Kennesaw State University CS 4491 Assigment 5

Kennesaw State University

Department of Computer Science

Advanced Topic in Computer Science CS 4491/2

Assignment # 5 / Polynomial Function

Dalibor Labudovic

01/16/2013

Initial Problem Statement:

CS4491 Assignment No. 5 (Due March 12, 2013)

1. In a typical spring day, the temperature varies according to the data recorded in Table 1. Develop a C program to compute first and second differences. Formulate the difference equations and functional equations for the temperature. Is this discrete or continuous data? Discuss. Plot the relevant data with Gnuplot.

Table 1: Temperature changes in 12-hour period.

Time	7	8	9	10	11	12	1	2	3	4	5	6
Temp. (F)	51	56	60	65	73	78	85	86	84	81	80	70

2. Develop a C program to evaluate the polynomial function y= 2x^6 – 1.5x^5 + 5x^4 – 6.5x^3 + 6x^2 – 3x + 4.5. Find an appropriate interval of x for which the function evaluation is done and plot the relevant data.

Develop a C program and use the data in Table 2 and apply curve fitting to derive a polynomial function of degree 2. Use this function to compute estimates of intermediate values of the number of patients. Produce a plot of the given and estimated data.

Table 2: Number of patients for years 1995 – 2002.

Year	1995	1996	1997	1998	1999	2000	2001	2002
Patients	5,500	8,500	13,500	20,500	29,500	40,500	53,500	68,500
Increase	0	3,000	5,000	7,000	9,000	11,000	13,000	15,000

Summary and purpose of the assignment activity:

The summary of this assignment is the proper use of additional libraries within the C programming community and the essential functionality of GSL libraries. The purpose of this assignment is use the given data and manipulate it into easy to read diagrams. The functionality of the C programming and the results is process of evolving raw data into useful information.

Detail description of the solution and used in the project:

1) SOURCE CODE

#include <stdio.h>

#include "basic_lib.h"

int main(){

const int N = 12; /* 12 data points */

int x[N];

int j;

/* Array with original*/

double T[] = { 51,56,60,65,73,78,85,86,84,81,80,70};/*temperture*/

double *d; /* first difference */

double *d2; /* second difference */

x[0] = 1;

for (j=1; j<N; j++)

x[j] = x[j-1] + 1;

/*compute first differences*/

d = diff(T,N);

/*compute second differences*/

d2 = diff(d, N-1);

/* data for plotting */

printf("\nData of differences for plotting");

printf("\nTime First Diff");

for(j=0;j<N-1;j++)

printf("\n%i %lf", x[j],d[j]);

printf("\n\n\n");

printf("\nTime Second Diff");

for(j=0;j<N-1;j++)

printf("\n%i %lf", x[j],d2[j]);

return 0;

}

CGP FILE

set title "First Differences" font "Verdana, 14"

set xlabel "Time" font "Verdana, 12"

set ylabel "Values of first differences" font "Verdana, 12"

set size 1.0, 1.0

#set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14

set terminal pngcairo size 800, 600 enhanced

set output "difference.png"

set samples 50

unset key

plot "difference.gpl" u 1:2 w linespoints

GPL FILE

#Data of differences for plotting

#Time First Diff

1 5.000000

2 4.000000

3 5.000000

4 8.000000

5 5.000000

6 7.000000

7 1.000000

8 -2.000000

9 -3.000000

10 -1.000000

11 -10.000000

#Time Second Diff

#1 -1.000000

#2 1.000000

#3 3.000000

#4 -3.000000

#5 2.000000

#6 -6.000000

#7 -3.000000

#8 -1.000000

#9 2.000000

#10 -9.000000

#11 0.000000

Second Difference CGP FILE

set title "Second Differences" font "Verdana, 14"

set xlabel "Time" font "Verdana, 12"

set ylabel "Values of second differences" font "Verdana, 12"

set size 1.0, 1.0

#set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14

set terminal pngcairo size 800, 600 enhanced

set output "difference2.png"

set samples 50

unset key

plot "difference2.gpl" u 1:2 w linespoints

Second Difference GPL FILE

#Data of differences for plotting

#Time First Diff

#1 5.000000

#2 4.000000

#3 5.000000

#4 8.000000

#5 5.000000

#6 7.000000

#7 1.000000

#8 -2.000000

#9 -3.000000

#10 -1.000000

#11 -10.000000

#Time Second Diff

1 -1.000000

2 1.000000

3 3.000000

4 -3.000000

5 2.000000

6 -6.000000

7 -3.000000

8 -1.000000

9 2.000000

10 -9.000000

#11 0.000000

2.) SOURCE CODE

#include <stdio.h>

#include <math.h>

#include <stdlib.h>

#include <gsl/gsl_poly.h>

#include "basic_lib.h"

