1. CS100A, Fall 1998, Lecture 201 CS100A, Fall 1998 Lecture 20, Tuesday Nov 10 More Matlab Concepts: plotting (cont.) 2-D arrays Control structures: while, if, for Defining new Matlab functions Readings: As before. Select from: Getting Started with Matlab Mastering Matlab Student Edition of Matlab User’s Guide

2. CS100A, Fall 1998, Lecture 202 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’)

3. CS100A, Fall 1998, Lecture 203 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

4. CS100A, Fall 1998, Lecture 204 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’);

5. CS100A, Fall 1998, Lecture 205 2-D Arrays Matlab’s basic data structure is a 2-D array of numbers (1-D arrays are a special case of this). There are various ways to create 2-D arrays. Easiest is to list the rows separated by semicolons: a = [1 2 3 4; 5 6 7 8; 9 10 11 12] Functions are provided to construct arrays with m rows and n columns initialized in various ways. ones(m,n)% m by n 1’s zeros(m,n)% m by n 0’s rand(m,n)% m by n random % numbers in the range % 0.0 to 1.0. If A is a 2-D array, size(A) is a 1-D array containing the number of rows and columns in A.

6. CS100A, Fall 1998, Lecture 206 2-D Array Subscripting Individual elements of a 2-D array a are accessed by listing the row and column numbers in parentheses a(1,3) a(3,1) a(2,2) Entire rows and columns can be accessed using a colon as a “wildcard” a(2, :) a(:, 3)

7. CS100A, Fall 1998, Lecture 207 2-D Array Subscripting The colon operator can be used to access arbitrary slices of an array. a(2:3, 1:2)% rows 2-3, cols 1-2 a(1:2, 4)% rows 1-2, col 4 a(1:2, :)% rows 1-2, all cols It can also be used to change the shape of an array by deleting rows, columns, or sub- matrices of a matrix. a(1:2, :) = []% removes rows 1-2 % from a

8. CS100A, Fall 1998, Lecture 208 Combining and Transposing 2-D arrays If A, B, C, and D are arrays, –[A B] or [A, B] is an array formed by combining the columns of A and B with A on the left. A and B must have the same number of rows. –[C ; D] is an array formed by stacking the rows of C above the rows of D. C and D must have the same number of columns. If A is an array with m rows and n columns, A’ (A quote-mark) is an array with n rows and m columns with A’(i,j) = A(j,i). The result is known as the transpose of A.

9. CS100A, Fall 1998, Lecture 209 Functions and 2-D Arrays Functions like sqrt, sin, cos that operate element-by-element on 1-D arrays work the same on 2-D arrays. m = 10 * rand(5,4) sqrt(sin(m)) Functions like sum, prod that produce a scalar result from a 1-D array produce a 1-D array result when applied to a 2-D array. The function is applied to columns of the 2-D array. a = [1 2 3; 4 5 6; 7 8 9; 10 11 12] sum(a) To apply these functions to rows in a 2-D array, transpose the array with the quote operator. sum(a’)

10. CS100A, Fall 1998, Lecture 2010 Control Structures in Matlab — if Like most programming languages, Matlab has loops and conditional statements, although these are needed far less often because of the available array operations. The punctuation differs from Java. if statement basic form: if logical expression statements end Example: if x > y temp = x; x = y; y = temp; end Semicolons are optional

11. CS100A, Fall 1998, Lecture 2011 Control Structures in Matlab — else if-else statement basic form: if logical expression statements else statements end Example: if x > y temp = x; x = y; y = temp; else x = y; end

12. CS100A, Fall 1998, Lecture 2012 Control Structures in Matlab — while while statement basic form: while logical expression statements end Example: while k>0 sum = sum + k; k = k - 1; end

13. CS100A, Fall 1998, Lecture 2013 Control Structures in Matlab — for The colon operator (or any array for that matter) can be used to generate index values for a loop. Example: Create an array with each element a(i,j) initialized to i+j. We allocate the array first to avoid array index out-of- bounds errors. a = zeros(25, 15); for r = 1 : 25 for c = 1 : 15 a(r,c) = r + c; end But — In Matlab there are often ways to do matrix operations without explicit loops. Don’t write loops if you don’t need them.

14. CS100A, Fall 1998, Lecture 2014 Creating New Functions —.m Files New functions can be defined by storing the commands to compute them in a file with a name that exactly matches the function name followed by.m. Function definition syntax: function [output vars ] = function_name ( input vars ) Example: File sqr.m. function [result] = sqr(x); % yield the square of the values in x result = x.* x; All variables are local to the function. Comments that immediately follow the function definition line are used by help and lookfor Functions may be applied to any Matlab data and will be applied element-by- element automatically if appropriate.