Transcript Matlab

Getting started with Matlab
Numerical Methods
Appendix B
http://www.mathworks.com/access/helpdesk/
help/techdoc/learn_matlab/learn_matlab.html
What Is MATLAB?
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Math and computation
Algorithm development
Data acquisition
Modeling, simulation, and prototyping
Data analysis, exploration, and visualization
Scientific and engineering graphics
Application development, including graphical
user interface building
The MATLAB System
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Development Environment.
The MATLAB Mathematical Function
Library.
The MATLAB Language.
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a high-level matrix/array language
Graphics.
The MATLAB External Interfaces (API).
MATLAB Online Help
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Desktop Tools and Development Environment
Mathematics
Programming
Graphics
3-D Visualization
Creating Graphical User Interfaces
External Interfaces/API
Matrices and Arrays
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To enter Dürer's matrix, simply type in the
Command Window
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>>A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15
14 1]
A=
16 3
 5 10
 9 6
 4 15
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2
11
7
14
13
8
12
1
sum, transpose, and diag
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sums of the columns of A
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>>sum(A)
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>>sum(A')'
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ans = 34 34 34 34
ans =
34
34
34
34
sum(diag(A))
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ans = 34
The transpose
operation is denoted
by an apostrophe or
single quote, '.
Subscripts
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>>A(1,4) + A(2,4) + A(3,4) + A(4,4)
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ans = 34
>>X = A;
>>X(4,5) = 17
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X=
16 3
5 10
9 6
4 15
2
11
7
14
13
8
12
1
0
0
0
17
The Colon Operator
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>> 1:10
ans =
1
2
3
4
5
6
7
8
9 10
>> 100:-7:50
ans = 100 93 86 79 72 65 58 51
>> 0:pi/4:pi
ans =
0 0.7854 1.5708 2.3562 3.1416
In subscript
>> A(1,1:4)
ans = 16
3
2
13
The magic Function
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>> B = magic(4)
B=
16
2
3 13
5 11 10
8
9
7
6 12
4 14 15
1
To make this B into Dürer's A, swap the two middle
columns:
A = B(:,[1 3 2 4])
Expressions
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Variables
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Numbers
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3 -99 0.0001 9.6397238
-3.14159j
3e5i
Operators
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num_students = 25
+-*/^
\
Left division
Functions
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help elfun
help specfun
help elmat
1.60210e-20 6.02252e23
1i
Working with Matrices
Generating Matrices
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zeros
All zeros
ones
All ones
rand
Uniformly distributed random elements
randn
Normally distributed random elements
ones(n,m)
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>> ones(3,4)
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ans =
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1
1
1
1
1
1
1
1
1
1
1
1
zeros(n,m)
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>> zeros(3,4)
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ans =
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0
0
0
0
0
0
0
0
0
0
0
0
rand(n,m)
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>> rand(3,4)
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ans =
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0.9501
0.2311
0.6068
0.4860
0.8913
0.7621
0.4565
0.0185
0.8214
0.4447
0.6154
0.7919
randn(3,4)
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>> randn(3,4)
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ans =
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-0.4326 0.2877 1.1892 0.1746
-1.6656 -1.1465 -0.0376 -0.1867
0.1253 1.1909 0.3273 0.7258
Load and Save .mat
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>>
>>
>>
>>
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>> load mydata.mat
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A = [1 2 3]
B = [4 5 6]
save mydata.mat
clear
eye(n), eye(size(A))
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>> eye(3)
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>> eye(size(A))
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ans =
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ans =
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1
0
0
0
1
0
0
0
1
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1
0
0
0
1
0
0
0
1
0
0
0
Load and save ASCII file
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>> a = magic(4); b = ones(2, 4) * -5.7; c = [8 6 4 2];
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>> save
>> clear
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>>
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-ascii mydata.dat
load mydata.dat
>> mydata
mydata =
16.0000
5.0000
9.0000
4.0000
-5.7000
-5.7000
8.0000
2.0000
11.0000
7.0000
14.0000
-5.7000
-5.7000
6.0000
3.0000
10.0000
6.0000
15.0000
-5.7000
-5.7000
4.0000
13.0000
8.0000
12.0000
1.0000
-5.7000
-5.7000
2.0000
Building Tables
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>> n = (0:9)';
pows = [n n.^2 2.^n]
pows =
0
0
1
1
1
2
2
4
4
3
9
8
4 16 16
5 25 32
6 36 64
7 49 128
8 64 256
9 81 512
MATLAB uses a dot, or decimal
point, as part of the notation for
multiplicative array operations.
Multivariate Data
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>>D = [
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3.2
3.5
7.1
2.4
1.2 ]
mean and standard deviation of each column, use
>>mu = mean(D), sigma = std(D)
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134
201
156
148
170
to obtain the
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72
81
69
82
75
mu =
75.8
161.8
3.48
sigma = 5.6303
25.499 2.2107
>>help datafun
>>help stats
Matlab Graphics
plot(x,y)
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t=[0:5:100]
y=t.^0.34-log10(t)+1./t
plot(t,y)
title(‘Plot of y versus t’)
grid
3D graphics
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[x,y]=meshgrid(-4.0:0.2:4.0,-4.0:0.2:4.0);
z=(-20*x.^2+x)+(-15*y.^2+5.*y);
surfl(x,y,z);
axis([-4 4 -4 4 -800 0])
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
Try yourself, and have fun!