Kennesaw State University CS 4491 Assigment 6


Kennesaw State University
Department of Computer Science
Advanced Topic in Computer Science CS 4491/2
Assignment # 6 / Water / Patients


Dalibor Labudovic


04/23/2013


















Initial Problem Statement:
CS4491 Assignment No. 5 (Due March 12, 2013)
1. In the original water treatment problem Case Study 2, compute the
levels of impurities after 8 repetitions of the application of solvents.
Use the growth factor from the case study and develop a C program
for these computations.

2. Develop a C program and use the data in Table 1 and apply curve fitting to derive a polynomial function of degree 5. Use this function
to compute estimates of intermediate values of the number of patients.
Produce a plot of the given and estimated data.
Table 1. 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 outcome of the first problem is the manipulation of the case study to calculate water purity at a different chemical treatment application. The purpose of this first problem is that calculating this type of water treatment is more efficient using a well structured formula then manipulating data to get the desired results.
The outcome of the second problem is the using given data to to set a plot then using interpolation to get a more fitted data to plot a graph. The purpose of this problem is the use of finite differences and intermediate points to form a graph.


Detail description of the solution and used in the project:
1.) The solution to the first problem is to incorporate basic_lib library to allocate the differences using a function from the sources code below. The program will define number of applications, constant factor and initial impurity of water. With the calculation of the acceptable impurity of water, the number of application can be adjusted.
2.) The solution to the second problem is to incorporate finite differences to form a foundation of data plots then utilizing the intermediate points to populate additional estimated points for a more accurate picture. The source code makes use of a library polyfitgsl and basic_lib.
1) SOURCE CODE
#include <stdio.h>
#include <math.h>
#include "basic_lib.h"


int main(){


const int N = 8; //number of applications
double s[N];
double x[N];
double f = 0.35; //constant factor
int n;
int j;
double xf;
s[0] = 405.0;// initial impurity of water
xf = N;
n = arraycol(x, 1.0, xf, 1.0);
printf("Initial impurity in water: %f\n", s[0]);
printf("Number of applicatons: %d\n",N);
printf("\n\nFactor: %f \n", f);
for (j = 0;j < N-1;j++)
s[j+1] = f * s[j];
printf("Impurities after each applications \n");
for(j=0;j<N;j++)
printf("%f %f \n", x[j], s[j]);
return 0;
}
2.) SOURCE CODE




#include <stdio.h>
#include <gsl/gsl_poly.h>
#include "basic_lib.h"
#include "polyfitgsl.h"
#define NC 5 /* size of coefficient vector */
void polyval(double p[], double xv[], double yv[], int n, int m);
int main()
{
const int NP = 8; // Number of given data points
const int M = 30; // number of calcualted data points
/* const int NC = 3; Number of coefficients */
double x[] = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0};
double y[] = {0.0, 3000.0,5000.0,7000.0,9000.0,11000.0,13000.0,15000.0};
double coeff[NC]; // vector of coefficients
int i;
double xc[M]; /* computed values for x using polynomial */
double yc[M];
printf("Program finds best fit polynomial of degree %d \n", NC-1);
printf("Data points (x,y): \n");
for (i = 0; i < NP; i++)
printf(" %f %f \n", x[i], y[i]);
polynomialfit(NP, NC, x, y, coeff);
printf("\n\nCoefficients of polynomial found\n");
for(i=0; i < NC; i++) {
printf("%lf\n", coeff[i]);
}
/* Evaluate the fitted polynomial */
linspace(xc, 0.0, 7.0, M);
polyval(coeff, xc, yc, NC, M);
printf("\nData points calculated with the polynomial \n");
for(i=0; i < M; i++)
printf("%d %+.18f %+.18f \n", i, xc[i], yc[i]);
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;
}
unset key
plot "interpol_original.gpl" u 1:3 w linespoints


Table of results:
1.)
Initial impurity in water: 405.000000
Number of applicatons: 8
Factor: 0.350000
Impurities after each applications
1.000000 405.000000
2.000000 141.750000
3.000000 49.612500
4.000000 17.364375
5.000000 6.077531
6.000000 2.127136
7.000000 0.744498
8.000000 0.260574
2.)
Program finds best fit polynomial of degree 4
Data points (x,y):
0.000000 0.000000
1.000000 3000.000000
2.000000 5000.000000
3.000000 7000.000000
4.000000 9000.000000
5.000000 11000.000000
6.000000 13000.000000
7.000000 15000.000000




Coefficients of polynomial found
26.515152
3404.671717
-629.734848
110.479798
-6.628788


