CSI 1100 Lab 10 November 1519

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CSI 1100 Lab 10November 15-19

• Slides by Alan Williams

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Matrix Example 1 Objective

• Design an algorithm that will create a matrix of
  wind chill values for various temperatures and
  wind speeds.
• The set of temperatures will be stored in an
  array
• The set of wind speeds will be stored in a second
  array
• An algorithm is already available that calculates
  the wind chill for a specific temperature and
  wind speed.
• Implement the algorithm in Java.
• For those of you who havent yet experienced an
  Ottawa winter, you may want to keep the results
  for future use ?

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Given algorithm Wind Chill calculation

• Suppose we are given the following algorithm
• Chill ? WindChill( Temperature, WindSpeed )
• that calculates the wind chill for a given
  temperature in C, and wind speed in km/hr.
• Restrictions
• WindSpeed ? 5.0 km/hr
• Temperature should be between -50.0C and 5.0C.
• More info http//www.msc.ec.gc.ca/education/windc
  hill/

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Wind Chill Table

• Design the following algorithm
• GIVENS
• TempArray (an array of temperatures in C)
• NT (length of TempArray)
• SpeedArray (an array of wind speeds in km/hr)
• NS (length of SpeedArray)
• RESULTS
• ChillTable (a matrix of wind chill values, with
  NT rows
• and NS
  columns)
• INTERMEDIATES
• (to be determined)
• HEADER
• ChillTable ? WindChillTable( TempArray, NT,
  SpeedArray, NS)

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Implementation in Java

• Get the following file from the virtual campus
  for lab 10
• WindChill.java
• The file WindChill.java already has a main( )
  method as well as an implementation of the method
• windChill( temperature, windSpeed )
• The file WindChill.java contains the method
• printTable( temperatureArray, speedArray,
  chillTable )
• used to print the matrix.

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Sample output

• CSI1100 Fall 2004, Lab 10, Example 2
• Name Alan Williams, Student 81069665
• Lab section 999, TA Grace Hopper
• Enter a set of temperatures between -50 and 5
• 5 0 -5 -10 -15 -20 -25 -30 -35 -40
• Enter a set of wind speeds
• 5 10 15 20 25 30 35 40
• Wind Chill Table
• Speed 5.0 10.0 15.0 20.0 25.0 30.0 35.0
  40.0
• --------------------------------------------------
  ------
• Temp.
• 5.0 4.1 2.7 1.7 1.1 0.5 0.1 -0.4
  -0.7
• 0.0 -1.6 -3.3 -4.4 -5.2 -5.9 -6.5 -7.0
  -7.4
• -5.0 -7.3 -9.3 -10.6 -11.6 -12.3 -13.0 -13.6
  -14.1
• -10.0 -12.9 -15.3 -16.7 -17.9 -18.8 -19.5 -20.2
  -20.8

Lowest value during winter 2003 in Ottawa (10th
coldest winter in past 56 years)
Jan. 1994 this value was achieved in Ottawa!
(coldest winter since 1948)
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Example 2 Matrix Transpose

• Write an algorithm that will take a matrix of
  integers A and transpose the matrix to produce a
  new matrix AT. The transpose of the matrix is
  such that element arc in the original matrix will
  be element aTcr in the transposed matrix. The
  number of rows in A becomes the number of columns
  in AT, and the number of columns in A becomes the
  number of rows in AT.
• For example

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Translate to Java

• Translate your matrix transpose algorithm to Java
• The header of the method should be as follows
• public static int transpose( int a )
• Get the following file from the virtual campus
  for lab 10
• MatrixLib.java
• The file MatrixLib.java has the following useful
  methods
• Method to read a matrix of integers, of specified
  dimension.
• public static int readIntMatrix( int
  numRows, int numCols )
• Method to print a matrix of integers with nice
  formatting.
• public static void printMatrix( int
  matrix )

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Example 3 Matrix Multiplication

• Suppose that A is an m n matrix and B is an n
  p matrix. The element at row i and column j in A
  is denoted by aij.
• Let C A B. Then, C will be an m  p matrix,
  and for 0 i lt m, and 0 j lt p,
• Write an algorithm to multiply two given
  matrices.
•  

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Translate to Java

• Translate your matrix multiplication algorithm to
  Java
• The header of the method should be as follows
• public static int product( int a,
  int b )
• Use the methods from MatrixLib.java to read and
  print the matrices.

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• solutions and extra information follow this
  slide

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The Wind Chill calculation

• Here is the complete wind chill algorithm, for
  your information. It has already been
  implemented in WindChill.java.
• Source Environment Canada
• GIVENS
• Temperature (a temperature in C between -50
  and 5)
• WindSpeed (a wind speed in km/hr must be ? 5
  km/hr)
• RESULTS
• Chill (the wind chill value)
• INTERMEDIATES
• VFactor (the wind speed raised to the power
  0.16)
• HEADER
• Chill ? WindChill( Temperature, WindSpeed )
• BODY
• VFactor ? (WindSpeed) 0.16
• Chill ? 13.12 0.6215 Temperature - 11.37
  VFactor
• 0.3965 Temperature VFactor

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Wind Chill Algorithm (page 1)

• GIVENS
• TempArray (an array of temperatures in C)
• NT (length of TempArray)
• SpeedArray (an array of wind speeds in km/hr)
• NS (length of SpeedArray)
• RESULTS
• ChillTable (a matrix of wind chill values, with
  NT rows
• and NS
  columns)
• INTERMEDIATES
• T (index into temperature array)
• S (index into speed array)
• HEADER
• ChillTable ? WindChillTable( TempArray, NT,
  SpeedArray, NS)

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Wind Chill Algorithm (page 2)
ChillTable ? MakeNewArray(NT) T ? 0
T lt NT
true
false
ChillTableT ? MakeNewArray(NS) S ? 0
S lt NS
false
true
ChillTableTS ? WindChill(TempArrayT,
SpeedArrayS) S ? S 1
T ? T 1
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Transpose Algorithm (page 1)

• GIVENS
• A (an array)
• NRows (number of rows in A)
• NCols (number of columns in A)
• RESULTS
• AT (the transposed array)
• INTERMEDIATES
• TRow (row index in transposed array)
• TCol (column index in transposed array)
• HEADER
• AT ? Transpose( A, NRows, NCols )

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Transpose Algorithm (page 2)
AT ? MakeNewArray(NCols) Row ? 0
TRow lt NCols
true
false
ATTRow ? MakeNewArray(NRows) TCol ? 0
TCol lt NRows
true
false
ATTRowTCol ? ATColTRow TCol ? TCol 1
TRow ? TRow 1
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Multiplication Algorithm (page 1)

• GIVENS
• A (an array of numbers)
• B (another array of numbers)
• NARows (number of rows in matrix A)
• NACols (number of columns in matrix A)
• NBRows (number of rows in matrix B)
• NBCols (number of columns in matrix B)
• RESULTS
• C (a matrix that is the product of A and B,
  with
• NARows rows and NBCols columns)
• INTERMEDIATES
• Row (row index for C)
• Col (column index for C)
• Index (summation index for matrix product)
• HEADER
• C ? Multiply( A, NARows, NACols, B, NBRows,
  NBCols)

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Multiplication Algorithm (page 2)
C ? MakeNewArray(NARows) Row ? 0
Row lt NARows
true
CRow ? MakeNewArray(NBCols) Col ? 0
false
Col lt NBCols
true
false
Sum ? 0 Index ? 0
Index lt NACols
true
false
CRowCol ? Sum Col ? Col 1
Sum ? Sum ARowIndexBIndexCol Index ?
Index 1
Row ? Row 1