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*> \brief \b ZPTEQR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZPTEQR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpteqr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpteqr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpteqr.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER COMPZ
* INTEGER INFO, LDZ, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * ), E( * ), WORK( * )
* COMPLEX*16 Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a
*> symmetric positive definite tridiagonal matrix by first factoring the
*> matrix using DPTTRF and then calling ZBDSQR 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 ZHETRD, ZHPTRD, or ZHBTRD 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.)
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] COMPZ
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix. N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*> Z is COMPLEX*16 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.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. LDZ >= 1, and if
*> COMPZ = 'V' or 'I', LDZ >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (4*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16PTcomputational
*
* =====================================================================
SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER COMPZ
INTEGER INFO, LDZ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * ), E( * ), WORK( * )
COMPLEX*16 Z( LDZ, * )
* ..
*
* ====================================================================
*
* .. Parameters ..
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DPTTRF, XERBLA, ZBDSQR, ZLASET
* ..
* .. Local Arrays ..
COMPLEX*16 C( 1, 1 ), VT( 1, 1 )
* ..
* .. Local Scalars ..
INTEGER I, ICOMPZ, NRU
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
*
IF( LSAME( COMPZ, 'N' ) ) THEN
ICOMPZ = 0
ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
ICOMPZ = 1
ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
ICOMPZ = 2
ELSE
ICOMPZ = -1
END IF
IF( ICOMPZ.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
$ N ) ) ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPTEQR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
IF( ICOMPZ.GT.0 )
$ Z( 1, 1 ) = CONE
RETURN
END IF
IF( ICOMPZ.EQ.2 )
$ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
*
* Call DPTTRF to factor the matrix.
*
CALL DPTTRF( N, D, E, INFO )
IF( INFO.NE.0 )
$ RETURN
DO 10 I = 1, N
D( I ) = SQRT( D( I ) )
10 CONTINUE
DO 20 I = 1, N - 1
E( I ) = E( I )*D( I )
20 CONTINUE
*
* Call ZBDSQR to compute the singular values/vectors of the
* bidiagonal factor.
*
IF( ICOMPZ.GT.0 ) THEN
NRU = N
ELSE
NRU = 0
END IF
CALL ZBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
$ WORK, INFO )
*
* Square the singular values.
*
IF( INFO.EQ.0 ) THEN
DO 30 I = 1, N
D( I ) = D( I )*D( I )
30 CONTINUE
ELSE
INFO = N + INFO
END IF
*
RETURN
*
* End of ZPTEQR
*
END
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