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cpteqr.f(3)				      LAPACK				      cpteqr.f(3)

NAME
       cpteqr.f -

SYNOPSIS
   Functions/Subroutines
       subroutine cpteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO)
	   CPTEQR

Function/Subroutine Documentation
   subroutine cpteqr (characterCOMPZ, integerN, real, dimension( * )D, real, dimension( * )E,
       complex, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerINFO)
       CPTEQR

       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:
	   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.

	   N

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

	   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.

	   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.

	   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.

	   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 REAL 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 i-th principal minor
				 was not positive definite.
			   > 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.

       Date:
	   September 2012

       Definition at line 146 of file cpteqr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      cpteqr.f(3)
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