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version 1.5, 2010/08/07 13:22:43 version 1.19, 2023/08/07 08:39:35
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   *> \brief \b ZPTCON
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZPTCON + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptcon.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zptcon.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zptcon.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, N
   *       DOUBLE PRECISION   ANORM, RCOND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   D( * ), RWORK( * )
   *       COMPLEX*16         E( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZPTCON computes the reciprocal of the condition number (in the
   *> 1-norm) of a complex Hermitian positive definite tridiagonal matrix
   *> using the factorization A = L*D*L**H or A = U**H*D*U computed by
   *> ZPTTRF.
   *>
   *> Norm(inv(A)) is computed by a direct method, and the reciprocal of
   *> the condition number is computed as
   *>                  RCOND = 1 / (ANORM * norm(inv(A))).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          The n diagonal elements of the diagonal matrix D from the
   *>          factorization of A, as computed by ZPTTRF.
   *> \endverbatim
   *>
   *> \param[in] E
   *> \verbatim
   *>          E is COMPLEX*16 array, dimension (N-1)
   *>          The (n-1) off-diagonal elements of the unit bidiagonal factor
   *>          U or L from the factorization of A, as computed by ZPTTRF.
   *> \endverbatim
   *>
   *> \param[in] ANORM
   *> \verbatim
   *>          ANORM is DOUBLE PRECISION
   *>          The 1-norm of the original matrix A.
   *> \endverbatim
   *>
   *> \param[out] RCOND
   *> \verbatim
   *>          RCOND is DOUBLE PRECISION
   *>          The reciprocal of the condition number of the matrix A,
   *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
   *>          1-norm of inv(A) computed in this routine.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16PTcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  The method used is described in Nicholas J. Higham, "Efficient
   *>  Algorithms for Computing the Condition Number of a Tridiagonal
   *>  Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )        SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, 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 ..
       INTEGER            INFO, N        INTEGER            INFO, N
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       COMPLEX*16         E( * )        COMPLEX*16         E( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZPTCON computes the reciprocal of the condition number (in the  
 *  1-norm) of a complex Hermitian positive definite tridiagonal matrix  
 *  using the factorization A = L*D*L**H or A = U**H*D*U computed by  
 *  ZPTTRF.  
 *  
 *  Norm(inv(A)) is computed by a direct method, and the reciprocal of  
 *  the condition number is computed as  
 *                   RCOND = 1 / (ANORM * norm(inv(A))).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (N)  
 *          The n diagonal elements of the diagonal matrix D from the  
 *          factorization of A, as computed by ZPTTRF.  
 *  
 *  E       (input) COMPLEX*16 array, dimension (N-1)  
 *          The (n-1) off-diagonal elements of the unit bidiagonal factor  
 *          U or L from the factorization of A, as computed by ZPTTRF.  
 *  
 *  ANORM   (input) DOUBLE PRECISION  
 *          The 1-norm of the original matrix A.  
 *  
 *  RCOND   (output) DOUBLE PRECISION  
 *          The reciprocal of the condition number of the matrix A,  
 *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the  
 *          1-norm of inv(A) computed in this routine.  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  The method used is described in Nicholas J. Higham, "Efficient  
 *  Algorithms for Computing the Condition Number of a Tridiagonal  
 *  Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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 *        m(i,j) =  abs(A(i,j)), i = j,  *        m(i,j) =  abs(A(i,j)), i = j,
 *        m(i,j) = -abs(A(i,j)), i .ne. j,  *        m(i,j) = -abs(A(i,j)), i .ne. j,
 *  *
 *     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.  *     and e = [ 1, 1, ..., 1 ]**T.  Note M(A) = M(L)*D*M(L)**H.
 *  *
 *     Solve M(L) * x = e.  *     Solve M(L) * x = e.
 *  *
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          RWORK( I ) = ONE + RWORK( I-1 )*ABS( E( I-1 ) )           RWORK( I ) = ONE + RWORK( I-1 )*ABS( E( I-1 ) )
    20 CONTINUE     20 CONTINUE
 *  *
 *     Solve D * M(L)' * x = b.  *     Solve D * M(L)**H * x = b.
 *  *
       RWORK( N ) = RWORK( N ) / D( N )        RWORK( N ) = RWORK( N ) / D( N )
       DO 30 I = N - 1, 1, -1        DO 30 I = N - 1, 1, -1
Removed from v.1.5  
changed lines
  Added in v.1.19

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