menu driven program to show the entered is: 1)diagonal matrix 2)lower triangular matrix 3)upper triangular matrix 4)symmetric matrix 5)tridiagonal matrixpull/186/head
Abhishek Kardam
5 years ago
committed by
GitHub
parent
88f03118ce
commit
40a2b60282
@ -0,0 +1,431 @@
|
||||
// PROGRAM:MAPPING OF 2 DIMENSIONAL MATRIX
|
||||
|
||||
#include<iostream>
|
||||
using namespace std;
|
||||
//m is number of rows.
|
||||
//n is number of columns.
|
||||
//a is a 2d array.
|
||||
//bis a 1d array.
|
||||
int i,j,k,m,n,a[10][10],b[100],found=0;;
|
||||
int enter() //function to enter a matrix.
|
||||
{
|
||||
cout<<"enter no. of rows:";
|
||||
cin>>m;
|
||||
cout<<"\n enter no. of columns:";
|
||||
cin>>n;
|
||||
cout<<"\n enter elements of matrix:"<<endl;
|
||||
for(i=0;i<m;i++) //loop to enter elements of matix.
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
cin>>a[i][j];
|
||||
}
|
||||
}
|
||||
cout<<"\n entered matrix:"<<endl;
|
||||
for(i=0;i<m;i++) //loop to display the matix.
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
cout<<a[i][j]<<" ";
|
||||
}
|
||||
cout<<endl;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
Diagonal matrix:
|
||||
1 0 0 0 0
|
||||
0 2 0 0 0
|
||||
0 0 3 0 0
|
||||
0 0 0 4 0
|
||||
0 0 0 0 5
|
||||
all the elements(except main diagonal) should be 0.
|
||||
*/
|
||||
int diagonal() //function to check whether matrix is diagonal or not.
|
||||
{
|
||||
found=0;
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
if(i!=j && a[i][j]!=0) //if non diagonal elements are not 0 then found=1.
|
||||
{
|
||||
found=1;
|
||||
}
|
||||
if(found==0) //if found=0 convert 2d array into 1d array.
|
||||
{
|
||||
k=i*n + j;
|
||||
b[k]=a[i][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
//if found is equal to 0 display new 1d array. if found is not equal to 0 display matrix is not diagonal.
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n entered matrix is a diagonal matrix";
|
||||
cout<<"\n new matrix:"<<endl;
|
||||
for(k=0;k<m*n;k++) //number of elements in new 1d array are m*n.
|
||||
{
|
||||
cout<<b[k]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
cout<<"\n entered matrix is not a diagonal matrix "<<endl;
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
Tridiagonal matrix:
|
||||
1 2 0 0 0
|
||||
3 4 5 0 0
|
||||
0 6 7 8 0
|
||||
0 0 9 10 11
|
||||
0 0 0 12 13
|
||||
all the elements(except tridiagonal) should be 0.
|
||||
*/
|
||||
int tridiagonal() //function to check whether matrix is tidiagonal or not.
|
||||
{
|
||||
int x;
|
||||
//matrix should be a square matrix.
|
||||
if(m==n)
|
||||
{
|
||||
found=0;
|
||||
x=3*n-2; //number of elements in new 1d array are 3*m-2.
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
k=(i-j);
|
||||
if((k<-1 || k>1) && a[i][j]!=0) //if non tridiagonal elements are not 0 then found is equal to 0.
|
||||
{
|
||||
found=1;
|
||||
}
|
||||
if(k>=-1 || k<=1) //if i-j is greater than -1 and less than 1. then (i,j) is tridiagonal element.
|
||||
{
|
||||
switch(k) // switch case for lower diagonal,main diagonal and upper diagonal.
|
||||
{
|
||||
case 1: //for lower diagonal.
|
||||
b[i-1]=a[i][j];
|
||||
break;
|
||||
case 0: //for main diagonal.
|
||||
b[n+i-1]=a[i][j];
|
||||
break;
|
||||
case -1: //for upper diagonal.
|
||||
b[2*n+i-1]=a[i][j];
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
//if found is 0 then display the new 1d array.
|
||||
// if found is not 0 then display matrix is not tridiagonal.
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n entered matrix is tridiagonal.";
|
||||
cout<<"\n new matrix:"<<endl;
|
||||
for(i=0;i<x;i++)
|
||||
{
|
||||
cout<<b[i]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
cout<<"\n entered matrix is not tridiagonal.";
|
||||
}
|
||||
else
|
||||
cout<<"\n enter matrix is not a square matrix.";
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
example of lower triangular matrix:
|
||||
1 0 0 0 0
|
||||
2 3 0 0 0
|
||||
4 5 6 0 0
|
||||
7 8 9 10 0
|
||||
11 12 13 14 15
|
||||
All the elements(except lower triangle elements) should be 0.
|
||||
There are two ways to map lower triangular matrix into 1d array:
|
||||
1.row major
|
||||
mapping formula-> i*(i+1)/2 +j.
|
||||
2.column major
|
||||
mapping formula-> (m*j) + i - (j*(j+1)/2)
|
||||
*/
|
||||
int lower_triangle() //function to check whether matrix is lower triangular or not.
