CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
Machine Problem 5 ( MP5 ) Instructions / Hints
Part 1 Description
This machine problem basically performs the following tasks:
•
A sequence of ( x , y ) ordered pair values are read from a sequential file named
mp5.inp .
•
As the ordered pairs are read, various variables are additively and / or multiplicatively
accumulating the individual x and y values.
•
A least squares line y = m x + b is formed using these formulas for the slope m and
the y - intercept b .
m = (sumx * sumy – count * sumxy) / (sumx * sumx – count * sumxx)
b = (sumy – m * sumx)/count
where
sumx
is the sum of all of the x values from the ordered pairs
sumy
is the sum of all of the y values from the ordered pairs
count
is the count of all the ordered pairs ( x , y )
sumxy
is the sum of all of the individual x y products from each ordered pair
sumxx
is the sum of all of the x squared values from the ordered pairs
•
The least squares line is then output to a sequential file mp5.out .
•
The correlation coefficient r is then computed to give us an idea of the " goodness of fit "
of the least squares line.
r = (count * sumxy – sumx * sumy) /
sqrt((count * sumxx – sumx * sumx)*(count * sumyy – sumy * sumy))
•
Finally the integral or area under the line of m x + b over the first x to the last x is
computed using the following computation.
m * xn * xn / 2.0 + b * xn - (m * x0 * x0 / 2.0 + b * x0)
© Copyright 2013 by P.E.P.
1
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
•
To calculate the integral, a function named integrate() is utilized. The function
receives four parameters
m
the slope of the least squares line
b
the y - intercept of the least squares line
x0
the first, i.e. the minimal x value from all of the ( x , y ) points
xn
the last, i.e. the maximal x value from all of the ( x , y ) points
and returns the area under the line between x 0 and x n .
Part 2 Navigation and File Construction
Here are some steps to complete MP5 :
(1)
Logon your Linux account using your Oakstar login name and your Bxxxxxxxx as your
password.
server:
(2)
csc.oakton.edu
Use the following command to travel to the mps directory that you created for MP0:
cd mps
(3)
Use the following command to create a new folder for MP 5 :
mkdir 5
(4)
Use the following command to travel to the 4 directory that you just created for M P5 :
cd 5
(5)
Use the following command to copy the existing skeletal code for MP 5 :
cp /samples/csc/171/mps/5/* .
CSC 171 command
cp /samples/csc/172/mps/5/* .
CSC 172 command
cp /samples/csc/173/mps/5/* .
CSC 173 command
(6) use the following command to open the MP 5 file using the pico text editor:
pico mp5.cpp
CSC 171 command
pico mp5.f90
CSC 172 command
pico mp5.java
CSC 173 command
(7)
Modify the initial MP 5 code within pico to complete the program.
(8)
Save your M P 5 file within pico by using this pico command: Ctrl + o
© Copyright 2013 by P.E.P.
2
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
(9)
Exit pico by using this pico command: Ctrl + x
(10)
Compile your file with this command:
(11)
(12)
g++ mp5.cpp -o mp5
CSC 171 command
f90 mp5.f90 -o mp5
CSC 172 command
javac mp5.java
CSC 173 command
Execute ( run ) the program with this command:
mp5
CSC 171 command
mp5
CSC 172 command
java mp5
CSC 173 command
List the contents of the output file of your program.
cat mp5.out
(13)
Observe the output of your program.
(14)
For Spring and Fall Semester students:
Submit the file with this command ( where 0c1 is the course section number ) :
submit csc1710c1 5
CSC 171 command
submit csc1720c1 5
CSC 172 command
submit csc1730c1 5
CSC 173 command
For Summer Semester students:
Submit the file with this command ( where 7c1 is the course section number ) :
submit csc1717c1 5
CSC 171 command
submit csc1727c1 5
CSC 172 command
submit csc1737c1 5
CSC 173 command
© Copyright 2013 by P.E.P.
3
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
Part 3 Starter Code
CSC 171 ( C ++ ) A Version of MP5
/************************************************************************
* Name: Your name
CSC 171
* Date: Today's date
MP 5
*************************************************************************
* Statement: Find the least squares line for the data in mp5.inp and
*
integrate it from the first x value to the last x value.
