One-dimensional Array

Transcription

1 One-dimensional Array ELEC 206 Prof. Siripong Potisuk 1 Defining 1-D Array Also known as a vector A list of numbers arranged in a row row vector or a column column vector A scalar variable is a one-element vector 1 2 score [ ] x y [25]

2 Creating 1-D Array MATLAB vector is created by assigning its elements to an array name without having to predefine its size Row vector: type the elements separated by a space or a comma inside square brackets Column vector: type the elements separated by a semicolon inside square brackets or press the Enter key after each element is typed 3 >> score = [ ] score = >> score = [65,78,90,85,93] score = >> x = [1; 2; 3; 4] x = >> y = [1-2j 3 5j] y = i i 4 2

3 The Colon (:) Operator Used in creating a row vector with constant spacing between elements variable_name = [first:spacing:last] The square brackets are optional If spacing is omitted, the default is 1 >> n = -3:4 n = >> x=[1:2:13] x = The linspace Command An alternative method for creating a row vector with constant spacing between elements variable_name = linspace(first:last:n] n is the number of elements (if omitted, the default is 100) >> v=linspace(0,8,6) v = >> w=linspace(30,20,6) w =

4 The Transpose Operator Changes a row vector into a column vector and vice versa Type a single quote ( ) after the vector >> aa = [3 8 1] aa = >> bb = aa' bb = Managing 1-D Array Associated with each element is an element number (index) starting at 1 from left to right The built-in function length(v) returns the number of elements in the vector v. To address any element in a vector, use v(k) where k is the element number or index v(k)is considered a scalar variable and can be used in a mathematical expression Use v(m:n) to address a group of elements in v, starting from the m th to the n th element 8 4

5 Built-in Functions for 1-D Array mean(v) returns the mean (average) value of the elements of v max(v) returns the largest element of v [d n] = max(v) returns the largest element of v along with its position min(v) returns the smallest element of v [d n] = min(v) returns the smallest element of v along with its position sum(v) returns the sum of elements of v 9 Built-in Functions for 1-D Array median(v) returns the median value of the elements of v std(v) returns the standard deviation of the elements of v sort(v) arranges the elements of v in ascending order dot(v,w) computes the scalar (dot) product of two vectors. The vectors can both be row or column vectors 10 5

6 Addition & Subtraction The two vectors must be of the same size Elements of the two vectors with the same index or element number are added or subtracted together A scalar can be added or subtracted from each element of a vector >> A = [ ]; B = [ ]; >> C = A+B C = [ ] >> D = 2+A D = [ ] 11 Multiplication Scalar multiplication: each element of a vector is multiplied by the same scalar >> A = [ ]; B = [ ]; >> 2*A ans = [ ] Dot Product: A row vector is multiplied by a column vector, both of the same length, to create a scalar result >> dot(a,b) ans =

7 Multiplication Matrix multiplication: a column vector is multiplied by a row vector, both of the same length, to create a matrix according to the rules of linear algebra >> A = [ ]; B = [ ]; >> A *B ans = Element-by-element Operation Can only be done with vectors of the same length Addition and subtraction are already element-byelement operation For multiplication, division and exponentiation, type a period in front of the operator >> A = [ ]; B = [ ]; >> A.*B ans = >> A.^2 ans =

8 Evaluating Mathematical expression Use element-by-element operations >> x = 1:8 x = >> y = x.^2-4*x y = Note that each element of vector x is used one at a time to evaluate the expression in y 15 Evaluating Built-in Functions >> x = [1 4 9] x = >> z = sqrt(x) z = >> rad = 0:pi/6:pi rad = >> y = cos(rad) y =

9 Create a row vector A = 4:3:13 and a column vector B = [14:-2:6]. Then only using the name of the vectors (A and B), create the following: a) A row vector C that is made from the elements of B followed by the elements of A. >> A = 4:3:13 A = >> B = [14:-2:6]' B = >> C = [B' A] C = b) A column vector D that is made from the elements of A followed by the elements of B. >> D = [A'; B] D =

10 c) A ten-element row vector E that is made from the first 3 elements of A followed by the last 4 elements of B and the rest is zeros >> E = [A(1:3) B(end-3:end)' zeros(1,3)] E = d) A row vector F that is made from the elements of A followed by the elements of B in reverse order >> F = [fliplr(a) flipud(b) ] F =