#define N 7 // number of coefficients

#define M 20

void polyval(double p[], double xv[], double yv[], int n, int m);

int main() {

int i;

int j;

/* coefficient of poly */

double a[N] = {4.5,-3,6,-6.5,5,1.5,2}; /* coefficients */

double xi, xf;

double x[M];

double y[M];

/*Evaluate the poly*/

xi = -6.0; /* 1st value of x */

xf = 7.0; /* 2nd value of x */

linspace(x, xi, xf, M); /*vector of x values*/

polyval(a,x,y,N,M);

printf("\n");

printf("Data points calcualted of the poly x y \n");

for(j=0;j<M;j++)

printf("%+.18f %+.18f \n", x[j], y[j]);

return 0;

}

void polyval (double p[], double xv[], double yv[], int n, int m) {

int j;

yv[0] = gsl_poly_eval(p, n, xv[0]);

for(j=1; j<m; j++) {

yv[j] = gsl_poly_eval(p,n, xv[j]);

}

return;

}

CGP CODE

set title "Polynomail Function" font "Verdana, 14"

set xlabel "X" font "Verdana, 12"

set ylabel "Y" font "Verdana, 12"

set size 1.0, 1.0

#set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14

set terminal pngcairo size 800, 600 enhanced

set output "poly.png"

set samples 50

unset key

plot "poly.gpl" u 1:2 w linespoints

GPL CODE

#Data points calcualted of the poly x y

-6.000000000000000000 +89770.500000000000000000

-5.315789473684210620 +43918.919850804792076815

-4.631578947368421240 +19639.394747788868698990

-3.947368421052631859 +7852.172010329663862649

-3.263157894736842479 +2730.641875884949058673

-2.578947368421053099 +802.106291632630473032

-1.894736842105263719 +196.288694529920917375

-1.210526315789474339 +41.584779791880251310

-0.526315789473684847 +9.054257789326985773

+0.157894736842104644 +4.153599366116664804

+0.842105263157894135 +6.209769575789209739

+1.526315789473683626 +55.634949837585040200

+2.210526315789473006 +388.882248511829686777

+2.894736842105262387 +1721.142399894687741835

+3.578947368421051767 +5676.781451632283278741

+4.263157894736841591 +15367.519440554198808968

+4.947368421052630971 +36118.350056926319666672

+5.631578947368420351 +76341.201297123072436079

+6.315789473684209732 +148556.337104719015769660

+6.999999999999999112 +270561.499999999825377017

3.) SOURCE CODE

#include <stdio.h>

#include <math.h>

#include <gsl/gsl_interp.h>

#include "basic_lib.h"

//number of discrete points

#define N 8

void linterp(double x[], double y[], double nx[], double ny[], int m, int n);

int main(){

int i;

int n;

double h;

double x[N];

double xi, xf;

double y[N] = {5500, 8500, 13500, 20500, 29500, 40500, 53500, 68500};

double xint[30];

double yint[30];

//data for linear interpolation

xi = 0.0;

xf = 7.0;

n = arraycol(x, xi, xf, 1.0);

printf("Discrete Points for Interpolation\n");

printf(" i x y\n");

for(i=0;i<N;i++)

printf("%3d %25.17e %25.17e\n", i, x[i], y[i]);

printf("\n");

h= 0.25;

n = arraycol(xint, xi, xf, h);

linterp(x, y, xint, yint, N, n);

printf(" x interpolated y \n");

for(i=0;i<n; i++)

printf("%25.17e %25.17e \n", xint[i], yint[i]);

return 0;

}

void linterp(double x[], double y[], double nx[], double ny[], int m, int n){

int i;

gsl_interp *workspace;

gsl_interp_accel *accel;

// define type of interpolation lienar

workspace = gsl_interp_alloc(gsl_interp_linear, m);

accel = gsl_interp_accel_alloc();

// initialize workspace

gsl_interp_init(workspace, x, y, m);

for(i = 0;i < n;i++)

ny[i] = gsl_interp_eval(workspace, x, y, nx[i], NULL);

//free memory

gsl_interp_free(workspace);

