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version 1.8, 2011/07/22 07:38:20 version 1.9, 2011/11/21 20:43:20
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   *> \brief \b ZSPTRF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZSPTRF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptrf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsptrf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsptrf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       COMPLEX*16         AP( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZSPTRF computes the factorization of a complex symmetric matrix A
   *> stored in packed format using the Bunch-Kaufman diagonal pivoting
   *> method:
   *>
   *>    A = U*D*U**T  or  A = L*D*L**T
   *>
   *> where U (or L) is a product of permutation and unit upper (lower)
   *> triangular matrices, and D is symmetric and block diagonal with
   *> 1-by-1 and 2-by-2 diagonal blocks.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangle of A is stored;
   *>          = 'L':  Lower triangle of A is stored.
   *> \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 upper or lower triangle of the symmetric matrix
   *>          A, packed columnwise in a linear array.  The j-th column of A
   *>          is stored in the array AP as follows:
   *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   *>
   *>          On exit, the block diagonal matrix D and the multipliers used
   *>          to obtain the factor U or L, stored as a packed triangular
   *>          matrix overwriting A (see below for further details).
   *> \endverbatim
   *>
   *> \param[out] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>          Details of the interchanges and the block structure of D.
   *>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
   *>          interchanged and D(k,k) is a 1-by-1 diagonal block.
   *>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
   *>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
   *>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
   *>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
   *>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
   *> \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) is exactly zero.  The factorization
   *>               has been completed, but the block diagonal matrix D is
   *>               exactly singular, and division by zero will occur if it
   *>               is used to solve a system of equations.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
   *>         Company
   *>
   *>  If UPLO = 'U', then A = U*D*U**T, where
   *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
   *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
   *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
   *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
   *>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
   *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
   *>
   *>             (   I    v    0   )   k-s
   *>     U(k) =  (   0    I    0   )   s
   *>             (   0    0    I   )   n-k
   *>                k-s   s   n-k
   *>
   *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
   *>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
   *>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
   *>
   *>  If UPLO = 'L', then A = L*D*L**T, where
   *>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
   *>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
   *>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
   *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
   *>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
   *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
   *>
   *>             (   I    0     0   )  k-1
   *>     L(k) =  (   0    I     0   )  s
   *>             (   0    v     I   )  n-k-s+1
   *>                k-1   s  n-k-s+1
   *>
   *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
   *>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
   *>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO )        SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
Line 14 Line 172
       COMPLEX*16         AP( * )        COMPLEX*16         AP( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZSPTRF computes the factorization of a complex symmetric matrix A  
 *  stored in packed format using the Bunch-Kaufman diagonal pivoting  
 *  method:  
 *  
 *     A = U*D*U**T  or  A = L*D*L**T  
 *  
 *  where U (or L) is a product of permutation and unit upper (lower)  
 *  triangular matrices, and D is symmetric and block diagonal with  
 *  1-by-1 and 2-by-2 diagonal blocks.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  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 upper or lower triangle of the symmetric matrix  
 *          A, packed columnwise in a linear array.  The j-th column of A  
 *          is stored in the array AP as follows:  
 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;  
 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  
 *  
 *          On exit, the block diagonal matrix D and the multipliers used  
 *          to obtain the factor U or L, stored as a packed triangular  
 *          matrix overwriting A (see below for further details).  
 *  
 *  IPIV    (output) INTEGER array, dimension (N)  
 *          Details of the interchanges and the block structure of D.  
 *          If IPIV(k) > 0, then rows and columns k and IPIV(k) were  
 *          interchanged and D(k,k) is a 1-by-1 diagonal block.  
 *          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and  
 *          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)  
 *          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =  
 *          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were  
 *          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.  
 *  
 *  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) is exactly zero.  The factorization  
 *               has been completed, but the block diagonal matrix D is  
 *               exactly singular, and division by zero will occur if it  
 *               is used to solve a system of equations.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services  
 *         Company  
 *  
 *  If UPLO = 'U', then A = U*D*U**T, where  
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,  
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to  
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1  
 *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as  
 *  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such  
 *  that if the diagonal block D(k) is of order s (s = 1 or 2), then  
 *  
 *             (   I    v    0   )   k-s  
 *     U(k) =  (   0    I    0   )   s  
 *             (   0    0    I   )   n-k  
 *                k-s   s   n-k  
 *  
 *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).  
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),  
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).  
 *  
 *  If UPLO = 'L', then A = L*D*L**T, where  
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,  
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to  
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1  
 *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as  
 *  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such  
 *  that if the diagonal block D(k) is of order s (s = 1 or 2), then  
 *  
 *             (   I    0     0   )  k-1  
 *     L(k) =  (   0    I     0   )  s  
 *             (   0    v     I   )  n-k-s+1  
 *                k-1   s  n-k-s+1  
 *  
 *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).  
 *  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),  
 *  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
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  Added in v.1.9

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