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version 1.7, 2010/12/21 13:53:35 version 1.8, 2011/11/21 20:43:01
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   *> \brief \b DPBSTF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DPBSTF + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbstf.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbstf.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbstf.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, KD, LDAB, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AB( LDAB, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DPBSTF computes a split Cholesky factorization of a real
   *> symmetric positive definite band matrix A.
   *>
   *> This routine is designed to be used in conjunction with DSBGST.
   *>
   *> The factorization has the form  A = S**T*S  where S is a band matrix
   *> of the same bandwidth as A and the following structure:
   *>
   *>   S = ( U    )
   *>       ( M  L )
   *>
   *> where U is upper triangular of order m = (n+kd)/2, and L is lower
   *> triangular of order n-m.
   *> \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] KD
   *> \verbatim
   *>          KD is INTEGER
   *>          The number of superdiagonals of the matrix A if UPLO = 'U',
   *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
   *>          On entry, the upper or lower triangle of the symmetric band
   *>          matrix A, stored in the first kd+1 rows of the array.  The
   *>          j-th column of A is stored in the j-th column of the array AB
   *>          as follows:
   *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
   *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
   *>
   *>          On exit, if INFO = 0, the factor S from the split Cholesky
   *>          factorization A = S**T*S. See Further Details.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KD+1.
   *> \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, the factorization could not be completed,
   *>               because the updated element a(i,i) was negative; the
   *>               matrix A is not positive definite.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  The band storage scheme is illustrated by the following example, when
   *>  N = 7, KD = 2:
   *>
   *>  S = ( s11  s12  s13                     )
   *>      (      s22  s23  s24                )
   *>      (           s33  s34                )
   *>      (                s44                )
   *>      (           s53  s54  s55           )
   *>      (                s64  s65  s66      )
   *>      (                     s75  s76  s77 )
   *>
   *>  If UPLO = 'U', the array AB holds:
   *>
   *>  on entry:                          on exit:
   *>
   *>   *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53  s64  s75
   *>   *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54  s65  s76
   *>  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
   *>
   *>  If UPLO = 'L', the array AB holds:
   *>
   *>  on entry:                          on exit:
   *>
   *>  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
   *>  a21  a32  a43  a54  a65  a76   *   s12  s23  s34  s54  s65  s76   *
   *>  a31  a42  a53  a64  a64   *    *   s13  s24  s53  s64  s75   *    *
   *>
   *>  Array elements marked * are not used by the routine.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO )        SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- 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..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       DOUBLE PRECISION   AB( LDAB, * )        DOUBLE PRECISION   AB( LDAB, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DPBSTF computes a split Cholesky factorization of a real  
 *  symmetric positive definite band matrix A.  
 *  
 *  This routine is designed to be used in conjunction with DSBGST.  
 *  
 *  The factorization has the form  A = S**T*S  where S is a band matrix  
 *  of the same bandwidth as A and the following structure:  
 *  
 *    S = ( U    )  
 *        ( M  L )  
 *  
 *  where U is upper triangular of order m = (n+kd)/2, and L is lower  
 *  triangular of order n-m.  
 *  
 *  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.  
 *  
 *  KD      (input) INTEGER  
 *          The number of superdiagonals of the matrix A if UPLO = 'U',  
 *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.  
 *  
 *  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)  
 *          On entry, the upper or lower triangle of the symmetric band  
 *          matrix A, stored in the first kd+1 rows of the array.  The  
 *          j-th column of A is stored in the j-th column of the array AB  
 *          as follows:  
 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;  
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).  
 *  
 *          On exit, if INFO = 0, the factor S from the split Cholesky  
 *          factorization A = S**T*S. See Further Details.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KD+1.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit  
 *          < 0: if INFO = -i, the i-th argument had an illegal value  
 *          > 0: if INFO = i, the factorization could not be completed,  
 *               because the updated element a(i,i) was negative; the  
 *               matrix A is not positive definite.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  The band storage scheme is illustrated by the following example, when  
 *  N = 7, KD = 2:  
 *  
 *  S = ( s11  s12  s13                     )  
 *      (      s22  s23  s24                )  
 *      (           s33  s34                )  
 *      (                s44                )  
 *      (           s53  s54  s55           )  
 *      (                s64  s65  s66      )  
 *      (                     s75  s76  s77 )  
 *  
 *  If UPLO = 'U', the array AB holds:  
 *  
 *  on entry:                          on exit:  
 *  
 *   *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53  s64  s75  
 *   *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54  s65  s76  
 *  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77  
 *  
 *  If UPLO = 'L', the array AB holds:  
 *  
 *  on entry:                          on exit:  
 *  
 *  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77  
 *  a21  a32  a43  a54  a65  a76   *   s12  s23  s34  s54  s65  s76   *  
 *  a31  a42  a53  a64  a64   *    *   s13  s24  s53  s64  s75   *    *  
 *  
 *  Array elements marked * are not used by the routine.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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