Introduction to matlab lecture 2 of 4

1. >> for = 5
??? for = 5
Error: The expression to the left of the equals sign is not a valid target
for an assignment
2. >> else =6
??? else = 6
Error: Illegal use of reserved keyword "else"
3. >> cos = 2; cos(0)
??? Subscript indices must either be real positive integers or logicals
4. >> A = [1,2,3]; sum(A)
ans = 6
>> sum = 7; sum(A)
??? Index exceeds matrix dimensions
2

5. >> 5>2
ans = 1
6. >> 5<4
ans = 0
7. >> 1.5<=1.5
ans = 1
8. >> 2>=pi
ans = 0
9. >> 1.8==1.801
ans = 0
10. >> 1.8~=2
ans = 1
11. >> 1.8==1.80000000000000000000000001
ans = 1
3

 Creating and manipulating matrices
 Built-in functions for matrices
4

 Matlab treats all variables as matrices.
 Vectors are special forms of matrices and contain only one row OR
one column (A row vector is a 1xn matrix, A column vector is an mx1
matrix).
 Scalars are matrices with only one row AND one column (A scalar is a
1x1 matrix)
 Every matrix element has a numerical value. Non-digit elements
linked to ASCII code digits
A → 65, B → 66, etc.
a → 97, b → 98, etc.
- → 45, _ → 95, etc.
 Logical truth values assigned to digits (true → 1, false → 0)
5

 A matrix with only one row is called a row
vector.
 A row vector can be created in Matlab as
follows (note the commas or you can use
spaces):
» rowvec = [12 , 14 , 63]
rowvec =
12 14 63
6

 A matrix with only one column is called a
column vector.
 A column vector can be created in MATLAB as
follows (note the semicolons):
» colvec = [13 ; 45 ; -2]
colvec =
13
45
-2
7

 A matrix can be created in Matlab as follows
 (note the commas AND semicolons):
 » matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]
matrix =
1 2 3
4 5 6
7 8 9
8

 A portion of a matrix can be extracted and stored in
a smaller matrix by specifying the names of both
matrices and the rows and columns to extract.
 The syntax is:
sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;
where r1 and r2 specify the beginning and ending
rows and c1 and c2 specify the beginning and
ending columns to be extracted to make the new
matrix.
9

 The matrix indices begin from 1 (not 0 (as in C))
 The matrix indices must be positive integer
12

 Accessing Single Elements of a Matrix A(i,j)
 Accessing Multiple Elements of a Matrix
A(1,4) + A(2,4) + A(3,4) + A(4,4)
A([1,3,4], :)= all of rows 1, 3 and 4
sum(A(1:4,4))
sum(A(:,end))
The keyword end refers to the last row or column.
 Deleting Rows and Columns: to delete the second column
of X, use X(:,2) = []
 Concatenating Matrices A and B C=[A;B]
13

Logic--searching with find
 Find--searches for the truth (or not false)
› b=[1 0 -1 0 0];
› I=find(b)
I=1 3 b(I) is an array without zeros
› I=find(ones(3,1)*[ 1 2 3]==2)
I= 4 5 6
› [I,J]=find(ones(3,1)*[ 1 2 3]==2)
I= 1 2 3
J= 2 2 2
15

 + addition
 - subtraction
 * multiplication
 ^ power
 ‘ complex conjugate transpose
 / right matrix division
same as right multiplication by divisor inverse
 left matrix division
same as left multiplication by divisor inverse
16

 Scalar functions –
used for scalars
and operate
element-wise when
applied to a matrix
or vector
 e.g. sin cos
tan atan
asin log abs
anglesqrt
roundfloor
17

 Vector functions –
operate on vectors
returning scalar
value
 e.g. max min
mean prod
sum length
18

 Matrix functions –
perform operations
on matrices
 e.g. eye size
inv det eig
 X = ones(r,c) %
Creates matrix full
with ones
19

 X = zeros(r,c) % Creates
matrix full with zeros
 A = diag(x) % Creates
squared matrix with vector
x in diagonal
 [r,c] = size(A) % Return
dimensions of matrix A
 B = rand(r,c) %creates a
matrix of random numbers.
20

 + - * / % Standard operations
 .+ .- .* ./ % Wise addition, subtraction,…
 v = sum(A) % Vector with sum of columns
21

 Note that
It is better to
multiply
A*inv(B)
instead of
divide A/B
24

25
Command flipud flips the matrix in UP/DOWN direction.
Command fliplr flips the matrix in LEFT/RIGHT direction

Some powerful matrix functions in Matlab
 X = A’ % Transposed matrix
(A transpose operation changes the column of a matrix into rows, and
rows into columns)
 X = inv(A) % Inverse matrix squared matrix
 X = pinv(A) % Pseudo inverse
 X = chol(A) % Cholesky decomp.
 d = det(A) % Determinant
 [X,D] = eig(A) % Eigenvalues and eigenvectors
 [Q,R] = qr(X) % QR decomposition
 [U,D,V] = svd(A) % singular value decomp
27

 maxVal =
max(aaa)
% finds the
maximum
value for a
matrix.
28

 minVal =
min(aaa);
% finds the
minimum
value for a
matrix.
29

 colSum =
sum(aaa);
% finds the
sum of each
column
30

 If A is a matrix,
sum(A) treats the
columns of A as
vectors, returning
a row vector of
the sums of each
column.
 B = sum(A,dim)
sums along the
dimension of A
specified by
scalar dim.
31

 B = sort(A,’ascend/descend’) % sorts a matrix. Default is
ascending mode.
32

1. A is a row vector. The first element in A is 0, and the
value vary from 0 to 10 with increment of 2
2. B is row vector with six elements, and every variable
in B is 2.5
3. Calculate the value of C, which is equal to the sum of
A and B
4. Calculate the value of D, which is equal to the
element-by element multiplication between A and B
5. Change A(1,3) to 8.
6. Calculate E = A./B
33

1. A=[1, 2.7, 8.9, -8, 4, 3.5]
2. B>0;
3. Return the sum and mean value of all the
elements in A.
4. Return the max value of all elements in A.
5. fix(A)
34

1. A=[1, 2.7, 8.9, -8, 4, 3.5; 6.5, 8.9, 5, -0.9,
3, 19] ;
2. Set every element in six column to be 0.7.
3. Remove the second column in A;
4. Return the mean value of every column in
A;
5. Return the mean value of whole A;
35

Introduction to matlab lecture 2 of 4

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Introduction to matlab lecture 2 of 4