dpteqr.f3

!>
!> DPTEQR computes all eigenvalues and, optionally, eigenvectors of a
!> symmetric positive definite tridiagonal matrix by first factoring the
!> matrix using DPTTRF, and then calling DBDSQR to compute the singular
!> values of the bidiagonal factor.
!>
!> This routine computes the eigenvalues of the positive definite
!> tridiagonal matrix to high relative accuracy.  This means that if the
!> eigenvalues range over many orders of magnitude in size, then the
!> small eigenvalues and corresponding eigenvectors will be computed
!> more accurately than, for example, with the standard QR method.
!>
!> The eigenvectors of a full or band symmetric positive definite matrix
!> can also be found if DSYTRD, DSPTRD, or DSBTRD has been used to
!> reduce this matrix to tridiagonal form. (The reduction to tridiagonal
!> form, however, may preclude the possibility of obtaining high
!> relative accuracy in the small eigenvalues of the original matrix, if
!> these eigenvalues range over many orders of magnitude.)
!> 

COMPZ

!>          COMPZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only.
!>          = 'V':  Compute eigenvectors of original symmetric
!>                  matrix also.  Array Z contains the orthogonal
!>                  matrix used to reduce the original matrix to
!>                  tridiagonal form.
!>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
!> 

N

!>          N is INTEGER
!>          The order of the matrix.  N >= 0.
!> 

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal
!>          matrix.
!>          On normal exit, D contains the eigenvalues, in descending
!>          order.
!> 

E

!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix.
!>          On exit, E has been destroyed.
!> 

Z

!>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
!>          On entry, if COMPZ = 'V', the orthogonal matrix used in the
!>          reduction to tridiagonal form.
!>          On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
!>          original symmetric matrix;
!>          if COMPZ = 'I', the orthonormal eigenvectors of the
!>          tridiagonal matrix.
!>          If INFO > 0 on exit, Z contains the eigenvectors associated
!>          with only the stored eigenvalues.
!>          If  COMPZ = 'N', then Z is not referenced.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z.  LDZ >= 1, and if
!>          COMPZ = 'V' or 'I', LDZ >= max(1,N).
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (4*N)
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, and i is:
!>                <= N  the Cholesky factorization of the matrix could
!>                      not be performed because the leading principal
!>                      minor of order i was not positive.
!>                > N   the SVD algorithm failed to converge;
!>                      if INFO = N+i, i off-diagonal elements of the
!>                      bidiagonal factor did not converge to zero.
!> 

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