Introduction to Matlab CS100A, Fall 1998 Lecture 18, Tuesday Nov 3 Introduction to Matlab Concepts: Matlab as a graphical calculator for scalars & arrays Readings: choose one of: Getting Started with Matlab, Pratap Mastering Matlab, Hanselman & Littlefield Student Edition of Matlab User’s Guide, Hanselman & Littlefield or any other basic Matlab book

Why Matlab? The premier package for numerical computing, particularly arrays (matrices). Widely used in science/engineering. Provides high-level interface to best-of-class numerical methods. Problem-solving without lower-level programming details. Powerful graphics and visualization tools. has variables, loops, conditionals, functions but much array/matrix computation can be done directly without loops.

Matlab Environment Enter expressions or commands in the console window. Commands are executed immediately. An expression is evaluated and its value is immediately displayed. Can define command scripts and new functions (future lecture). Most important feature: help command. Enter help to get a general list of available topics, or help topic for information on topic. Enter more on in the console window to pause output after each full screen. Hit space to continue. Anything following a % is ignored. Use it to include notes or comments in a session. To leave Matlab, enter quit

^ is exponentiation (2 ^ 10) Expressions The usual basic arithmetic operations are provided (+, –, *, /, and ^). Everything is floating-point†, although integer values are displayed without a fractional part. 9/10 is 0.9 in Matlab ^ is exponentiation (2 ^ 10) Logical operations treat 1 as the value true and 0 as false. Comparisons: <, <=, ==, ~=, >=, > Logical Operators: &, |, ~ Examples: 3 * 4 + 5 3 * 4 + 5 / 2 3 * (4 + 5) / 2 (3 < 2 ^ 2) & ~ (3 < 2) (3 < 2 ^ 2) | ~ (3 < 2) † Actually, everything in Matlab is a matrix containing complex, floating-point numbers. But for now we can restrict ourselves to integers and real numbers.

Variables Variables are created when they are first assigned a value. x = 17 y = 3 * x All variables are global (for now). A variable exists from the time it is created until you quit Matlab. Variable names are case-sensitive. Entering a = 17 A = 42 creates two separate variables. Several variables containing useful constants are already defined pi 3.14159… Inf i, j sqrt(–1) NaN 0/0

Syntax: function-name ( arg1, arg2, … ) Examples: x = 3; y = 4; Functions Matlab provides a rich collections of standard functions. Trigonometry: sin, cos, tan, cot, asin, acos, atan, atan2… Exponential: exp, log, log10, sqrt Complex: real, imag, abs, … Rounding: floor, ceil, round, rem, sign Specialized: bessel, gamma, erf, log2, rat, … Syntax: function-name ( arg1, arg2, … ) Examples: x = 3; y = 4; d = sqrt(x ^ 2 + y ^ 2) sin(pi / 2) exp(1) sqrt(–1)

Output and Input The value of a Matlab expression or statement is displayed immediately unless it is followed by a semicolon. z = x ^ 2 w = x ^ 3; To change the precision of the output enter format long format short Other formats are also available. (Enter help format for details.) You can edit and reenter previous console input. Use the up- and down-arrow keys to access previous entries.

A single value, called a scalar, is simply an array of size 1. Arrays (Vectors) All data in Matlab is actually an array — a 1- or 2-dimensional table of numbers. (We only consider 1-D arrays in this lecture.) 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] x = [–5 sqrt(2) 17 2^3] Individual elements are accessed using a parenthesized subscript. x(3) The first element of array x is x(1). Can assign to elements of array as in Java. y(1) = 0 The number of elements in array x is given by the built-in function length(x)

Array Functions An array of evenly-spaced values can be generated by linspace(minVal, maxVal, nVals) Example: array of 100 values spaced from 0 to 2. v = linspace(0, 2*pi, 100); There are many functions to compute facts about arrays. min(x) max(x) mean(x) sum(x) x(1) + … +x(length(x)) prod(x) x(1) * … * x(length(x)) cumsum(x) cumulative sum

Creating Arrays 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]];

Creating Arrays 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)