Finding the determinant of a matrix

[curiously enough]

I am having trouble making this recursive C function work for square matrices of size greater than 3 rows and columns.

#include<stdio.h>
#include<conio.h>
#include<math.h>
int M[100];
float DET(float A[][100],int dim)
{
int i=100,j,k,l;
static int det=0;
static int DIM=dim;
if(dim>2)
    for(i=0;i<DIM;i++)
    {
    if(i==0&&DIM==dim)for(j=0;j<100;j++)M[j]=100;
    for(j=DIM-1;j>=2;j--)
    if(M[j]==i)continue;
    M[dim-1]=i;
    det+=pow(-1,i+dim-1)*A[dim-1][i]*DET(A,dim-1);
    }
    if(i==DIM-1)M[dim-1]=100;
if(dim==2)
      {
    for(i=0;i<DIM;i++)
    {
    k=0;
      for(j=DIM-1;j>=2;j--)
    if(i!=M[j])k++;
    if(k==DIM-2)break;
    }
    for(j=0;j<DIM;j++)
    {
    k=0;
    for(l=DIM-1;l>=2;l--)
    if(j!=M[l])k++;
    if(k==DIM-2&&j!=i)break;
    }
    return(A[0][i]*A[1][j]-A[0][j]*A[1][i]);
      }
if(dim==1)return(A[0][0]);
return(det);
}
 
 
void main()
{
float A[100][100];
int n,k,l;
puts("Input size of square matrix:");
scanf("%d",&n);
puts("Input square matrix:");
for(k=0;k<n;k++)
{
printf("\n");
for(l=0;l<n;l++)
{
printf("Input a%d%d: ",k+1,l+1);
scanf("%f",&A[k][l]);
}
}
printf("\n\nThe determenant of the matrix is %0.2f",DET(A,n));
getch();
}
 

If anyone can tell me where I went wrong in writing the program I would be grateful.
P.S.:Here are some points to make the program clearer:
_This program works by using method of minor.
_M[100] is an array of integers used to store in decreasing order of its elements which column in the matrix does not belong to the minor associated with the element chosen on a certain row.
_In the function, dim represents wich row is being used, while i(in the first for loop) represents which column is being used.

[arnaudk]

As noted in a recent thread, finding the determinant by a minors expansion is very slow (O(n!) for an nxn matrix), there are much better methods like the finding the LU decomposition which is O(n^3). Also, there are a number of libraries which can do all this for you, such as GSL.

[curiously enough]

As noted in a recent thread, finding the determinant by a minors expansion is very slow (O(n!) for an nxn matrix), there are much better methods like the finding the LU decomposition which is O(n^3). Also, there are a number of libraries which can do all this for you, such as GSL.

I know there are other methods , but I want to use this one, so please read the program and try it and maybe you'll know what's wrong with it.

[arnaudk]

What kind of problems are you having with your code? Does it compile? Does it give you the wrong answer?

[curiously enough]

What kind of problems are you having with your code? Does it compile? Does it give you the wrong answer?

it compiles,but It gives the wrong answer for square matrices of order greater than or equal to 4

[arnaudk]

Since there is probably an arithmetic error in your code, why not get the function DET to print out the matrix that it is given in a nice tabular form, as well as the cofactor so that you can check that everything is working as expected and you are getting the correct cofactor and associated minor?

Some general suggestions:

• The return type of main is int, not void.
• Use more intuitive variable names, if i represents a column, call it col.
• Use brief comments to explain what's going on if you ever want anyone else to lay eyes on your code.
• Scrunching up code like if(i==0&&DIM==d im)for(j=0;j<10 0;j++)M[j]=100; makes it hard to read.
• Use const wherever you don't expect a variable to be changed, this is to prevent accidentally changing it and to enable some compiler optimizations: float DET(const float A[100][100], const int dim)
• Using static variables in a recursively called function is arcane. Rather than using static variables, why not pass the variables to each new function call, in this case, pass det and DIM as arguments to the function DET(), the first call to DET will be called with arguments det=0 and DIM=dim.
• You don't need a special case for dim==2; you can do a cofactor expansion on a 2x2 matrix as well, the minors in this case are just rank 1 matrices (i.e. numbers).

[newb16]

Why is det int while A is float?

[curiously enough]

Since there is probably an arithmetic error in your code, why not get the function DET to print out the matrix that it is given in a nice tabular form, as well as the cofactor so that you can check that everything is working as expected and you are getting the correct cofactor and associated minor?