|
||||
{
|
||||
int rc;
|
||||
found=0;
|
||||
//matrix should be a square matrix.
|
||||
if(m==n)
|
||||
{
|
||||
//switch case to choose how to display 1d array(row major or column major).
|
||||
cout<<"1.row major"<<endl;
|
||||
cout<<"2.column major"<<endl;
|
||||
cout<<"choose(1/2):";
|
||||
cin>>rc;
|
||||
switch(rc)
|
||||
{
|
||||
case 1: //for row major lower triangular matrix
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
if(i<j && a[i][j]!=0) //if non lower triangle elements are not 0 then found is 1.
|
||||
{
|
||||
found=1;
|
||||
}
|
||||
if(i>=j) //for lower triangle elements if condition is correct convert 2d array into 1d array.
|
||||
{
|
||||
k=(i*(i+1)/2 + j); //formula for row major mapping of upper triangular matrix.
|
||||
b[k]=a[i][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
//if found is 0 display the new 1d array in row major.
|
||||
//if found is not 0 display matrix is not lower triangular.
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n matrix is lower triangular";
|
||||
cout<<"\n new matrix row major:"<<endl;
|
||||
for(k=0;k<m*(m+1)/2;k++) //number of elemets in new 1d array are m*(m+1)/2.
|
||||
{
|
||||
cout<<b[k]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
cout<<"\n matix is not lower triangular"<<endl;
|
||||
}
|
||||
break;
|
||||
case 2: //for column major lower triangular matrix
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
if(i<j && a[i][j]!=0) //if non lower triangle elements are not 0 then found is 1.
|
||||
{
|
||||
found=1;
|
||||
}
|
||||
if(i>=j) //for lower trianle elements if condition is correct convert 2d array into 1d array.
|
||||
{
|
||||
k=((m*j) + i - j*(j+1)/2); //formula for column major mapping of upper triangular matrix
|
||||
b[k]=a[i][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
// if found is 0 display the new 1d array in column major.
|
||||
//if found is not 0 display matrix is not lower triangular
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n matrix is lower triangular";
|
||||
cout<<"\n new matrix column major:"<<endl;
|
||||
for(k=0;k<m*(m+1)/2;k++) //number of elememts in new 1d array are m*(m+1)/2
|
||||
{
|
||||
cout<<b[k]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
cout<<"\n matrix is not lower triangular"<<endl;
|
||||
}
|
||||
break;
|
||||
default: //in case user enters wrong number.
|
||||
cout<<"\n enter 1 or 2.";
|
||||
break;
|
||||
}
|
||||
}
|
||||
else
|
||||
cout<<"\n sorry,matrix is not a square matrix"<<endl;
|
||||
return 0;
|
||||
}
|
||||
/* example of upper triangular matrix:
|
||||
1 2 3 4 5
|
||||
0 6 7 8 9
|
||||
0 0 10 11 12
|
||||
0 0 0 13 14
|
||||
0 0 0 0 15
|
||||
All elements(except upper triangle elements) should be 0.
|
||||
there are 2 ways to map upper triangular matrix.
|
||||
1.row major
|
||||
mapping formula->(n*i) + j - i*(i+1)/2.
|
||||
2.column major
|
||||
mapping formula->j*(j+1)/2 + i.
|
||||
*/
|
||||
int upper_triangle() //function to check whether matrix is upper triangular or not.
|
||||
{
|
||||
int rc;
|
||||
found=0;
|
||||
//matrix should be a square matrix.
|
||||
if(m==n)
|
||||
{
|
||||
//switch case to choose how to display 1d array(row major or column major).
|
||||
cout<<"1.row major"<<endl;
|
||||
cout<<"2.column major"<<endl;
|
||||
cout<<"choose(1/2):";
|
||||
cin>>rc;
|
||||
switch(rc)
|
||||
{
|
||||
case 1: //for row major upper triangular matrix
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
if(i>j && a[i][j]!=0) //if non upper triangle elements are not 0 then found is 1.
|
||||
found=1;
|
||||
if(i<=j) //for upper triangular elements if condition is correct convert 2d array into 1d array.
|
||||
{
|
||||
k=((n*i) + j - i*(i+1)/2); //formula for row major mapping of upper triangular matrix.
|
||||
b[k]=a[i][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
//if found is 0 display new 1d array in row major.
|
||||
//if found is 1 display matrix is not upper triangular.
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n matrix is upper triangular";
|
||||
cout<<"\n new matrix row wise:";
|
||||
for(k=0;k<m*(m+1)/2;k++) //number of elements in new 1d array are m*(m+1)/2.
|
||||
{
|
||||
cout<<b[k]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
cout<<"\n matrix is not upper triangular"<<endl;
|
||||
break;
|
||||
case 2: //for column major upper triangular matrix
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
if(i>j && a[i][j]!=0) //if non upper triangle elements are not 0 then found is 1.
|
||||
found=1;
|
||||
if(i<=j) //for upper triangular elements if condition is correct convert 2d array into 1d array.
|
||||
{
|
||||
k=(j*(j+1)/2 + i); //formula for column major mapping of upper triangular matrix.
|
||||
b[k]=a[i][j];
|
||||
}
|
||||
}
|
||||
}
|
||||
//if found is 0 display new 1d array in row major.
|
||||
//if found is 1 display matrix is not upper triangular.
