Predefined MATLAB Functions
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Transcript Predefined MATLAB Functions
Predefined MATLAB Functions
ELEC 206
Computer Applications for
Electrical Engineers
Dr. Ron Hayne
Elementary Math Functions
abs(x)
sqrt(x)
sign(x)
round(x), fix(x)
ceil(x), floor(x)
rem(x,y)
exp(x)
log(x), log2(x), log10(x)
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Trigonometric Functions
Angle in radians (180 degrees = pi radians)
sin(x), cos(x), tan(x)
asin(x), acos(x), atan(x)
Angle in degrees
sind(x), cosd(x), tand(x)
asind(x), acosd(x), atand(x)
angle_deg = angle_rad*(180/pi);
angle_rad = angle_deg*(pi/180);
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Data Analysis Functions
Minimum and Maximum
max(x), [a,b]=max(x), max(x,y)
min(x), [a,b]=min(x), min(x,y)
Averages
median(x), mean(x), std(x)
Sums and Products
sum(x), prod(x)
cumsum(x), cumprod(x)
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Data Analysis Functions
Sorting
sort(x)
Size
size(x), [a,b]=size(x)
length(x)
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Random Numbers
Uniform Random Numbers
rand('seed',n), rand(n), rand(m,n)
Interval 0 to 1
Interval a to b
x = (b - a)*r + a;
Gaussian Random numbers
randn('seed',n), randn(n), randn(m,n)
Normal Distribution
Mean = 0, Standard Deviation = 1.0
Modified Distribution
Mean = b, Standard Deviation = a
x = a*r + b;
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Problem Solving Applied
Weather Data
Problem Statement
Using the data in the file Weather_Data.xls, find the
total monthly precipitation, the total precipitation for
the year, and the day on which it rained the most.
Input/Output Description
Total Monthly Precipitation
Total Precipitation
Day of Most Rain
Weather_Data.xls
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Problem Solving Applied
Hand Example
12x31 Matrix
Rows = Months
Columns = Days
Hundreths of inches
Invalid = -99999
tot_jan = 2.72 in
tot_feb = 1.66 in
tot_jan+feb = 4.38 in
max = Jan 3
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0
0
272
0
61
103
0
2
2
0
17
27
260
1
0
0
47
0
0
0
0
0
30
42
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
14
1
163
5
0
0
0
0
0
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Problem Solving Applied
Algorithm Development
Import spreadsheet into matrix
Change -99999 values to 0
Interchange rows and columns
Monthly Totals (inches) = sum columns/100
Yearly Total = sum Monthly Totals
Find max and location
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MATLAB Solution
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MATLAB Solution
clc
% Example 3.3 - Weather Data
% Find the total precipitation for each month, and
% for the entire year, using a data file
%
wd=Weather_Data;
wd(2,29)=0;
% Change -99999 values to 0
wd(2,30)=0;
wd(2,31)=0;
wd(4,31)=0;
wd(6,31)=0;
wd(9,31)=0;
wd(11,31)=0;
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MATLAB Solution
% Use transpose operator to change rows to columns
wd = wd';
% Sum of each column is sum for each month
monthly_total = sum(wd)/100
% Find the annual total
yearly_total = sum(monthly_total)
% Find the annual maximum, and month
[maximum_precip,month] = max(max(wd));
% Find the annual maximum, and day
[maximum_precip,day] = max(max(wd'));
% Print max data
maximum_precip = maximim_precip/100
month
day
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Manipulating Matrices
Defining Matrices
A = [1 2 3; 4 5 6];
A = [1 2 3;
4 5 6];
B = [1 2 3]
B = [1 2 ...
3];
C = [A; B]
= [1 2 3; 4 5 6; 1 2 3];
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(2x3)
(1x3)
(3x3)
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Manipulating Matrices
Changing Matrices
D = [3 4 5];
D(2) = 8;
D =
3 8 5
D(5) = 7;
D =
3 8 5 0 7
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Manipulating Matrices
Defining Matrices with the Colon Operator
E = 1:4
E =
1 2 3 4
F = 0.0:0.5:2.0
F =
0.0 0.5 1.0 1.5 2.0
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Manipulating Matrices
Extracting Data with the Colon Operator
G = [1 2 3; 2 3 4; 3 4 5; 4 5 6];
x = G(3, :)
x =
3 4 5
y = G(:, 2:3)
y =
2 3
3 4
4 5
5 6
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Manipulating Matrices
Extracting Data with
the Colon Operator
G = [1 2
2 3
3 4
4 5
G(3,2)
ans = 4
G(7)
ans = 4
3;
4;
5;
6];
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G(:)
ans =
1
2
3
4
2
3
4
5
3
...
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Computational Limitations
Double Range
Double Precision
10-308 to 10+308
Exponent Overflow
Divide by Zero
y = 2e200;
y^2
ans = Inf
Exponent Underflow
eps
ans = 2.2204e-016
x = 2e-200
x/y
ans = 0
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y/0
ans = Inf
0/0
ans = NaN
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Special Values and Functions
Special Values
pi
i
j
Inf
NaN
Special Functions
clock
Year Month Day Hour Minute Seconds
date
dd-Mth-yyyy
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Summary
MATLAB Functions
Math, Trig, Data Analysis, Random Numbers
Problem Solving Applied
Manipulating Matrices
Special Values and Functions
End of Chapter Summary
MATLAB Summary
Characters, Commands and Functions
Key Terms
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