programming-examples/c++/Computational_Geometry/C++ Program to Implement GAUSS ELIMINATION METHOD TO SOLVE LINEAR EQUATIONS.cpp
2019-11-15 12:59:38 +01:00

79 lines
2.8 KiB
C++

/*-------- GAUSS ELIMINATION METHOD TO SOLVE LINEAR EQUATIONS ---------*/
/* THE PROGRAM SOLVES THE SYSTEM OF LINEAR EQUATIONS USING
GAUSS ELIMINATION METHOD.
INPUTS : 1) Number of variables in the equation.
2) Coefficient's of linear equations.
OUTPUT : Calculated values of x1,x2,x3,...,xn etc. */
/*------------------------------ PROGRAM --------------------------*/
#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#include<conio.h>
void main()
{
double a[10][10],x[10],ratio,coefsum;
/* ARRAY OF a[n][n] STORING COEFFICIENTS OF EQUATIONS */
int i,j,n,k;
clrscr();
printf("\n Computational Techniques - J. S. CHITODE");
printf("\n GAUSS ELIMINATION METHOD TO SOLVE LINEAR EQUATIONS");
printf("\n\n The form of equations is as follows\n\n"
" a11x1 + a12x2 + ... + a1nxn = b1\n"
" a21x1 + a22x2 + ... + a2nxn = b2\n"
" a31x1 + a32x2 + ... + a3nxn = b3\n"
" ................................\n"
" an1x1 + an2x2 + ... + annxn = bn\n"
"\n\nHere a11,a22,a33,a44,.....etc. should not be zero\n");
printf("\n\nEnter the number of variables (max 10) = ");
/* ENTER THE NUMBER OF VARIABLES IN THE EQUATION */
scanf("%d",&n);
for(i = 1; i <= n; i++)
{
/* LOOP TO GET COEFFICIENTS a11,a12...,ann & so on */
for(j = 1; j <= n; j++)
{
printf("a%d%d = ",i,j);
scanf("%lf",&a[i][j]);
}
printf("b%d = ",i);
scanf("%lf",&a[i][j]);
x[i] = 0;
}
for(k = 1; k <= n-1; k++)
{
/* LOOP TO GENERATE UPPER TRIANGULAR SYSTEM */
for(i = k+1; i <= n; i++)
{
ratio = a[i][k]/a[k][k];
for(j = k+1; j <= n+1; j++)
{
a[i][j] = a[i][j] - ratio * a[k][j];
}
}
for(i = k+1; i <= n; i++) a[i][k] = 0;
}
x[n] = a[n][n+1]/a[n][n];
for(i = n-1; i >= 1; i--)
{
/* LOOP FOR BACKWARD SUBSTITUTION */
coefsum = 0;
for(j = i+1; j <= n; j++) coefsum = coefsum + a[i][j] * x[j];
x[i] = (a[i][n+1] - coefsum)/a[i][i];
}
printf("\n\nThe values of variables in the given equations are "
"as follows....\n");
for(i = 1; i <= n; i++) printf("\n x%d = %lf ",i,x[i]);
/* LOOP TO PRINT VALUES OF x1,x2,...xn etc */
}
/*-------------------------------- END OF PROGRAM ----------------------*/