Nonsymmetric Eigenvalue Problem

Nonsymmetric Eigenvalue Problem

Hello all!

Eigenvalues that I obtained all come right, but eigenvectors turned out to be just zeros. Could you please help me to solve this problem (to determine eigenvectors).

  int n = 3;
 
  myComplex *A = new myComplex[n*n];
  for(int i = 0; i < n; i++)
    for(int j = 0; j < n; j++)
      A[i+j*n] = zeroC;
 
  real(A[0]) = 1.; real(A[1]) = 6.; real(A[2]) = -1.;
  real(A[3]) = 2.; real(A[4]) = -1; real(A[5]) = -2.;
  real(A[6]) = 1.; real(A[7]) = 0.; real(A[8]) = -1.;
 
  myComplex *w = new myComplex[n];
  for(int i = 0; i < n; i++)
    w[i] = zeroC;
 
  myComplex *vr = new myComplex[n*n];
  for(int i = 0; i < n; i++)
    for(int j = 0; j < n; j++)
      vr[i+j*n] = zeroC;

  int ilo = 1;
  int ihi = n;
  int lda = std::max(1,n);
  myComplex* tau = new myComplex[std::max(1,n-1)];
  myComplex* work = new myComplex[std::max(1,n*n)];
  int lwork = std::max(1,n);
  int info;
 
  ZGEHRD(
         &n,
         &ilo,
         &ihi,
         (MKL_Complex16*)A,
         &lda,
         (MKL_Complex16*)(&tau[0]),
         (MKL_Complex16*)(&work[0]),
         &lwork,
         &info
        );
 
  myComplex *ACopy = new myComplex[n*n];
  for(int i = 0; i < n; i++)
    for(int j = 0; j < n; j++)
      ACopy[i+j*n] = A[i+j*n];
 
  const char job = 'S';
  const char compz = 'V';
  int ldh = std::max(1,n);
  int ldz = std::max(1,n);
 
  ZHSEQR(
         &job,
         &compz,
         &n,
         &ilo,
         &ihi,
         (MKL_Complex16*)A,
         &ldh,
         (MKL_Complex16*)(&w[0]),
         (MKL_Complex16*)ACopy,
         &ldz,
         (MKL_Complex16*)(&work[0]),
         &lwork,
         &info
        );
 
  const char side = 'R';
  const char howmny = 'S';
  int* select = new int[std::max(1,n)];
  int ldt = std::max(1,n);
  int ldvl = 1;
  int ldvr = n;
  int m = n;
  int mm = m;
  double* rwork = new double[std::max(1,n)];
 
  ZTREVC(
         &side,
         &howmny,
         select,
         &n,
         (MKL_Complex16*)A,
         &ldt,
         (MKL_Complex16*)&zeroC,
         &ldvl,
         (MKL_Complex16*)(&vr[0]),
         &ldvr,
         &mm,
         &m,
         (MKL_Complex16*)(&work[0]),
         &rwork[0],
         &info
        );

  std::cout << "\nEigenvalues: ";
  for(int i = 0; i < n; i++)
    std::cout << "\n" << w[i];
 
  std::cout << "\nEigenvectors: ";
  for(int j = 0; j < n; j++)
    for(int i = 0; i < n; i++)
      std::cout << "\n" << vr[i+j*n];
 
  delete[] A; delete[] w; delete[] vr;

  delete[] ACopy;
  delete[] tau;
  delete[] work;
  delete[] select;

Thanks a lot in advance!

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