Array Accessing and Strings ENGR 1187 MATLAB 3

Today's Topics § Array Addressing (indexing) § Vector Addressing (indexing) § Matrix Addressing (indexing)

What is Addressing (indexing)? § Each element in a vector has an address, also called an index § MATLAB indexing starts at 1 (not at 0!) § We can access/retrieve/extract the individual elements by referring to their addresses § Useful for transforming data or doing calculations with only part of a vector

Array Accessing In The Real World Recall from the previously class that seismic data is important in structural design for civil engineers. Accessing data from an array at a certain location in California allows engineers to design their structures according to vibrational data in a specific region. This allows the building to be designed to this standard but not overdesigned to more extreme data in other regions.

Today's Topics § Array Addressing (indexing) § Vector Addressing (indexing) § Matrix Addressing (indexing)

Vector Addressing Example § Define a vector with 9 elements: >> v = [ 12 15 18 21 24 27 30 33 36]; • We can access the elements individually: • >> v(4) ans = 21

Vector Addressing Example We can retrieve any element by indexing: We can assign individual vector elements to variables: >> v(7) ans = 30 >> B= v(7) B= 30 >> v(9) ans = 36 >> C=v(9) C= 36

Vector Addressing Examples We can add elements together. Recall: B = v(7), C = v(9) >> D= B + C D= 66 We can also add elements directly: >> v(4) + v(7) ans = 51

Changing Element Values § We can change an element in a vector by directly assigning a new value to a specific address. § Let’s change the 6 th element of v to 90: v= [12 15 18 21 24 27 30 33 36] >> v(6) = 90; >> v v= 12 15 18 21 24 90 30 33 36

Addressing Column Vectors Addressing (indexing) an element in a column vector works the same way as with a row vector: >> col = [25; 30; 35; 40; 45; 50] >> t = col(4) t= 40

Vector Functions § MATLAB has MANY built-in functions we can use with vectors max() min() sum() length() …etc.

Vector Functions Examples length() gives us the number of elements in a vector >> fun = [4 6 8 10 12]; >> length(fun) ans = 5

Vector Functions Examples Zeros() gives us a vector or matrix of zeros >> nothing = zeros (1 , 7) nothing = 0 0 0 0

Vector Functions Examples ones() gives us a vector/matrix of all ones >> single = ones(1, 12) single = 1 1 1

Addressing a Range of Elements § The colon operator allows us to access a range of elements in a vector § This is useful if we want to extract or alter only a portion of an existing vector

Example: Addressing a Range Define a vector: >> vec = [ 1 3 5 7 9 11 13 15 ]; Select elements 3 through 7 in 'vec': >> vec(3: 7) vec = 5 7 9 11 13

Example: Addressing a Range We can access a range of elements in any vector and assign them to a new variable. Recall that vec = [ 1 3 5 7 9 11 13 15 ] >> t= vec(2: 5) t= 3 5 7 9

Vector Modifications We can add elements to any existing vector. Recall that 'vec' has 8 elements: vec = [ 1 3 5 7 9 11 13 15 ] >> vec(9: 12)= [ 2 4 6 8] vec = 1 3 5 7 9 11 13 15 2 4 6 8

Vector Modifications We can create new vectors made up of elements from previously defined vectors: >> E = [ 3 6 9 12 ]; >> G = [ 2 4 8 5]; >> K = [ E(1: 3) G(3: 4)] K= 3 6 9 8 5

Today's Topics § Array Addressing (indexing) § Vector Addressing (indexing) § Matrix Addressing (indexing)

Matrix Addressing § Matrix addressing works very similarly to vector addressing § Individual elements are addressed by their row number and column number: (m, n)

Matrix Addressing Example Let's define a matrix, then access some elements: >> data = [ 2 3 4 5 ; 1 6 8 9] data = 2 3 4 5 1 6 8 9 >> data (2, 3) ans = 8

Matrix Addressing Example We can perform mathematical operation with matrix elements. Let's add two values from our matrix called 'data': data = 2 3 4 5 1 6 8 9 >> data_sum= data(1, 2) + data(2, 4) data_sum = 12

Colon Operator With Matrices § A(: , 3) Elements in all rows of column 3 § A(2, : ) Elements in all columns of row 2 § A(: , 2: 5) Elements in columns 2 to 5 in all rows § A(2: 4 , : ) Elements in rows 2 to 4 in all columns § A(1: 3 , 2: 4) Elements in rows 1 to 3 and in columns 2 to 4

Extracting Matrix Elements § We can extract a portion of a matrix and assign it to a new variable § new_matrix =matrix( r 1 : r 2, c 1 : c 2) • r 1 is the starting row • r 2 is the ending row • c 1 is the starting column • c 2 is the ending column

Example: Extracting Elements >> A = [ 1 3 5 7 2468 3 6 9 12 4 8 12 16] A= 1 2 3 4 3 5 7 4 6 8 6 9 12 8 12 16 >> B = A(1: 3, 2: 4) B= 3 5 7 4 6 8 6 9 12

Example: Extracting Elements >> C = A(1: 3 , : ) >> D = A( : , 2: 4) C= 1 3 5 7 2 4 6 8 3 6 9 12 D= 3 4 6 8 5 6 9 12 7 8 12 16 Remember

Important Takeaways § An element in a defined vector can be accessed with v(x) - an element in a vector can be defined, or re-defined with v(x)=z § An element in a defined matrix can be accessed with v(x: y)- an element in a matrix can be defined, or re-defined with v(x: y)=z § Strings are lines of text and can be used instead of numerical values - they are defined inside single apostrophes, e. g. ‘Your text here. ’

Preview of Next Class § Array Operations • Scalar – vector operations • Vector – vector operations ¡ Dot operator, when to use it • Built-in vector functions ¡ Ex: max, min, mean etc. • Examples

What’s Next? § Review today’s Quiz #03 § Open the in-class activity from the EEIC website and we will go through it together. § Then, start working on MAT-03 homework. § Before next class, you will read about array operations, this is an introduction of mathematical operations in MATLAB and basics of linear algebra.