Data points calculated with the polynomial
0 +0.000000000000000000 +26.515151515142889593
1 +0.241379310344827597 +813.172863273697998920
2 +0.482758620689655193 +1535.456370840211548057
3 +0.724137931034482762 +2201.878117492446563119
4 +0.965517241379310387 +2820.410482131026583374
5 +1.206896551724137900 +3398.485779279436883371
6 +1.448275862068965525 +3942.996259084022312891
7 +1.689655172413793149 +4460.294107313990934927
8 +1.931034482758620774 +4956.191445361408113968
9 +2.172413793103448398 +5435.960330241205156199
10 +2.413793103448275801 +5904.332754591169759806
11 +2.655172413793103203 +6365.500646671953290934
12 +2.896551724137930606 +6823.115870367066236213
13 +3.137931034482758008 +7280.290225182881840738
14 +3.379310344827585411 +7739.595446248635198572
15 +3.620689655172412813 +8203.063204316418705275
16 +3.862068965517240215 +8672.185105761187514872
17 +4.103448275862067618 +9147.912692580759539851
18 +4.344827586206895020 +9630.657442395811813185
19 +4.586206896551722423 +10120.290768449882307323
20 +4.827586206896549825 +10616.144019609369934187
21 +5.068965517241377228 +11117.008480363538183155
22 +5.310344827586204630 +11621.135370824502388132
23 +5.551724137931032033 +12126.235846727246098453
24 +5.793103448275859435 +12629.480999429617440910
25 +6.034482758620686838 +13127.501855912318205810
26 +6.275862068965514240 +13616.389378778912941925
27 +6.517241379310341642 +14091.694466255828956491
28 +6.758620689655169045 +14548.427952192345401272
29 +6.999999999999996447 +14981.060606060626014369




Comments and Conclusion:
In conclusion this assignment has thought me a real world application of mathematical model in a computational environment. The case study is scientifically applicable and I see how the use of computing can contribute to the wellness of people. The data analysis in the second people has showed me a different way of manipulating the given data to give me a visualization of the raw data. Even without the polynomial function and only with given points the assignment has caught me to how to form a function.


Script:
Script started on Thu 18 Apr 2013 05:07:41 PM EDT
]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P1dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P1$ nano water.c
File: water.c
#include <stdio.h>
#include <math.h>
#include "basic_lib.h"

int main(){

const int N = 8; //number of applications
double s[N];
double x[N];
double f = 0.35; //constant factor
int n;
int j;
double xf;
s[0] = 405.0;// initial impurity of water
xf = N;
n = arraycol(x, 1.0, xf, 1.0);
printf("Initial impurity in water: %f\n", s[0]);
printf("Number of applicatons: %d\n",N);
printf("\n\nFactor: %f \n", f);
for (j = 0;j < N-1;j++)
s[j+1] = f * s[j];
printf("Impurities after each applications \n");
for(j=0;j<N;j++)
printf("%f %f \n", x[j], s[j]);
return 0;
}



dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P1dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P1$ [K]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P1dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P1$ [K]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P1dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P1$ nano water.cls[Ktypescript > script.txtscript[K[4Plscd Documents/CS4491/assign_06/P2exit[Kgnuplot./patients.out > patients.txt[Kgcc -Wall patients.c -o patients.out basic_lib.h polyfitgsl.c -lgsl -lgslcblas -lm Cnano patients.c[Kgcc -Wall patients.c -o patients.out basic_lib.h polyfitgsl.c -lgsl -lgslcblas -lm Cnano patients.c[K[8Pgnuplot./patients.out > patients.txt[14Pnano patients.c[9Pscript./patients.outls[Kgcc -Wall patients.c -o patients.out basic_lib.h polyfitgsl.c -lgsl -lgslcblas -lm nano polyfitgsl.c[K[5Ppolyfitgsl.hnano patients.cls[Kgcc -Wall patients.c -o partients.out basic_lib.h polyfitgsl.h -lgsl -lgslcblas -lm[1Ptients.out basic_lib.o polyfitgsl.o interpol.c -o interpol.out basic_lib patients.c -o patients.out -basic_lib.h -polyfitgsl.h
nano basic_lib.h[K[1Ppatients.cls[Kcd Documents/CS4491/assign_06/P2exit[K./patients.outgcc -Wall patients.c -o patients.out basic_lib.h polyfitgsl.c -lgsl -lgslcblas -lm
nano patients.c[K[3Pwater.cgcc -Wall water.c -o water.out basic_lib.h -lm
water.c: In function :
water.c:11:6: warning: variable set but not used [-Wunused-but-set-variable]
]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P1dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P1$ ./water.out
Initial impurity in water: 405.000000
Number of applicatons: 8


Factor: 0.350000
Impurities after each applications
1.000000 405.000000
2.000000 141.750000
3.000000 49.612500
4.000000 17.364375
5.000000 6.077531
6.000000 2.127136
7.000000 0.744498
8.000000 0.260574
]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P1dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P1$ exit
exit 

Script done on Thu 18 Apr 2013 05:08:38 PM EDT

Script started on Thu 18 Apr 2013 04:43:40 PM EDT 
?]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P2?dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P2$ nano patients.c 