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n matrix is upper triangular";
|
||||
cout<<"\n new matrix column wise:";
|
||||
for(k=0;k<m*(m+1)/2;k++) //number of elements in new 1d array are m*(m+1)/2.
|
||||
{
|
||||
cout<<b[k]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
cout<<"\n matrix is not upper triangular"<<endl;
|
||||
break;
|
||||
default: //in case user enters wrong number
|
||||
cout<<"\n enter 1 or 2.";
|
||||
break;
|
||||
}
|
||||
}
|
||||
else //to show that entered matrix is not a square matrix
|
||||
cout<<"\n sorry,matrix is not square matrix"<<endl; //and triangular matrices are square matices.
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
example of symmetric matrix :
|
||||
0 1 2 3 4
|
||||
1 0 5 6 7
|
||||
2 5 0 8 9
|
||||
3 6 8 0 10
|
||||
4 7 9 10 0
|
||||
All the main diagonal elements should be 0 and (i,j)th element of matrix must be equal to (j,i)th element of matrix.
|
||||
if we map in row major then column major elements will be covered as row major elements are equal to column major elements.
|
||||
*/
|
||||
int symmetric() //to check whether matrix is symmetric or not
|
||||
{
|
||||
found=0;
|
||||
//matrix should be a square matrix.
|
||||
if(m==n)
|
||||
{
|
||||
for(i=0;i<m;i++)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
{
|
||||
if(a[i][j]!=a[j][i] || a[i][i]!=0) //if (i,j)th element is not equal to (j,i)th element then found is 1.
|
||||
found=1;
|
||||
else //else convert 2d matrix into 1 d array.
|
||||
{
|
||||
if(i<=j) //if condition is correct convert 2d array into 1d array
|
||||
{
|
||||
k=((n*i) + j - i*(i+1)/2); ////formula for row major mapping of upper triangular matrix.
|
||||
b[k]=a[i][j];
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
//if found is 0 display new 1d array.
|
||||
//else display matri is not symmetric.
|
||||
if(found==0)
|
||||
{
|
||||
cout<<"\n matrix is symmetric";
|
||||
cout<<"\n new matrix:"<<endl;
|
||||
for(k=0;k<m*(m+1)/2;k++) //number of element in new 1d array are m*(m+1)/2.
|
||||
{
|
||||
cout<<b[k]<<" ";
|
||||
}
|
||||
}
|
||||
else
|
||||
cout<<"\n matrix is not symetric."<<endl;
|
||||
}
|
||||
else
|
||||
cout<<"sorry,enter matrix is not square matrix.";
|
||||
return 0;
|
||||
}
|
||||
// main menu
|
||||
//function to display number of operations.
|
||||
int menu()
|
||||
{
|
||||
cout<<"\n MAIN MENU"<<endl;
|
||||
cout<<"1.enter matrix"<<endl;
|
||||
cout<<"2.diagonal matrix"<<endl;
|
||||
cout<<"3.lower triangular matrix"<<endl;
|
||||
cout<<"4.upper triangular matrix"<<endl;
|
||||
cout<<"5.symmetric matrix"<<endl;
|
||||
cout<<"6.tridiagonal matrix"<<endl;
|
||||
return 0;
|
||||
}
|
||||
//main function
|
||||
int main()
|
||||
{
|
||||
int ch;
|
||||
char ch1;
|
||||
do
|
||||
{
|
||||
menu();
|
||||
cout<<"\n choose:";
|
||||
cin>>ch;
|
||||
switch(ch) //switch case to choose between operation.
|
||||
{
|
||||
menu();
|
||||
case 1:enter(); //to enter a mXn matrix
|
||||
break;
|
||||
case 2:diagonal(); //to find whether matrix is diagonal or not
|
||||
break;
|
||||
case 3:lower_triangle(); //to find whether matrix is lower triangular or not
|
||||
break;
|
||||
case 4:upper_triangle(); //to find whether matrix is upper triangular or not
|
||||
break;
|
||||
case 5:symmetric(); //to find whether matrix is symmetric or not
|
||||
break;
|
||||
case 6:tridiagonal(); //to find whether matrix is tridiagonal or not
|
||||
break;
|
||||
default: //in case user enters wrong number.
|
||||
cout<<"\n enter from menu.";
|
||||
break;
|
||||
}
|
||||
cout<<"\n want to enter more(y/n)?"; //if user want to choose again.
|
||||
cin>>ch1;
|
||||
if(ch1=='y' || ch1=='Y')
|
||||
cout<<"\n enter again:"<<endl;
|
||||
}
|
||||
while(ch1=='y' || ch1=='Y'); //switch case will run while you say yes.
|
||||
return 0;
|
||||
}
|
||||
//----------X----------X----------X----------X-----END-----X----------X----------X----------X----------X----------
|
||||
Loading…
Reference in new issue