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version 1.8, 2011/07/22 07:38:11 version 1.9, 2011/11/21 20:43:03
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   *> \brief <b> DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSPSV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspsv.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspsv.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspsv.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          UPLO
   *       INTEGER            INFO, LDB, N, NRHS
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   AP( * ), B( LDB, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSPSV computes the solution to a real system of linear equations
   *>    A * X = B,
   *> where A is an N-by-N symmetric matrix stored in packed format and X
   *> and B are N-by-NRHS matrices.
   *>
   *> The diagonal pivoting method is used to factor A as
   *>    A = U * D * U**T,  if UPLO = 'U', or
   *>    A = L * D * L**T,  if UPLO = 'L',
   *> where U (or L) is a product of permutation and unit upper (lower)
   *> triangular matrices, D is symmetric and block diagonal with 1-by-1
   *> and 2-by-2 diagonal blocks.  The factored form of A is then used to
   *> solve the system of equations A * X = B.
   *> \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 number of linear equations, i.e., the order of the
   *>          matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] NRHS
   *> \verbatim
   *>          NRHS is INTEGER
   *>          The number of right hand sides, i.e., the number of columns
   *>          of the matrix B.  NRHS >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] AP
   *> \verbatim
   *>          AP is DOUBLE PRECISION 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.
   *>          See below for further details.
   *>
   *>          On exit, the block diagonal matrix D and the multipliers used
   *>          to obtain the factor U or L from the factorization
   *>          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
   *>          a packed triangular matrix in the same storage format as A.
   *> \endverbatim
   *>
   *> \param[out] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>          Details of the interchanges and the block structure of D, as
   *>          determined by DSPTRF.  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[in,out] B
   *> \verbatim
   *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
   *>          On entry, the N-by-NRHS right hand side matrix B.
   *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of the array B.  LDB >= max(1,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) is exactly zero.  The factorization
   *>                has been completed, but the block diagonal matrix D is
   *>                exactly singular, so the solution could not be
   *>                computed.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERsolve
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  The packed storage scheme is illustrated by the following example
   *>  when N = 4, UPLO = 'U':
   *>
   *>  Two-dimensional storage of the symmetric matrix A:
   *>
   *>     a11 a12 a13 a14
   *>         a22 a23 a24
   *>             a33 a34     (aij = aji)
   *>                 a44
   *>
   *>  Packed storage of the upper triangle of A:
   *>
   *>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )        SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.3.1) --  *  -- LAPACK driver 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
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       DOUBLE PRECISION   AP( * ), B( LDB, * )        DOUBLE PRECISION   AP( * ), B( LDB, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSPSV computes the solution to a real system of linear equations  
 *     A * X = B,  
 *  where A is an N-by-N symmetric matrix stored in packed format and X  
 *  and B are N-by-NRHS matrices.  
 *  
 *  The diagonal pivoting method is used to factor A as  
 *     A = U * D * U**T,  if UPLO = 'U', or  
 *     A = L * D * L**T,  if UPLO = 'L',  
 *  where U (or L) is a product of permutation and unit upper (lower)  
 *  triangular matrices, D is symmetric and block diagonal with 1-by-1  
 *  and 2-by-2 diagonal blocks.  The factored form of A is then used to  
 *  solve the system of equations A * X = B.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The number of linear equations, i.e., the order of the  
 *          matrix A.  N >= 0.  
 *  
 *  NRHS    (input) INTEGER  
 *          The number of right hand sides, i.e., the number of columns  
 *          of the matrix B.  NRHS >= 0.  
 *  
 *  AP      (input/output) DOUBLE PRECISION 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.  
 *          See below for further details.  
 *  
 *          On exit, the block diagonal matrix D and the multipliers used  
 *          to obtain the factor U or L from the factorization  
 *          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as  
 *          a packed triangular matrix in the same storage format as A.  
 *  
 *  IPIV    (output) INTEGER array, dimension (N)  
 *          Details of the interchanges and the block structure of D, as  
 *          determined by DSPTRF.  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.  
 *  
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)  
 *          On entry, the N-by-NRHS right hand side matrix B.  
 *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= max(1,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) is exactly zero.  The factorization  
 *                has been completed, but the block diagonal matrix D is  
 *                exactly singular, so the solution could not be  
 *                computed.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  The packed storage scheme is illustrated by the following example  
 *  when N = 4, UPLO = 'U':  
 *  
 *  Two-dimensional storage of the symmetric matrix A:  
 *  
 *     a11 a12 a13 a14  
 *         a22 a23 a24  
 *             a33 a34     (aij = aji)  
 *                 a44  
 *  
 *  Packed storage of the upper triangle of A:  
 *  
 *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. External Functions ..  *     .. External Functions ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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