cpteqr()

subroutine cpteqr	(	character	compz,
		integer	n,
		real, dimension( * )	d,
		real, dimension( * )	e,
		complex, dimension( ldz, * )	z,
		integer	ldz,
		real, dimension( * )	work,
		integer	info )

CPTEQR

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Purpose:

!>
!> CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
!> symmetric positive definite tridiagonal matrix by first factoring the
!> matrix using SPTTRF and then calling CBDSQR 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 positive definite Hermitian matrix
!> can also be found if CHETRD, CHPTRD, or CHBTRD 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.)
!> 

Parameters

[in]	COMPZ	!> COMPZ is CHARACTER*1 !> = 'N': Compute eigenvalues only. !> = 'V': Compute eigenvectors of original Hermitian !> matrix also. Array Z contains the unitary matrix !> used to reduce the original matrix to tridiagonal !> form. !> = 'I': Compute eigenvectors of tridiagonal matrix also. !>
[in]	N	!> N is INTEGER !> The order of the matrix. N >= 0. !>
[in,out]	D	!> D is REAL array, dimension (N) !> On entry, the n diagonal elements of the tridiagonal matrix. !> On normal exit, D contains the eigenvalues, in descending !> order. !>
[in,out]	E	!> E is REAL array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix. !> On exit, E has been destroyed. !>
[in,out]	Z	!> Z is COMPLEX array, dimension (LDZ, N) !> On entry, if COMPZ = 'V', the unitary matrix used in the !> reduction to tridiagonal form. !> On exit, if COMPZ = 'V', the orthonormal eigenvectors of the !> original Hermitian 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. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> COMPZ = 'V' or 'I', LDZ >= max(1,N). !>
[out]	WORK	!> WORK is REAL array, dimension (4*N) !>
[out]	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. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.