +K v i-1 +K > v max Yes End In the next lectures you will learn how to implement in MATLAB such algorithm

11 11 Creating a row vector: entering the values as a range (2) In MATLAB: use the colon operator : B = {v i v min <=v i <=v max,v i =v i-1 +K, v 1 =v min, i=2,..} B = v min :K:v max Example This syntax is an implementation of the previously defined algorithm >> B = 1:3:20 B =

12 12 Creating a vector: as equally distributed in a linear space C = [v 1, v 2,, v N ]={N equally spaced points between X min and X max } Example: N=11, X min =0 and X max =20 C=[ ] MATLAB offers the linspace built-in function: C = linspace (Xmin, Xmax, N) Example >> C = linspace(0,20,11) C =

13 13 Flow diagram k holds the distance between x i and x i+1 Start read: X min, X max, N k (X max -X min )/(N-1) i 1, v i v min i i+1 v i v i-1 +k No i > N Yes End

14 14 Creating a vector: filled with 0, 1, or random values B = [v 1, v 2,, v N ]; v i =0 for i=1,..,n v i =1 for i=1,..,n v i =x k where x k is a pseudorandom value uniformly or normally distributed All the cases can use the same algorithm x = 0 or 1 or Normal() or Uniform()

15 15 Flow diagram Start read: N i 0 i i+1 v i x No i > N Yes x = 0 or 1 or Normal() or Uniform() End

16 16 Creating a vector: filled with 0, 1, or random values MATLAB offers built-in functions to implement the previous algorithm: zeros, ones, rand, or randn %B = [v 1, v 2,, v N ]; B=zeros(1,n); %v i =0 for i=1,..,n B=ones(1,n); %v i =1 for i=1,..,n B=rand(1,n); %v i =x k where x k is a %pseudorandom value %uniformly distributed B=randn(1,n); %v i =x k where x k is a %pseudorandom value %normally distributed