#include <stdio.h> 
#include <gsl/gsl_poly.h> 
#include "basic_lib.h" 
#include "polyfitgsl.h" 
#define NC 5   /* size of coefficient vector */ 
void polyval(double p[], double xv[], double yv[], int n, int m); 
int main() 
{ 
  const int NP = 8;      // Number of given data points 
  const int M = 30;      // number of calcualted data points 
  /* const int NC = 3;      Number of coefficients */ 
  double x[] = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0}; 
  double y[] = {0.0, 3000.0,5000.0,7000.0,9000.0,11000.0,13000.0,15000.0}; 
  double coeff[NC];  // vector of coefficients 
  int i; 
  double xc[M]; /* computed values for x using polynomial */ 
  double yc[M];  
  printf("Program finds best fit polynomial of degree %d \n", NC-1); 
  printf("Data points (x,y): \n"); 
  for (i = 0; i < NP; i++) 
     printf(" %f %f \n", x[i], y[i]); 
  polynomialfit(NP, NC, x, y, coeff); 
  printf("\n\nCoefficients of polynomial found\n"); 
  for(i=0; i < NC; i++) { 
    printf("%lf\n", coeff[i]); 
  } 
  /* Evaluate the fitted polynomial */ 
  linspace(xc, 0.0, 7.0, M); 
  polyval(coeff, xc, yc, NC, M); 
  printf("\nData points calculated with the polynomial \n"); 
  for(i=0; i < M; i++) 
     printf("%d  %+.18f  %+.18f \n", i, xc[i], yc[i]);	 
  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; 
} 







dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P2?dlabudovic@ubuntu:~/gcc -Wall patients.c -o patients.out basic_lib.h polyfitgsl.c -lgsl -lgslcblas -lm 
?]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P2?dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P2$ ./patients.out 
Program finds best fit polynomial of degree 4 
Data points (x,y): 
 0.000000 0.000000 
 1.000000 3000.000000 
 2.000000 5000.000000 
 3.000000 7000.000000 
 4.000000 9000.000000 
 5.000000 11000.000000 
 6.000000 13000.000000 
 7.000000 15000.000000 


Coefficients of polynomial found 
26.515152 
3404.671717 
-629.734848 
110.479798 
-6.628788 

Data points calculated with the polynomial 
0  +0.000000000000000000  +26.515151515142889593 
1  +0.241379310344827597  +813.172863273697998920 
2  +0.482758620689655193  +1535.456370840211548057 
3  +0.724137931034482762  +2201.878117492446563119 
4  +0.965517241379310387  +2820.410482131026583374 
5  +1.206896551724137900  +3398.485779279436883371 
6  +1.448275862068965525  +3942.996259084022312891 
7  +1.689655172413793149  +4460.294107313990934927 
8  +1.931034482758620774  +4956.191445361408113968 
9  +2.172413793103448398  +5435.960330241205156199 
10  +2.413793103448275801  +5904.332754591169759806 
11  +2.655172413793103203  +6365.500646671953290934 
12  +2.896551724137930606  +6823.115870367066236213 
13  +3.137931034482758008  +7280.290225182881840738 
14  +3.379310344827585411  +7739.595446248635198572 
15  +3.620689655172412813  +8203.063204316418705275 
16  +3.862068965517240215  +8672.185105761187514872 
17  +4.103448275862067618  +9147.912692580759539851 
18  +4.344827586206895020  +9630.657442395811813185 
19  +4.586206896551722423  +10120.290768449882307323 
20  +4.827586206896549825  +10616.144019609369934187 
21  +5.068965517241377228  +11117.008480363538183155 
22  +5.310344827586204630  +11621.135370824502388132 
23  +5.551724137931032033  +12126.235846727246098453 
24  +5.793103448275859435  +12629.480999429617440910 
25  +6.034482758620686838  +13127.501855912318205810 
26  +6.275862068965514240  +13616.389378778912941925 
27  +6.517241379310341642  +14091.694466255828956491 
28  +6.758620689655169045  +14548.427952192345401272 
29  +6.999999999999996447  +14981.060606060626014369 
?]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P2?dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P2$ ./patients.out > patients.txt 
?]0;dlabudovic@ubuntu: ~/Documents/CS4491/assign_06/P2?dlabudovic@ubuntu:~/Documents/CS4491/assign_06/P2$ gnuplot 
	G N U P L O T 
	Version 4.6 patchlevel 0    last modified 2012-03-04 
	Build System: Linux x86_64 

	Copyright (C) 1986-1993, 1998, 2004, 2007-2012 
	Thomas Williams, Colin Kelley and many others 

	gnuplot home:     http://www.gnuplot.info 
	faq, bugs, etc:   type "help FAQ" 
	immediate help:   type "help"  (plot window: hit 'h') 

Terminal type set to 'wxt' 


gnuplot> o??[K?load 'patients.cgp' 
gnuplot> exit 


Script done on Thu 18 Apr 2013 04:46:23 PM EDT

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