1. CS100A, Fall 1998, Lecture 191 CS100A, Fall 1998 Lecture 19, Thursday Nov 05 Matlab Concepts: Matlab arrays Matlab subscripting Matlab plotting

2. CS100A, Fall 1998, Lecture 192 Arrays (review) All data in Matlab is actually an array (or a vector) — a 1- or 2-dimensional table of numbers. A single value, called a scalar, is simply an array of size 1. To construct a 1-D array, list its elements surrounded by square brackets. y = [4 -5 10 0 5.2] Individual elements are accessed using a parenthesized subscript. x(3) The first element of array x is x(1). The number of elements in array x is given by the built-in function length(x)

3. CS100A, Fall 1998, Lecture 193 Creating Arrays (review) An array of evenly-spaced values can be generated by linspace(minVal, maxVal, nVals) Two arrays can be combined with a comma and brackets: x = [1 2 3]; y = [4 5 6]; [x, y](is [1 2 3 4 5 6]) z = [x, [x, y]];

4. CS100A, Fall 1998, Lecture 194 Creating Arrays (colon) The colon can be used to generate a sequence of values. Forms: lowValue : highValue lowValue : step : highValue Examples: 1 : 10 1 : 2 : 10 1 : 0.5 : 10 10 : –1 : 1 0 : 0.01 : 0.5 A sequence of values is an array value. a = 0 : 2 : 16 b = [1 : 6] / 3 A sequence of integers can also be used to select a segment of an array. a(3:6)

5. CS100A, Fall 1998, Lecture 195 Array Functions There are many functions to compute facts about arrays. min(x), max(x), mean(x),... Array Operations Basic operations on arrays are performed element-by-element. Example: function applications: x = [4.2 7.89 2.4 -42.1 ] floor(x) An operation may involve an array and a scalar. The operation is performed on each element of the array and the result is an array of these values. x / 2

6. CS100A, Fall 1998, Lecture 196 Array Operations (cont.) Operations may combine two arrays if they have exactly the same length. x = [1 3 5 7] y = [10 20 30 40] x + y y - x The operations + and – work as expected. For element-by-element multiplication, division, and exponentiation, use.*,./, and.^. (Explanation: The usual operators *, /, and ^ perform matrix [Linear algebra] operations between arrays. We will not cover that in CS100.)

7. CS100A, Fall 1998, Lecture 197 Multiple Subscripts In general, an array of integers can be used as a subscript. The result is an array consisting of the elements selected by the subscripts in the order given. a = 10 * [0:9] a([3 4 5]) a(3:5) a([5 4 3]) a([1 1 7 4 6]) a(10:-1:1)

8. CS100A, Fall 1998, Lecture 198 Logical Operations & Arrays — 0/1 Arrays Logical operations yield 0 (false) or 1 (true). When performed on arrays, an array of 0’s and 1’s is the result. a = [5 8 6 12 9] b = [2 3 6 7 10] a > b a ~= b a > 5 rem(a, 3) rem(a, 3) == 0 The functions any and all yield 1 if, respectively, any or all of the elements in their array argument are non-zero.

9. CS100A, Fall 1998, Lecture 199 Selecting Elements with 0/1 Arrays If a vector of 0’s and 1’s is used as a subscript of an array of the same length, the result is a new array containing only those elements of the old array with a 1 subscript. This is especially useful when the result of a logical expression is used as a subscript to select array elements based on some condition. a = [12 7 21 3 8 14 0 6] a([0 1 1 0 0 0 1 0]) b = a - 10 b > 0 b( b > 0 ) a( rem(a,3) ~= 0 )

10. CS100A, Fall 1998, Lecture 1910 Managing the Work Session clc Clears the Command window clear Removes variables from memory help name Searches online help for the topic name lookfor nameSearches the help entries for the specified keyword name quitStops Matlab whoLists the variables currently in memory whosLists the current variables and sizes, and indicates whether they have imaginary parts

11. CS100A, Fall 1998, Lecture 1911 Basic Plotting If x and y are two arrays with the same number of elements, plot(x,y) draws a plot of x (horizontal) vs y (vertical) x = linspace(0, 4*pi, 250); y = sin(x); plot(x,y) Normally the graph is scaled so the full range of x and y values fill the plot. To have equal spacing on the axes, enter axis(‘equal’) after the plot has been drawn (using straight quote marks). You can label the axes and title the graph after it has been drawn: xlabel(‘x axis label’) ylabel(‘y axis label’) title(‘A Fabulous Graph’)

12. CS100A, Fall 1998, Lecture 1912 Plot Options The plot command has an optional third argument that can be used to specify the line color and style. Examples: v = -10:0.5:10; fv = 3*pi*sin(v).^2 - v; plot(v, fv, ‘g’); % green line plot(v, fv, ‘b:’); % blue dotted line plot(v, fv, ‘r+’); % red crosses plot(v, fv, ‘c--’); % cyan dashed line Use help plot to find other possibilities

13. CS100A, Fall 1998, Lecture 1913 Multiple Plots Normally each new plot is drawn in a blank window, replacing whatever is there. Use hold on to retain the previous plot so you can draw a new one over it. Use hold off to release the previous plot so the next one will appear in a blank window. Example: x = linspace(0, 6*pi, 1000); y = sin(x); z = cos(x); plot(x, y, ‘r’); hold on plot(x, z, ‘g’);