* Specifications:
* Input - a sequence of (x, y) values from a sequential file
* Output - to a sequential file
*
- the least squares line y = m*x + b
*
- the correlation coefficient
*
- the integral of m*x+b over the first x to the last
************************************************************************/
#include <fstream>
#include <cmath>
using namespace std;
// prototype of function integrate
double integrate(double, double, double, double);
int main()
{
// numeric variable declarations
double x, y, sumx, sumy, sumxy, sumxx, sumyy, m, b, firstx, lastx, r;
int count;
// file variable declarations and initialization
ifstream fin;
ofstream fout;
// 1) file variable initializations
fin.open("mp5.inp");
fout.open("mp5.out");
// 2) reduction variable initialization
sumx = sumy = sumxy = sumxx = sumyy = 0.0;
count = 0;
// 3) loop over the input file
for (;;)
{
// 4) attempt to input an ordered pair
fin >> x >> y;
// 5) test for end of file
if (fin.eof())
// 6) leave when true
© Copyright 2013 by P.E.P.
4
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
break;
// 7) test for first pass
if ( count == 0 )
// 8) save lower limit of integration
firstx = x;
else
// 9) save upper limit of integration
lastx = x;
// 10) update reduction variables
//place additional code here
}
// 11) calculate slope, y intercept and correlation coefficient
m = ________________________________________________________ ;
b = ________________________________________________________;
r = ________________________________________________________;
// 12) display linear equation, correlation coefficient and area
fout << "y = " << m << " * x + " << b<< "\n";
fout << "Correlation Coefficient = " << r << endl;
fout << "Integral = " << integrate(m, b, firstx, lastx) << endl;
// 13) disconnect from files
fin.close();
fout.close();
}
/*Function integrate
*
*receives - Slope m of least squares line
*
- y intercept of least squares line
*
- limit of integration
*returns
- the antiderivative m*x^2/2 + b*x evaluated at x
*************************************************************************/
// Define function integrate below
double integrate(double m, double b, double x0, double xn)
{
//place additional code here
return m * xn * xn / 2.0 + b * xn - (m * x0 * x0 / 2.0 + b * x0);
}
© Copyright 2013 by P.E.P.
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CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
CSC 172 ( FORTRAN ) A Version of MP5
!************************************************************************
! Name: Your name
CSC 172
! Date: Today's date
MP 5
!************************************************************************
! Statement: Find the least squares line for the data in mp5.inp and
!
integrate it from the first x value to the last x value.
! Specifications:
! Input - a sequence of (x, y) values from a sequential file
! Output - to a sequential file
!
- the least squares line y = m*x + b
!
- the correlation coefficient
!
- the integral of m*x+b over the first x to the last
!***********************************************************************/
program mp5
! function integrate declaration
real, external :: integrate
! numeric variable declarations
real :: x, y, sumx, sumy, sumxy, sumxx, sumyy, m, b, firstx, lastx, r
integer :: count, ierror
! file variable declarations and initialization
integer :: fin = 3, fout = 4
! 1) file variable initializations
open(unit = fin, file = "mp5.inp", action = "read")
open(unit = fout, file = "mp5.out", action = "write")
! 2) reduction variable initialization
sumx = 0.0
sumy = 0.0
sumxy = 0.0
sumxx = 0.0
sumyy = 0.0
count = 0
! 3) loop over the input file
do
! 4) attempt to input an ordered pair
read(fin, *, iostat = ierror) x, y
! 5) test for end of file
if (ierror /= 0) then
! 6) leave if true
exit
endif
! 7) test for first pass
if ( count == 0 ) then
! 8) save lower limit of integration
firstx = x
© Copyright 2013 by P.E.P.
6
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
else
! 9) save upper limit of integration
lastx = x
endif
! 10) update reduction variables
//place additional code here
enddo
!
m
b
r
11) calculate slope, y intercept and correlation coefficient
= ______________________________________________________________
= ______________________________________________________________
= ______________________________________________________________
! 12) display linear equation, correlation coefficient and area
write(fout, *) "y = ", m, " * x + ", b
write(fout, *) "Correlation Coefficient = ", r
write(fout, *) "Integral = ", integrate(m,b,firstx,lastx)
! 13) disconnect from files
close(fin)
close(fout)
end program mp5
! Function integrate
!
! receives - Slope m of least squares line
!
- y intercept of least squares line
!
- limit of integration
! returns
- the antiderivative m*x^2/2 + b*x evaluated at x
!*************************************************************************/
! Define function integrate below
real function integrate( m, b, x0, xn)
real, intent(in) :: m, b, x0, xn
integrate = m * xn * xn / 2.0 + b * xn - (m * x0 * x0 / 2.0 + b * x0)
end function integrate
© Copyright 2013 by P.E.P.
7
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
CSC 173 ( Java ) A Version of MP5
/************************************************************************
* Name: Your name
CSC 173
* Date: Today's date
MP 5
*************************************************************************
* Statement: Find the least squares line for the data in mp5.inp and
*
integrate it from the first x value to the last x value.