Some general suggestions:

• The return type of main is int, not void.
• Use more intuitive variable names, if i represents a column, call it col.
• Use brief comments to explain what's going on if you ever want anyone else to lay eyes on your code.
• Scrunching up code like if(i==0&&DIM==d im)for(j=0;j<10 0;j++)M[j]=100; makes it hard to read.
• Use const wherever you don't expect a variable to be changed, this is to prevent accidentally changing it and to enable some compiler optimizations: float DET(const float A[100][100], const int dim)
• Using static variables in a recursively called function is arcane. Rather than using static variables, why not pass the variables to each new function call, in this case, pass det and DIM as arguments to the function DET(), the first call to DET will be called with arguments det=0 and DIM=dim.
• You don't need a special case for dim==2; you can do a cofactor expansion on a 2x2 matrix as well, the minors in this case are just rank 1 matrices (i.e. numbers).

Thanks for your first advice, I printed all the minors like you said but still can't figure out what's wrong, and sorry if the randomly chosen variable names cuased you a headache, so if there is something unclear to you I will clear it up. Here's the program:

#include<stdio.h>
#include<conio.h>
#include<math.h>
int M[100];
float DET(float A[][100],int dim)
{
int i=100,j,k,l,m;
static float det=0;
static int DIM=dim;
if(dim>2)
    for(i=0;i<DIM;i++)
    {
    if(i==0&&DIM==dim)for(j=0;j<100;j++)M[j]=100;
    for(j=DIM-1;j>=2;j--)
    if(M[j]==i)continue;
       /*here printing starts*/
                  for(k=0;k<dim;k++)
                  {
               printf("\n");
                  for(j=0;j<DIM;j++)
        {
        m=0;
        for(l=DIM-1;l>=dim;l--)
        if(j!=M[l])m++;
        if(m==DIM-dim)printf("%0.0f   ",A[k][j]);
        }
                           }
                  printf("\n\n");
                /*here printing ends*/
    M[dim-1]=i;
    det+=pow(-1,i+dim-1)*A[dim-1][i]*DET(A,dim-1);
    }
    if(i==DIM-1)M[dim-1]=100;
if(dim==2)
 {
      /*here printing starts*/
       for(k=0;k<dim;k++)
       {
                    printf("\n");
                       for(j=0;j<DIM;j++)
        {
        m=0;
        for(l=DIM-1;l>=dim;l--)
        if(j!=M[l])m++;
        if(m==DIM-dim)printf("%0.0f   ",A[k][j]);
        }
               }
               printf("\n\n");
      /*here printing ends*/
    for(i=0;i<DIM;i++)
    {
    k=0;
      for(j=DIM-1;j>=2;j--)
    if(i!=M[j])k++;
    if(k==DIM-2)break;
    }
    for(j=0;j<DIM;j++)
    {
    k=0;
    for(l=DIM-1;l>=2;l--)
    if(j!=M[l])k++;
    if(k==DIM-2&&j!=i)break;
    }
    return(A[0][i]*A[1][j]-A[0][j]*A[1][i]);
 }
if(dim==1)return(A[0][0]);
return(det);
}
 
 
void main()
{
float A[100][100];
int n,k,l;
puts("Input size of square matrix:");
scanf("%d",&n);
puts("Input square matrix:");
for(k=0;k<n;k++)
{
printf("\n");
for(l=0;l<n;l++)
{
printf("Input a%d%d: ",k+1,l+1);
scanf("%f",&A[k][l]);
}
}
printf("\n\nThe determenant of the matrix is %0.2f",DET(A,n));
getch();
}
 

[arnaudk]

So... were the minors displayed correct or not? For example, run your program on this invertible matrix and check the minors and cofactors are correct and have the right sign

.
   (1 2 3 4)
det(1 2 1 1) = -12
   (1 1 2 1)
   (5 6 7 8)
 

and [code]...[/code] tags are good. Please use them.

[JosAH]

So... were the minors displayed were correct or not? For example, run your program on this invertible matrix and check the minors and cofactors are correct and have the right sign

.
   (1 2 3 4)
det(1 2 1 1) = -12
   (1 1 2 1)
   (5 6 7 8)
 

and [code]...[/code] tags are good. Please use them.

Yup correct (using my LUP function) ;-)

kind regards,

Jos