MATLAB Programming

數值方法 2008, Applied Mathematics NDHU 1

• Matrix Manipulation• Plotting

MATLAB Programming


Matrix creation

Matrix generation eye ones zeros diag rand repmat reshape

Vector generation linspace equi-spacing


Exercise

matrix creation


rand

rand(m,n)Create a matrix composed of m rows and n

columns. All of its elements are uniformly sampled from [0 1]


Matrix size

A=rand(m,n)size(A)

Return row and column numbers of matrix A


eye(n), ones(n), zeros(n)

eye(n)Create an nxn identical matrix

ones(n)Create an nxn matrix with all elements

identical to onezeros(n)

Create an nxn zero matrix


Diagonal matrix

v=[1 2 3 4 5]diag(v)

Create an diagonal matrix whose diagonal vector is identical to v


Matrix multiplication

Validity A*B is valid if the column number of A is

identical to the row number of Bones(5,1)*[1 2 3 4 5]

Form a 5x5 matrix. Each of its five rows equals [1 2 3 4 5]


Matrix replication

v=[1 2 3 4 5]repmat(v,n,m)

Repeat v n times vertically Repeat the result m times horizontally

repmat(v,5,1)


Reshape

A=rand(m,n)

B=reshape(A,p,q)Validity: mxn needs identical to pxqB is a pxq matrixColumn major reshaping of a matrix


Column major

A=[1 2 3;4 5 6];

B=reshape(A,3,2)

1 5

4 3

2 6


Column major

6

3

5

2

4

1A

6

3

5

2

4

1

B

B=reshape(A,3,2)


Column major

A=[1 2 3;4 5 6;7 8 9;10 11 12]B=reshape(A,3,4)


Vector creation

Direct inputa=[1 2 3 4 5 6 7 8 9 10]

Spacinga=1:10a=1:1:10a=1:2:100A=100:-5:1


Linspace

v=linspace(a,b,n)v is a vector which consists of n elementsThese elements equally partition the interval

[a b]


Plot

Plot pointsplot(x,y,’.’)x and y have same length, such as nThis instruction draws n points, denoted by

{(xi yi)}i

xi denotes the ith element of vector x

yi denotes the ith element of vector x


Plot points and lines

plot(x,y)n points and lines connecting two

consecutive points


Plot a function

x=linspace(-5,5,100);

y=cos(x);

plot(x,y)The output contains a set of points

specified by vectors x and yTwo consecutive points are connected


subplot

x=linspace(-5,5,100);

subplot(2,1,1)

plot(x,cos(x))

subplot(2,1,2)

plot(x,sin(x))

MATLAB Programming

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