Predefined MATLAB Functions

ELEC 206

Computer Applications for Electrical Engineers

Dr. Ron Hayne

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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

Weather_Data.xlsDay of Most Rain

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Problem Solving Applied

Hand Example12x31 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 inmax = Jan 3

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 matrixChange -99999 values to 0 Interchange rows and columnsMonthly Totals (inches) = sum columns/100Yearly Total = sum Monthly TotalsFind 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]; (2x3) A = [1 2 3;

4 5 6]; B = [1 2 3] (1x3) B = [1 2 ...

3]; C = [A; B]

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

G(3,2)

ans = 4 G(7)

ans = 4

G(:)

ans =

1

2

3

4

2

3

4

5

3

...

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Computational Limitations

Double Range 10-308 to 10+308

Exponent Overflow y = 2e200; y^2

ans = Inf

Exponent Underflow x = 2e-200 x/y

ans = 0

Double Precision eps

ans = 2.2204e-016

Divide by Zero 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