Introduction to Scientific Computing

Statements

foo = x^2 + sin(5*y) / exp(67*z);

The semicolon at the end is optional.

Built-in MATLAB functions

sin(x),cos(x),exp(x),log(x),atan(x),cosh(x),sinh(x),mean(x),median(x),etc.

Array

x = [1,3,9,11,-10.2];
foo = x(3); % extracts third element in the array
x(2) = 27; % reassign element in the array

x = 1:15 % creates an array with the number 1 through 15
x = 4:2:28; % creates an array starting at 4 and going up by 2 until it gets to 28
x = -1.3:0.1:1.3; %creates an array starting at -1.3 and going up by 0.1 until it gets to 1.3

x = 1:2:6; % x = [1,3,5]

Operations on arrays

x = 0:0.1:10;
y = exp(5*x).*sin(x); % evaluate an expression on every element in the array x producing a new array called y
plot(x,y);

x = [1,2,3,4,5];
y = [7,8,9,10,11];
z = x + y; % element-wise addition adds corresponding elements
z = x.*y; % element-wise multiplication
z = x./y; % element-wise division

Overflow

X = uint8(78); Y = uint8(190);
Z = X + Y;
% overflow - value will be clipped to 255

Scientific notation

Note that numbers in scientific notation have the following components

• A sign - positive or negative
• A mantissa(尾数) - ex. 2.13
• An exponent - ex. 17 e.g. +2.13e17

Arrays and numerical types

When an array variable is created all of the numeric values in that array share the same numeric type. For example we can talk about an array of uint16s or an array of doubles.
x = single(0:0.1:100);make an array of single precision（单精度） numbers

A few useful MATLAB commands

• whos Lists all of the variables currently in your workspace and shows you their types
• clear Clears all of the variables in your workspace – you can also use this to clear specific variables
• clc Just clears the command window – has no effect on the workspace

Function

function f = fact(n)
    f = prod(1:n);
end

function [output1,output2,output3] = myFunction(input1,input2,input3)

Naming a Function

Must start with a letter from the alphabet

Special Functions

function out1 = testFunction(in1)
% A test function
% this would report, in the help function, all of functionality of the function
% in1 = function input (units: not specified)
% out2 = function output (units : not specified)

(in the command window)

lookfor 'a test function'

% testFunction            - A test function

help testFunction

% A test 
% this would report, in the help function, all of functionality of the function
% in1 = function input (units: not specified)
% out2 = function output (units : not specified)

Search paths

• The working folder at startup can be changed using the userpath function

userpath('C:\ATRI')

• Paths can also be “permanently” added to the search path using the addpath() function
• Paths can be removed using the rmpath() function

Commenting

• Highlight a selection or place your cursor on a line and press “ctrl+r” to comment a section or line of code, respectively
• “ctrl+t” uncomments the code

Anonymous Function

function_name = @ (arguments) expression

FtoC = @ (F) 5*(F-32)./9

% examples
FA = @ (x) exp(x^2)/sqrt(x^2+5)
FA(2)
FA = @ (x) exp(x.^2)./sqrt(x.^2+5)
FA([1 0.5 2])

Function Handles

f = @sin;
m = fminbnd(f,0,2*pi)

q = integral(@cubicPoly,0,1);

Vectors(Arrays)

% Linspace and logspace
x = linspace(1,5,5)
x = logspace(1,5,5)

x = [5, 9, 4, 1, 7, 3, 4, 8]
% Accessing vector elements
y = x(1)
y = x(1:3)
y = x(end)
y = x(end-2)
y = x([1,3,6])  % y = [5,4,3]

% The indices start at 1, not 0.

% Overwriting
x(end) = 1;

%Add ending indices
x(end+1) = 8
x(end+1:end+2) = [6,9]

%Removing elements 
x(1) = []; % Remove the first element
x(end-3,end) = [];

Iteration

for jj = 1:20
    disp(jj)
end

a = 1;
while a < 10
    a = a + 1;
end

Array Operation vs Iteration

The if statement

a = 1;
b = 2;
if a == 1;
    disp('a is equal to 1! Yeah');
end

elseif a == 1 && b == 2;
    disp('...')
end

Logical Operators

Logical Vectors

a = [1 6 5] < 2
% a = [1,0,0]

x = [5 9 2 4 3];
v = logical([1 0 1 0 1]);
xp = x(v);
% xp = [5,2,3]

Vocabulary

• Scalars 标量