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