Toeplitz Matrix (diagonal-constant matrix)

Newbie
,
1

Hello all,

I want to create a Toeplitz matrix which I need to invert. Do anyone know a good way to create one? The way I have take way too many steps.

Int_t n = 3; // n x n matrix
Double_t a[] = {1,2,3};
TVectorD aa;
aa.Use(n,a); 

TMatrixD A(n,n);
TMatrixDRow(A,0) = aa;

//here is a for to reallocate the elements and fill the matrix 
for(Int_t i = 1; i<n; i++){ // this for to fill the matrix
  Double_t temp = aa[0];
  aa[0] = aa[n-1];
  for(Int_t j = 1; j<n;j++){
    Double_t temp2 = aa[j];
    aa[j] = temp; 
    temp = temp2; 
  }
  TMatrixDRow(A,i) = aa;
 }
for(Int_t i = 0; i<n; i++){
  for(Int_t j = 0; j<n; j++){
    cout << A[i][j] << " ";
  }
  cout << "\n";
}

OBS.: The application is for Wiener Filter :slight_smile:

Cheers,
Henrique

ROOT Version: 6.26/02
Platform: Ubuntu 21.10 impish (x86-64)
Compiler: (gcc/g++ 11.2.0)

2

I guess you should just follow the definition of such matrix.

3

Sorry, I didn’t follow you. I am using the definition of the matrix there. It is just that root does not accept negative values, so I though it would be easy this way.

4

Ak ok… sorry. @moneta oneta may have an idea in that case.

5

Hi Henrique,

Not sure what you expect because what you wrote is already quite compact.
The swapping could be done in one line :

void toeplitz()
{
  Int_t n = 3; // n x n matrix
  Double_t a[] = {1,-2,3};
  TVectorD aa;
  aa.Use(n,a);

  TMatrixD A(n,n);
  TMatrixDRow(A,0) = aa;

  //here is a for to reallocate the elements and fill the matrix 
  for(Int_t i = 1; i<n; i++){ // this for to fill the matrix
    Double_t temp = aa[0];
    aa[0] = aa[n-1];
    for(Int_t j = 1; j<n;j++)
      std::swap(aa[j],temp);
    TMatrixDRow(A,i) = aa;
  }

  A.Print();
}

or are you looking for something more “elegant” ? It could be done with TMatrixDDiag and TMatrixDSub but it will not be shorter .

-Eddy

6

Hi @Eddy_Offermann,

Thanks a lot for the reply. I liked the std::swap method there.
I was wondering if there was any function member of TMatrixD that could do it :slight_smile:
I’ve stepped into a solution for M x M matrices:

Int_t M = 3; // M x M matrix
Double_t a[] = {1,-2,3};
TMatrixD A(M,M);

for (int i=0; i<M; i++)
  {
  	for (int j=0; j<M; j++)
  	{
  		A[i][j] = aa[abs(i-j)];
  	}
  }

Thanks again.

Cheers,
Henrique

7

Just for the record, your code examples do create Toeplitz matrices but very specific ones, where the last one is symmetric and the first one permutates the off-diagonal values.

Any Toeplitz can be written by the following code (Notice the upper and lower boundary of the TVectorD:

 Int_t M = 3; // M x M matrix
 TMatrixD A(M,M);
 Double_t a[] = {1,2,3,4,5};

 TVectorD aa(-M+1,M-1);
 aa.Use(-M+1,M-1,a);

 for (int i=0; i<M; i++)
 {
   for (int j=0; j<M; j++)
   {
     A[i][j] = aa[j-i];
   }
 }