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version 1.6, 2010/08/13 21:03:56 version 1.18, 2023/08/07 08:39:05
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   *> \brief \b DPTEQR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DPTEQR + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpteqr.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpteqr.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpteqr.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          COMPZ
   *       INTEGER            INFO, LDZ, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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.)
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] COMPZ
   *> \verbatim
   *>          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.
   *> \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 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.
   *> \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.
   *
   *> \ingroup doublePTcomputational
   *
   *  =====================================================================
       SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )        SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          COMPZ        CHARACTER          COMPZ
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       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )        DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  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.)  
 *  
 *  Arguments  
 *  =========  
 *  
 *  COMPZ   (input) 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       (input) INTEGER  
 *          The order of the matrix.  N >= 0.  
 *  
 *  D       (input/output) 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       (input/output) DOUBLE PRECISION array, dimension (N-1)  
 *          On entry, the (n-1) subdiagonal elements of the tridiagonal  
 *          matrix.  
 *          On exit, E has been destroyed.  
 *  
 *  Z       (input/output) 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     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1, and if  
 *          COMPZ = 'V' or 'I', LDZ >= max(1,N).  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (4*N)  
 *  
 *  INFO    (output) 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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.6  
changed lines
  Added in v.1.18

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