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version 1.2, 2010/04/21 13:45:38 version 1.18, 2023/08/07 08:39:37
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   *> \brief \b ZSPTRI
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZSPTRI + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptri.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsptri.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsptri.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       COMPLEX*16         AP( * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZSPTRI computes the inverse of a complex symmetric indefinite matrix
   *> A in packed storage using the factorization A = U*D*U**T or
   *> A = L*D*L**T computed by ZSPTRF.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          Specifies whether the details of the factorization are stored
   *>          as an upper or lower triangular matrix.
   *>          = 'U':  Upper triangular, form is A = U*D*U**T;
   *>          = 'L':  Lower triangular, form is A = L*D*L**T.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] AP
   *> \verbatim
   *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
   *>          On entry, the block diagonal matrix D and the multipliers
   *>          used to obtain the factor U or L as computed by ZSPTRF,
   *>          stored as a packed triangular matrix.
   *>
   *>          On exit, if INFO = 0, the (symmetric) inverse of the original
   *>          matrix, stored as a packed triangular matrix. The j-th column
   *>          of inv(A) is stored in the array AP as follows:
   *>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
   *>          if UPLO = 'L',
   *>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
   *> \endverbatim
   *>
   *> \param[in] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>          Details of the interchanges and the block structure of D
   *>          as determined by ZSPTRF.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 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
   *>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
   *>               inverse could not be computed.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16OTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )        SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, 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          UPLO        CHARACTER          UPLO
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       COMPLEX*16         AP( * ), WORK( * )        COMPLEX*16         AP( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZSPTRI computes the inverse of a complex symmetric indefinite matrix  
 *  A in packed storage using the factorization A = U*D*U**T or  
 *  A = L*D*L**T computed by ZSPTRF.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          Specifies whether the details of the factorization are stored  
 *          as an upper or lower triangular matrix.  
 *          = 'U':  Upper triangular, form is A = U*D*U**T;  
 *          = 'L':  Lower triangular, form is A = L*D*L**T.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)  
 *          On entry, the block diagonal matrix D and the multipliers  
 *          used to obtain the factor U or L as computed by ZSPTRF,  
 *          stored as a packed triangular matrix.  
 *  
 *          On exit, if INFO = 0, the (symmetric) inverse of the original  
 *          matrix, stored as a packed triangular matrix. The j-th column  
 *          of inv(A) is stored in the array AP as follows:  
 *          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;  
 *          if UPLO = 'L',  
 *             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.  
 *  
 *  IPIV    (input) INTEGER array, dimension (N)  
 *          Details of the interchanges and the block structure of D  
 *          as determined by ZSPTRF.  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit  
 *          < 0: if INFO = -i, the i-th argument had an illegal value  
 *          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its  
 *               inverse could not be computed.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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 *  *
       IF( UPPER ) THEN        IF( UPPER ) THEN
 *  *
 *        Compute inv(A) from the factorization A = U*D*U'.  *        Compute inv(A) from the factorization A = U*D*U**T.
 *  *
 *        K is the main loop index, increasing from 1 to N in steps of  *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.  *        1 or 2, depending on the size of the diagonal blocks.
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 *  *
       ELSE        ELSE
 *  *
 *        Compute inv(A) from the factorization A = L*D*L'.  *        Compute inv(A) from the factorization A = L*D*L**T.
 *  *
 *        K is the main loop index, increasing from 1 to N in steps of  *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.  *        1 or 2, depending on the size of the diagonal blocks.
Removed from v.1.2  
changed lines
  Added in v.1.18

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