}

CGP CODE

set title "Interpolation: Number of Patients" font "Verdana, 14"

set xlabel "X" font "Verdana, 12"

set ylabel "Y" font "Verdana, 12"

set size 1.0, 1.0

#set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14

set terminal pngcairo size 800, 600 enhanced

set output "Interpol_interpol.png"

set samples 50

unset key

plot "interpol.gpl" u 1:2 w linespoints

GPL CODE

#Discrete Points for Interpolation

# i x y

# 0 0.00000000000000000e+00 5.50000000000000000e+03

# 1 1.00000000000000000e+00 8.50000000000000000e+03

# 2 2.00000000000000000e+00 1.35000000000000000e+04

# 3 3.00000000000000000e+00 2.05000000000000000e+04

# 4 4.00000000000000000e+00 2.95000000000000000e+04

# 5 5.00000000000000000e+00 4.05000000000000000e+04

# 6 6.00000000000000000e+00 5.35000000000000000e+04

# 7 7.00000000000000000e+00 6.85000000000000000e+04

# x interpolated y

0.00000000000000000e+00 5.50000000000000000e+03

2.50000000000000000e-01 6.25000000000000000e+03

5.00000000000000000e-01 7.00000000000000000e+03

7.50000000000000000e-01 7.75000000000000000e+03

1.00000000000000000e+00 8.50000000000000000e+03

1.25000000000000000e+00 9.75000000000000000e+03

1.50000000000000000e+00 1.10000000000000000e+04

1.75000000000000000e+00 1.22500000000000000e+04

2.00000000000000000e+00 1.35000000000000000e+04

2.25000000000000000e+00 1.52500000000000000e+04

2.50000000000000000e+00 1.70000000000000000e+04

2.75000000000000000e+00 1.87500000000000000e+04

3.00000000000000000e+00 2.05000000000000000e+04

3.25000000000000000e+00 2.27500000000000000e+04

3.50000000000000000e+00 2.50000000000000000e+04

3.75000000000000000e+00 2.72500000000000000e+04

4.00000000000000000e+00 2.95000000000000000e+04

4.25000000000000000e+00 3.22500000000000000e+04

4.50000000000000000e+00 3.50000000000000000e+04

4.75000000000000000e+00 3.77500000000000000e+04

5.00000000000000000e+00 4.05000000000000000e+04

5.25000000000000000e+00 4.37500000000000000e+04

5.50000000000000000e+00 4.70000000000000000e+04

5.75000000000000000e+00 5.02500000000000000e+04

6.00000000000000000e+00 5.35000000000000000e+04

6.25000000000000000e+00 5.72500000000000000e+04

6.50000000000000000e+00 6.10000000000000000e+04

6.75000000000000000e+00 6.47500000000000000e+04

7.00000000000000000e+00 6.85000000000000000e+04

ORIGINAL DATA CGP CODE

#Discrete Points for Interpolation

# i x y

0 0.00000000000000000e+00 5.50000000000000000e+03

1 1.00000000000000000e+00 8.50000000000000000e+03

2 2.00000000000000000e+00 1.35000000000000000e+04

3 3.00000000000000000e+00 2.05000000000000000e+04

4 4.00000000000000000e+00 2.95000000000000000e+04

5 5.00000000000000000e+00 4.05000000000000000e+04

6 6.00000000000000000e+00 5.35000000000000000e+04

7 7.00000000000000000e+00 6.85000000000000000e+04

# x interpolated y

# 0.00000000000000000e+00 5.50000000000000000e+03

# 2.50000000000000000e-01 6.25000000000000000e+03

# 5.00000000000000000e-01 7.00000000000000000e+03

# 7.50000000000000000e-01 7.75000000000000000e+03

# 1.00000000000000000e+00 8.50000000000000000e+03

# 1.25000000000000000e+00 9.75000000000000000e+03

# 1.50000000000000000e+00 1.10000000000000000e+04

# 1.75000000000000000e+00 1.22500000000000000e+04

# 2.00000000000000000e+00 1.35000000000000000e+04

# 2.25000000000000000e+00 1.52500000000000000e+04

# 2.50000000000000000e+00 1.70000000000000000e+04

# 2.75000000000000000e+00 1.87500000000000000e+04

# 3.00000000000000000e+00 2.05000000000000000e+04

# 3.25000000000000000e+00 2.27500000000000000e+04

# 3.50000000000000000e+00 2.50000000000000000e+04

# 3.75000000000000000e+00 2.72500000000000000e+04

# 4.00000000000000000e+00 2.95000000000000000e+04

# 4.25000000000000000e+00 3.22500000000000000e+04

# 4.50000000000000000e+00 3.50000000000000000e+04

# 4.75000000000000000e+00 3.77500000000000000e+04

# 5.00000000000000000e+00 4.05000000000000000e+04

# 5.25000000000000000e+00 4.37500000000000000e+04

# 5.50000000000000000e+00 4.70000000000000000e+04

# 5.75000000000000000e+00 5.02500000000000000e+04

# 6.00000000000000000e+00 5.35000000000000000e+04

# 6.25000000000000000e+00 5.72500000000000000e+04

# 6.50000000000000000e+00 6.10000000000000000e+04

# 6.75000000000000000e+00 6.47500000000000000e+04

# 7.00000000000000000e+00 6.85000000000000000e+04

ORIGINAL DATE GLP CODE

