Predefined MATLAB Functions

1
Predefined MATLAB Functions

• ELEC 206
• Computer Applications for Electrical Engineers
• Dr. Ron Hayne

2
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)

3
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)

4
Data Analysis Functions

• Minimum and Maximum
• max(x), a,bmax(x), max(x,y)
• min(x), a,bmin(x), min(x,y)
• Averages
• median(x), mean(x), std(x)
• Sums and Products
• sum(x), prod(x)
• cumsum(x), cumprod(x)

5
Data Analysis Functions

• Sorting
• sort(x)
• Size
• size(x), a,bsize(x)
• length(x)

6
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 ar b

7
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_janfeb 4.38 in
• max Jan 3

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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
• wdWeather_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)

15
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 14
• E
• 1 2 3 4
• F 0.00.52.0
• 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(, 23)
• 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 10308
• Exponent Overflow
• y 2e200
• y2
• 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