// DigitTest.java

import java.io.*;
import java.awt.*;
import java.lang.Math;

class DigitTest{

   static int row=10,col=10,dim=3,counter_zero;
   
   static double A[][]=new double[row][col];
   static double B[][]=new double[row][col];
   static double E[][]=new double[row][col];
   static double N[][]=new double[row][col];
   static double C[][]=new double[row][col];

      static int counter=0,loop=0,fail=0;
      static double digit=100000;

public static void main(String args[]){

for(int ave=0;ave<1;ave++){

counter=0;fail=0;

for(int loop=0;loop<1;loop++){

//DetSet();  // specific matrix test

RnDetSet();  // set random matrix 
SetB();      // set E

//double det = Det2(A[0][0],A[0][1],A[1][0],A[1][1]);
double det = Det3(A[0][0],A[0][1],A[0][2],A[1][0],A[1][1],A[1][2],A[2][0],A[2][1],A[2][2]);
//double det = Det4(A[0][0],A[0][1],A[0][2],A[0][3],A[1][0],A[1][1],A[1][2],A[1][3],A[2][0],A[2][1],A[2][2],A[2][3],A[3][0],A[3][1],A[3][2],A[3][3]);

if(det!=0){

System.out.println("det= "+det);

Rev();       // inverse
Digitrim();  // digit trimming
Digiright(); // digit recovering
SetB();      // reset E    
Rev(); 

MatComp();   // comparing  before, after calculation

}else{ counter++;
System.out.println("det is zero ,"+counter+"\n");
}

}

System.out.println("\n"+"det=0 :"+counter+" , fail :"+fail+"   ");

}

}



public static void RnDetSet(){

int n1=48,n2=0;

for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

while(true){

n2=(int)(75*Math.random());

if((n2>=10 && n2<=16) || (n2>=43 && n2<=49)){

}else{

    A[i][j]=n1+n2;
    break;

}

}

}}

// saving to other matirx
for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

 C[i][j]=A[i][j];
System.out.print(A[i][j]+" ");  
}
System.out.println();
}
System.out.println();
}


public static void SetB(){

for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

  if(i==j){ B[i][j]=1;}
  else{B[i][j]=0;}

}}

// print
for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

  System.out.print(B[i][j]+" ");
  
}System.out.println();}
//

}

public static double Det2(double a11, double a12, double a21, double a22){

double rdet2=a11*a22*-a12*a21;

//System.out.print("det2= "+rdet2);

return rdet2;

}


public static double Det3(double a11, double a12, double a13, double a21, double a22, double a23, double a31, double a32, double a33){

double rdet3=a11*(a22*a33-a23*a32)-a21*(a12*a33-a13*a32)+a31*(a12*a23-a22*a13);

//System.out.print("det3= "+rdet3);

return rdet3;

}



public static double Det4(double a11, double a12, double a13, double a14, double a21, double a22, double a23, double a24,double a31, double a32, double a33, double a34, double a41, double a42, double a43, double a44){

double rdet4=a11*Det3(a22,a23,a24,a32,a33,a34,a42,a43,a44)-a21*Det3(a12,a13,a14,a32,a33,a34,a42,a43,a44)+a31*Det3(a12,a13,a14,a22,a23,a24,a42,a43,a44)-a41*Det3(a12,a13,a14,a22,a23,a24,a32,a33,a34);

//System.out.print("det4= "+rdet4);

return rdet4;

}



public static void Rev(){  // inverse transpose

int i,j;
double gau;

for(i=0;i<dim;i++){

gau =A[i][i];
System.out.println("gau "+gau);

if(gau==0){System.out.print("A["+i+"]"+"["+i+"]"+" = 0");System.exit(0);}

for(j=0;j<dim;j++){

A[i][j]/=gau;
B[i][j]/=gau;

}

for(int k=0;k<dim;k++){
if(i!=k){
gau=A[k][i];

for(int m=0;m<dim;m++){

A[k][m]-=gau*A[i][m];
B[k][m]-=gau*B[i][m];

}
}
}


//print
if(i==(dim-1)){

for(int p=0;p<dim;p++){
for(int q=0;q<dim;q++){
System.out.print(A[p][q]+" ");
}
for(int r=0;r<dim;r++){
System.out.print(B[p][r]+" ");
}
System.out.println("\n");
}

}
// print

}
}


public static void Digitrim(){

for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

N[i][j]=Math.rint(B[i][j]*digit);

}}


//print

for(int p=0;p<dim;p++){
for(int q=0;q<dim;q++){
System.out.print(N[p][q]+" ");
}System.out.println("\n");
}

// print

}


public static void Digiright(){

for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

A[i][j]=N[i][j]/digit;

}}


//print

for(int p=0;p<dim;p++){
for(int q=0;q<dim;q++){
System.out.print(A[p][q]+" ");
}
System.out.println("\n");
}

// print
}


public static void MatComp(){

int xflag=0;

for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

//if(Math.rint(B[i][j])!=C[i][j]){ error code
if(Math.abs(B[i][j]-C[i][j])>=0.5){

System.out.print("x ["+i+","+j+"] ="+Math.rint(B[i][j])+" "+C[i][j]);
xflag=1;break;
}

} if(xflag==1){fail++;


/* print (failure) 

for(int m=0;m<dim;m++){
for(int n=0;n<dim;n++){
 System.out.print(C[m][n]+" ");
}
System.out.print(" , ");
}

System.exit(1);
*/

break;}


}

}


public static void DetSet(){ // test for specific matrix

      A[0][0]=1;
      A[0][1]=2;
      A[0][2]=3;
      A[1][0]=4;
      A[1][1]=5;
      A[1][2]=6;
      A[2][0]=7;
      A[2][1]=8;
      A[2][2]=9;


for(int i=0;i<dim;i++){
for(int j=0;j<dim;j++){

  C[i][j]=A[i][j];
  System.out.print(A[i][j]+" ");
  
}
System.out.print(" , ");
}

System.out.print("\n\n");
}




}