set title "Original Data: Number of Patients" font "Verdana, 14"

set xlabel "X" font "Verdana, 12"

set ylabel "Y" font "Verdana, 12"

set size 1.0, 1.0

#set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14

set terminal pngcairo size 800, 600 enhanced

set output "interpol_original.png"

set samples 50

unset key

plot "interpol_original.gpl" u 1:3 w linespoints

Table of results:

1)

2.)

3.)

Discussion of how the system modeled can be improved and extended to include other service: If the process of data input or loading of data into a seemingly single program which allows the user to chose the type of function desired to render the graphical model such as a graph.

Comments and Conclusion:

The difficulty of the programming this type of assignment is high, but the type of experience developed during this assignment is a real world experience which can be very helpful in the future. The process of raw data transformation into useful information is a task of a lot of hard work.

Script:

Script started on Sun 31 Mar 2013 04:36:48 PM EDT
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P1#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P1$ nano d##[K##[K##[K##[K##[K##[Knano ds##[K##[Kscript##[K##[K##[K##[K##[K##[Kdifference.c
#[?1049h#[1;24r#(B#[m#[4l#[?7h#[?12l#[?25h#[?1h#=#[?1h#=#[?1h#=#[39;49m#[39;49m#(B#[m#[H#[2J#(B#[0;7m  GNU nano 2.2.6             File: difference.c                                 #[3;1H#(B#[0;1m#[36m#include#[39m#(B#[m #(B#[0;1m#[33m<stdio.h>
difference.c:2:23: fatal error: basic_lib.h: No such file or directory
compilation terminated.
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P1#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P1$ gcc -Wall difference.c -o diff


#[?1049h#[1;24r#(B#[m#[4l#[?7h#[?12l#[?25h#[?1h#=#[?1h#=#[?1h#=#[39;49m#[39;49m#(B#[m#[H#[2J#(B#[0;7m  GNU nano 2.2.6             File: difference.c                                 #[3;1H#(B#[0;1m#[36m#include#[39m#(B#[m #(B#[0;1m#[33m<stdio.h>

gcc: error: basic_lib.h: No such file or directory
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P1#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P1$ ./a##[Kdiffernce.c##[Ko
bash: ./differnce.o: No such file or directory
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P1#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P1$ d##[K./a##[Kdifference.o
bash: ./difference.o: cannot execute binary file
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P1#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P1$ ./difference.o
bash: ./difference.o: cannot execute binary file
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P1#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P1$ ./differnece##[K##[K##[K##[K##[K##[K##[K##[Kfference

Data of differences for plotting
Time     First Diff
1        5.000000
2        4.000000
3        5.000000
4        8.000000
5        5.000000
6        7.000000
7        1.000000
8        -2.000000
9        -3.000000
10        -1.000000
11        -10.000000



Time     Second Diff
1      -1.000000
2      1.000000
3      3.000000
4      -3.000000
5      2.000000
6      -6.000000
7      -3.000000
8      -1.000000
9      2.000000
10      -9.000000
11      0.000000#]0;dlabudovic@ubuntu: 


Script started on Sun 31 Mar 2013 04:45:27 PM EDT
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P2#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P2$ nano sc##[K##[K##[K poly.c
#[?1049h#[1;24r#(B#[m#[4l#[?7h#[?12l#[?25h#[?1h#=#[?1h#=#[?1h#=#[39;49m#[39;49m#(B#[m#[H#[2J#(B#[0;7m  GNU nano 2.2.6               File: poly.c                                     #[4;1H#(B#[0;1m#[36m#include#[39m#(B#[m #(B#[0;1m#[33m<stdio.h>
491/assign_05/P2$ poly.out ba#[1@s#[A




