>> x = [1 2 3 4 5];y = 2*x

y =

2 4 6 8 10

Arrays

x and y are one dimensional arrays called vectors.

In MATLAB all variables are arrays. They allowfunctions with many values to be described.

EGR 106 – Week 2 – Arrays

Definition, size, and terminology Construction methods Addressing and sub-arrays Some useful functions for arrays Character arrays Arrays chapter 2, pages 33 - 50 Scripts chapter 4, pages 85 - 93

Recall from Last Week

Variables: placeholders for numerical data– equal sign is an assignment operator

c = 7.5 c = c + 1– naming restrictions (not pi, etc. ) – can be complex valued ( x = 3 + i 7 )

Basic math on numbers and variables:

Precedence ( ) ^ * / + -

Names for special sizes– scalar: 1 x 1 array 4 or [4]

– row vector: 1 x C array

[ 9 7 5 4 2 ] is a 1 x 5 row vector

– column vector: R x 1 array

is a 3 x 1 column vector

134

Uniformly Spaced Vectors

Colon operatorfirst : increment : maximum

yields a row vector of equally spaced values– examples:

0 : 2 : 10 [ 0 2 4 6 8 10 ] 1 : 5 [ 1 2 3 4 5 ]

7 : -2 : -3 [ 7 5 3 1 -1 -3 ] 1 : 2 : 8 [ 1 3 5 7 ]

– default for increment is 1 Note – does not hit 8!!

Arrays

Fundamental data unit in Matlab– all variables are stored as arrays

Data values organized into rows and columns

– numeric or alphanumeric entries

4 5 3 91 0 4 6 6 2 01 8 -3 2 0

y ie ld =

M a rtyJ a m e sB o b

na m e =

Array Construction

Direct specification:– Name followed by an equal sign ( = ),

just like variables– List values within a pair of brackets ( [ ] )– Enter data one row at a time

left to right, top to bottom order space or comma between the values rows separated by semicolons or the enter key

Size or dimension of an array:– number of rows and columns– written as R by C or R x C

where R = number of rows

C = number of columns

e.g.

yield is 3 by 4

test is 1 by 5

4 5 3 91 0 4 6 6 2 01 8 -3 2 0

y ie ld =

4 5 3 5 0 te s t =

Building Arrays

>>a = [1 2 3; 4 5 6; 7 8 9; 10 11 12] >>a = [1:3; 4:6; 7:9; 10:12]

– Can use simple math operations as well as numerics as the entries:

– Note the common format of all entries in the response (exp(1) = e = 2.71828, log10(100) = 2, 2-12 = 0.00024414)

– MATLAB scales the exponent to the largest entry !!

– This scaling is sometimes deceptive:

Not really zero

Really zero

Concatenation – gluing arrays together

if a = [ 1 2 3 ] b = [ 4 5 6 ]

– Attaching left to right – use a comma [ a, b ]

– Attaching top to bottom – use a semicolon

[ a; b ] 1 2 3 4 5 6

1 2 3 4 5 6

semicolon

comma

– Note that sizes must match for this to work:

if a = [ 1 2 3 ] then

[ a, b ] = ?? [ a; b ] = ??

– Size needs for concatenation:# of rows the same for side by side (comma)# of columns the same for top to bottom

(semicolon)

4 51 0 4

b =

Addressing and Sub-Arrays

How to indicate a particular element within an array:

– use parentheses after the array name– list desired row, comma, desired column– e.g. yield(2,4)

4 5 3 91 0 4 6 6 2 01 8 -3 2 0

y ie ld =

How About More than One Entry?

Can specify a rectangular sub-array– again, use parenthesis after the array name– list desired rows, comma, desired columns

as a vector, typically in brackets – e.g. yield([1 2],[3 4])

4 5 3 91 0 4 6 6 2 01 8 -3 2 0

y ie ld =

Used to read a value from an array (right hand side of = )

Addressing Errors

Things that do Work

Single indexing of matrices counts down columns, starting at the top left

Some Useful Array Operators

Transpose (single quote symbol ' )– switches rows and columns

Useful Array Functions

length(A) is the number of elements in the vector A

[m n] = size(A), where A is a matrix with m rows and n columns

ones(n) is an n x n matrix of ones zeros(n) is an n x n matrix of zeros

CHANGE THE MATRIX

sample =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

>> sample(1,3)=9

sample =

1 2 9 4 5 6 7 8 9 10 11 12 13 14 15 16

Used to read a sub-array ( rhs of =)

Note – scalar row choice does not need brackets!

Character Arrays

Rows of the array are strings of alphanumeric characters, one array entry per character

Enter using a single quotation mark ( ' ) at each end

Assigning values with too large an index just grows the array

Scalars work for sub-array replacement – they just scale up to the right size

Replacing with a null matrix is the same as deleting – but it only works for entire rows or columns

Rules of the road for arrays:Symbols to use:

brackets to glue elements together to make an array (left to right or top to bottom)comma (or space) and semicolon (or enter) for separating column/row elementsparentheses after the array name for addressing

Be careful to match array sizesRemember – rows first, then columns in addressing

Scripts – Simple Programs

So far, commands have been typed in the command window: – Executed by pressing “enter”– Edited using the arrow keys or

the history window

Script (m-file) Concept

A file containing Matlab commands – Can be re-executed – Is easily changed/modified or e-mailed to someone

Commands are executed one by one sequentially– File is executed by typing its name (without .m)– Results appear in the command window (or use ; )

Can be created using any text editor – .m extension– Listed in Current Directory window

Sample Scripts

DIFFUSION

Diffusion – is the movement of matter driven by

chemical and thermal processes such as

concentration gradients and heating. Both are

needed as it is an activation controlled

process.

Atoms will diffuse down a concentration gradient

provided they have overcome the

activation energy needed for the process.

Copper atoms will diffuse into the

Nickel until an equal concentration is

Achieved. Remember that Cu-Ni system

Is one of complete solid solubility.

Position

Cu

Practical Example

Decarburization at 1200F after quench crack in material. The crack left enough open surfaceFor the carbon to diffuse out and leave a ferrite layer either side of the crack.

ARRAYS FOR DIFFUSION

DIFFUSION RATE AGAINST TEMPERATURE

STRENGTH AGAINST CARBON CONTENT