//this is the program for gaussian elimination method for solving system of equations
#include<stdio.h> //preprocessor library used in the program
//prototypes
void starter(); //this function displays the start of the program
void getvalues(int R,int C,float A[][C+1]);//this function get values of augmented values
void printmatrix(int R,int C,float A[][C+1]); //function will print the matrix
void Swap(int R,int C,float A[][C+1]); //function will swap the rows of the matrix
float Echelon(int R1,int C1,float A1[][C1+1]);//function will convert matrix in echelon form
float Infinite(int R2,int C2,float A2[][C2+1],float X1[]); //function for infinite sol. case
float Unique(int R3,int C3, float A3[][C3+1],float X2[]); //function for no sol. case
void solution(int R,int C,float A[][C+1],float X[]); //function shows the solution result
void endresult(); //function which ends the program
int main() //main function starts here
{
starter(); //call to starter function
int i,j,R,C; //declaration of variables used in main
//now it will take user input for how many unknown variables of each equation
printf("\n\tEnter Number of unknown variables.\n\t"); //ask the user
scanf(" %d",&R); //get the value from user
C=R; //no.of unknown vaariables is always equal to no of equations
float A[R][C+1]; //declaration of array which contains the augmented matrix
float X[10]={0}; //declaring array which contains row to swap
getvalues(R,C,A); //call for getting the input for augmented matrix
printf("\tThe augmented matrix of the system of equations is\n");
printmatrix(R,C,A); //call to show the matrix before echelon form
Swap(R,C,A); //call to check the matrix for any zero value and then swap
Echelon(R,C,A); //call for converting in echelon form
printf("\tAfter reducing the matrix in echelon form\n");
printmatrix(R,C,A); //print the matrix after echelon form
solution(R,C,A,X); //call to display the final result
endresult(); //call to end the program
return 0; //ensures program ends
}
//main bloack ends
//function for starting page starts here
void starter()//definition of the funtion starter of void type
{
//the very first welcoming screen display
printf("\n_______________________________________________________________");
printf("\n!! ****************** ASSLAM U ALAIKUM ****************** !!");
printf("\n!! \t \t!!");
printf("\n!! \t \t!!");
printf("\n!! \t WELCOME TO THE WORLD OF LINEAR EQUATIONS \t!!");
printf("\n!! \t YOU CAN SOLVE ANY KIND OF EQUATION USING \t!!");
printf("\n!! \t \t!!");
printf("\n!! \t \tGAUSSIAN ELIMINATION METHOD \t\t!!");
printf("\n!! \t \t!!");
printf("\n!! \t \t!!");
printf("\n!!______________________________________________________________!!\n");
printf("\n!! ----------------GENERAL INSTRUCTION------------------- !!");
printf("\n!! 1)Number of equations and variables should be equal. !!");
printf("\n!! 2)Gaussian method is applicable for square matrices. !!");
printf("\n!! 3)Equations in the form of matrix are as AX=B \t!!\n!!\t where\t\t\t\t\t\t\t!!\n!!\t A is the matrix of coefficients.\t\t\t!!");
printf("\n!! B is matrix for constants.\t\t\t\t!!");
printf("\n!! X is the unknown matrix which contains variables. !!");
printf("\n!!______________________________________________________________!!\n");
//general instructions for the user are also included so that he could understand
// what he is doing
}
//starter function ends here
//definition of getvalues function starts here
//it will get the co efficient of the variables and adjust them in an array
void getvalues(int R,int C,float A[][C+1])
{
int i,j; //declare i for row check and j for colomn check
printf("\n\tEnter coefficients which are the elements of matrix A\n");
int equno=0; //asking user for input and equno is used to checkfor no of equation
for (i=0; i<R; i++) //this for loop will move through each row
{
equno++; //increment in variable
printf("\tequation %d \n",equno); //show equation no.whose values are entered
for (j=0;j<C; j++) //for loop will move through each coloumn
{
printf("\t A[%d][%d] ",i+1,j+1);
scanf("%f",&A[i][j]); //takes user input and adjust in the array
}
printf("\n"); //switch lines
}
printf("\tEnter Elements Of Matix B\n"); //asks for values in constant matrix
for (i=0; i<R; i++) //loop for rows
{
for (j=C; j<C+1; j++) //loop for coloumn
{
printf("\t B[%d][%d] ",i+1,j+1);
scanf("%f",&A[i][j]); //takes input and adjust in last colomn of array
}
printf("\n"); // switch lines