 -o interpol.o#[1P#[A

gcc: error: basic_lib.o: No such file or directory
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P2#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P2$ ./poly.out

Data points calcualted of the poly x y 
-6.000000000000000000 +89770.500000000000000000 
-5.315789473684210620 +43918.919850804792076815 
-4.631578947368421240 +19639.394747788868698990 
-3.947368421052631859 +7852.172010329663862649 
-3.263157894736842479 +2730.641875884949058673 
-2.578947368421053099 +802.106291632630473032 
-1.894736842105263719 +196.288694529920917375 
-1.210526315789474339 +41.584779791880251310 
-0.526315789473684847 +9.054257789326985773 
+0.157894736842104644 +4.153599366116664804 
+0.842105263157894135 +6.209769575789209739 
+1.526315789473683626 +55.634949837585040200 
+2.210526315789473006 +388.882248511829686777 
+2.894736842105262387 +1721.142399894687741835 
+3.578947368421051767 +5676.781451632283278741 
+4.263157894736841591 +15367.519440554198808968 
+4.947368421052630971 +36118.350056926319666672 
+5.631578947368420351 +76341.201297123072436079 
+6.315789473684209732 +148556.337104719015769660 
+6.999999999999999112 +270561.499999999825377017 
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P2#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P2$ ##exit
exit

Script done on Sun 31 Mar 2013 04:46:46 PM EDT

Script started on Sun 31 Mar 2013 04:48:41 PM EDT
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P3#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P3$ exit####./poly.out##########gcc -Wall poly.c -o poly.out b




gcc: error: basic_lib.o: No such file or directory
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P3#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P3$ .inte##[K##[K##[K##[K/interpol.out
Discrete Points for Interpolation
  i             x                      y
  0   0.00000000000000000e+00   5.50000000000000000e+03
  1   1.00000000000000000e+00   8.50000000000000000e+03
  2   2.00000000000000000e+00   1.35000000000000000e+04
  3   3.00000000000000000e+00   2.05000000000000000e+04
  4   4.00000000000000000e+00   2.95000000000000000e+04
  5   5.00000000000000000e+00   4.05000000000000000e+04
  6   6.00000000000000000e+00   5.35000000000000000e+04
  7   7.00000000000000000e+00   6.85000000000000000e+04

           x                 interpolated y              
  0.00000000000000000e+00   5.50000000000000000e+03 
  2.50000000000000000e-01   6.25000000000000000e+03 
  5.00000000000000000e-01   7.00000000000000000e+03 
  7.50000000000000000e-01   7.75000000000000000e+03 
  1.00000000000000000e+00   8.50000000000000000e+03 
  1.25000000000000000e+00   9.75000000000000000e+03 
  1.50000000000000000e+00   1.10000000000000000e+04 
  1.75000000000000000e+00   1.22500000000000000e+04 
  2.00000000000000000e+00   1.35000000000000000e+04 
  2.25000000000000000e+00   1.52500000000000000e+04 
  2.50000000000000000e+00   1.70000000000000000e+04 
  2.75000000000000000e+00   1.87500000000000000e+04 
  3.00000000000000000e+00   2.05000000000000000e+04 
  3.25000000000000000e+00   2.27500000000000000e+04 
  3.50000000000000000e+00   2.50000000000000000e+04 
  3.75000000000000000e+00   2.72500000000000000e+04 
  4.00000000000000000e+00   2.95000000000000000e+04 
  4.25000000000000000e+00   3.22500000000000000e+04 
  4.50000000000000000e+00   3.50000000000000000e+04 
  4.75000000000000000e+00   3.77500000000000000e+04 
  5.00000000000000000e+00   4.05000000000000000e+04 
  5.25000000000000000e+00   4.37500000000000000e+04 
  5.50000000000000000e+00   4.70000000000000000e+04 
  5.75000000000000000e+00   5.02500000000000000e+04 
  6.00000000000000000e+00   5.35000000000000000e+04 
  6.25000000000000000e+00   5.72500000000000000e+04 
  6.50000000000000000e+00   6.10000000000000000e+04 
  6.75000000000000000e+00   6.47500000000000000e+04 
  7.00000000000000000e+00   6.85000000000000000e+04 
#]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_05/P3#dlabudovic@ubuntu:~/Documents/CS4491/assign_05/P3$ exit
exit

Script done on Sun 31 Mar 2013 04:49:14 PM EDT