* Specifications:
* Input - a sequence of (x, y) values from a sequential file
* Output - to a sequential file
*
- the least squares line y = m*x + b
*
- the correlation coefficient
*
- the integral of m*x+b over the first x to the last
************************************************************************/
/* Sample output for mp5.inp
y = 2.00115 * x + -2.85169
Correlation Coefficient = 0.997368
Integral = 72.2013
*/
import java.io.*;
public class mp5
{
public static void main(String[] args)
{
mp5 MP5 = new mp5();
// numeric variable declarations
double x, y, sumx, sumy, sumxy, sumxx, sumyy, m, b, firstx = 0, lastx = 0, r;
int count;
// 1) reduction variable initialization
sumx = sumy = sumxy = sumxx = sumyy = 0.0;
count = 0;
try {
// 2) file variable declarations and initializations
BufferedReader fin = new BufferedReader(
new FileReader("mp5.inp"));
PrintWriter fout = new PrintWriter( new BufferedWriter(
new FileWriter("mp5.out")));
StreamTokenizer st = new StreamTokenizer(fin);
// 3) loop over the input file
for (;;)
© Copyright 2013 by P.E.P.
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CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
{
// 4) attempt to input an x value
st.nextToken();
// 5) test for end of file
if (st.ttype == st.TT_EOF)
// 6) leave when true
break;
// 7) input an x value
x = st.nval;
// 8) attempt to input and input a y value
st.nextToken();
y = st.nval;
// 9) test for first pass
if ( count == 0 )
// 10) save lower limit of integration
firstx = x;
else
// 11) save upper limit of integration
lastx = x;
// 12) update reduction variables
//place additional code here
}// for
// 13) calculate slope, y intercept and correlation coefficient
m = ________________________________________________________ ;
b = ________________________________________________________;
r = ________________________________________________________;
// 14) display linear equation, correlation coefficient and area
fout.println("y = " + m + " * x + " + b );
fout.println("Correlation Coefficient = " + r);
fout.println("Integral = " + MP5.integrate(m,b,firstx,lastx));
// 15) disconnect from files
fin.close();
fout.close();
}// try
// 16) catch I/O exceptions
catch (FileNotFoundException e)
{
System.err.println("FileNotFound\n");
}
catch (IOException e)
© Copyright 2013 by P.E.P.
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CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
{
System.err.println("IOException\n");
}
}// main
/*Method integrate
*
*receives - Slope m of least squares line
*
- y intercept of least squares line
*
- limit of integration
*returns
- the antiderivative m*x^2/2 + b*x evaluated at x
*************************************************************************/
// Define method integrate below
public double integrate(double m, double b, double x0, double xn)
{
return m * xn * xn / 2.0 + b * xn - (m * x0 * x0 / 2.0 + b * x0);
}
}// mp5
Contents of the companion data file mp5.inp
0.33
0.63
0.82
0.92
0.99
1.21
1.21
1.27
1.42
1.48
1.6
1.81
1.88
1.99
2.1
2.18
2.19
2.51
2.53
2.58
2.62
2.85
3.05
3.19
-1.93
-1.63
-1.5
-1.02
-0.71
-0.22
-0.76
-0.21
0
0.3
-0.05
0.45
0.58
1.9
2.12
1.06
1.21
1.99
2.04
2.38
2.91
2.63
3.56
3.56
© Copyright 2013 by P.E.P.
10
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
3.37
3.59
3.61
3.62
3.85
3.95
4.45
4.54
4.54
4.74
4.82
4.89
5.03
5.12
5.12
5.23
5.26
5.27
5.44
5.63
5.66
5.75
3.64
3.87
4.69
4.98
4.43
5.0
6.12
5.64
5.89
6.99
6.91
7.07
6.62
7.03
7.41
7.73
7.86
7.73
8.25
8.58
8.53
8.68
5.99
6.08
6.19
6.31
6.47
6.55
6.58
7.14
7.31
7.34
7.39
7.46
7.49
7.5
7.62
8.05
8.13
8.91
8.93
8.94
8.99
9.06
9.07
9.59
9.63
9.68
9.75
9.92
9.21
9.62
10.09
9.83
9.92
9.8
11.92
11.73
11.48
12.17
12.94
11.74
12.32
12.97
13.05
11.88
15.94
15.12
15.27
14.85
15.0
15.5
15.82
17.01
16.24
16.91
© Copyright 2013 by P.E.P.
11
CSC 170 Introduction to Numerical Methods MP5 Instructions / Hints
Student Name ________________________________________ Section ___ Date _______
9.98
9.99
17.25
16.67
Part 4 Sample Program Run
Here is a sample run of the MP5 problem.
Notice that when you run the mp5 executable, the program lacks the usual console input and
output.
© Copyright 2013 by P.E.P.
12