}
}//getvalues function ends here
//function for printing matrix
//printing the values of the array in augmented matrix
void printmatrix(int R,int C,float A[][C+1])
{
int i,j; //declare i for row check and j for colomn check
for (i=0; i<R; i++) //this for loop will move through each row
{
for (j=0; j<C+1; j++) //loop for coloumn
{
if(j!=C) //print the values of matrix A
{printf("\t%.1f ",A[i][j]);}
if(j==C) //prints the vaalues of matrix B
{printf("|\t%.1f ",A[i][j]);}
}
printf("\n");//switch lines
}
printf("\n\n");//switch lines
}//printmatrix funcion ends here
//function for swapping rows
//this swap rows if there is zero in the diagonal
void Swap(int R,int C,float A[][C+1])
{
int i,j,Counter1,Counter2,Counter3,Temp2,red=0; //declaration variables
float Temp[C+1]; //declare an array for swaping assistance
for (i=0; i<R; i++) //loop for rows
{
for (j=0; j<C+1; j++) //loop for coloumn
{ if (i==j) //checks only for element in diagonal
{ if (A[i][i]==0) //check for 0 in diagonal
{ for (Counter3=0; Counter3<R; Counter3++)
{ if (A[Counter3][j]!=0)
{
Temp2=Counter3;
}
}
{
for (Counter2=0; Counter2<C+1; Counter2++)
{ //this will swap the rows
Temp[Counter2]=A[i][Counter2];
A[i][Counter2]=A[Temp2][Counter2];
A[Temp2][Counter2]=Temp[Counter2];
}
}
}
}
}
}
}//swap function will end here
//echelon funcion starts here
//it will convert matrix in upper trangular form
float Echelon(int R1,int C1,float A1[][C1+1])
{
int i,j,Pass1,Pass2,Pass3,K3; //declaration variables
//K3 for storing divisor //all pass1,2,3 for sorting assistance
Pass2=0; // initialization of variables
for (j=0; j<C1; j++) //loop for rows
{
Pass2++; //increment
K3=1; //initalize divisor at 1
for (i=Pass2; i<R1+1; i++) //loop for coloumn
{
if (j==i-1) //
{
float K1=A1[i-1][j]; //stores value for division
for (Pass1=0; Pass1<C1+1; Pass1++) //check for rows
{
if (i==R1 && A1[R1-1][C1-1]==0 && A1[R1-1][C1]!=0)
{
break;
}
if (i==R1 && A1[R1-1][C1-1]==0 && A1[R1-1][C1]==0)
{
break;
}
A1[j][Pass1]=A1[j][Pass1]/K1;
}
}
if (i==R1)
{
break;
}
float K2=A1[i][j];
for (Pass3=0; Pass3<C1+1; Pass3++)
{
A1[i][Pass3]=A1[i][Pass3]-(K2*A1[i-K3][Pass3]);
}
K3++;
}
}
} //echelon function ends
// infinite function starts
//function willoperate for infinte solutions
float Infinite(int R2,int C2,float A2[][C2+1],float X1[])
{
int i,j,Pass6,Pass7;
Pass6=0;
for (i=0; i<(R2-1); i++)
{
Pass6++;
if (Pass6>1)
{
for (j=1; j<Pass6; j++)
{
int Pass7;
Pass7=A2[R2-(i+2)][C2-1];
X1[i]=X1[i]-Pass7-X1[i-1]*A2[R2-(i+2)][C2-(j+1)];
if(j==1)
{
Pass7=0;
}
}
}
else
{
X1[i]=-A2[R2-2][C2-1];
}
}
}//infinite function ends here
//function for unique solution
//back substitution of unique answers held here
float Unique(int R3,int C3, float A3[][C3+1],float X2[])
{
int i,j,Pass4,Pass5; //declaration variables
Pass4=0;
for (i=0; i<R3; i++) //loop for rows
{
Pass4++;
if (Pass4>1)
{
for (j=1; j<Pass4; j++) //loop for coloumn
{
X2[i]=X2[i]+A3[R3-(i+1)][C3] -X2[j-1]*A3[R3-(i+1)][C3-j];
if (j==1)
{
A3[R3-(i+1)][C3]=0;
}
}
}
else
{
X2[i]=A3[R3-1][C3];
}
}
} //unique function ends here
//function for displaying answrs starts
//will show the respective solution of the matrices
void solution(int R,int C,float A[][C+1],float X[])
{
int i,j; //declare i for row check and j for colomn check
printf("\n\t******HERE IS THE ANSWER******\t\n");
if (A[R-1][C-1]==0 && A[R-1][C]!=0) //condition for no solution
{
printf("\n\n\t The given system of equation has no solution\n");
}
if (A[R-1][C-1]==0 && A[R-1][C]==0) //condition for infinite solution
{
Infinite(C,R,A,X); //calls infinite function
printf("\n\tThe given system of equation has Infinite Solutions\n\t");
for (i=0; i<(R-1); i++) //loop for rows
{
printf("\tX[%d] = %.2ft\n",i+1,X[R-(i+2)]);
} //displays the result of infinite answer
printf("\tX[%d] = t\n",R);
printf("\tWhere -Infinity < t < +Infinity\n");
}
if (A[R-1][C-1]!=0)// condition for unique solution
{
Unique(R,C,A,X);//calls for unique function
printf("\tEach unknown variable has unique solution\n");
for (i=0; i<R; i++) //loop for rows
{
printf("\t\tX[%d] = %.2f \n",1+i,X[R-i-1]);
} //display result for unique solutions
}
} // solution function ends here
//this will display the good bye screen
//and will show the group members
void endresult()
{
printf("\n\n\t**************THANK YOU FOR USING THIS PROGRAM*****************");
}//function end result will end here
//the program will end
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