cptts2.f

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*> \brief \b CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
* 
*       .. Scalar Arguments ..
*       INTEGER            IUPLO, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       REAL               D( * )
*       COMPLEX            B( LDB, * ), E( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CPTTS2 solves a tridiagonal system of the form
*>    A * X = B
*> using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] IUPLO
*> \verbatim
*>          IUPLO is INTEGER
*>          Specifies the form of the factorization and whether the
*>          vector E is the superdiagonal of the upper bidiagonal factor
*>          U or the subdiagonal of the lower bidiagonal factor L.
*>          = 1:  A = U**H *D*U, E is the superdiagonal of U
*>          = 0:  A = L*D*L**H, E is the subdiagonal of L
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the tridiagonal 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] D
*> \verbatim
*>          D is REAL array, dimension (N)
*>          The n diagonal elements of the diagonal matrix D from the
*>          factorization A = U**H *D*U or A = L*D*L**H.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is COMPLEX array, dimension (N-1)
*>          If IUPLO = 1, the (n-1) superdiagonal elements of the unit
*>          bidiagonal factor U from the factorization A = U**H*D*U.
*>          If IUPLO = 0, the (n-1) subdiagonal elements of the unit
*>          bidiagonal factor L from the factorization A = L*D*L**H.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX array, dimension (LDB,NRHS)
*>          On entry, the right hand side vectors B for the system of
*>          linear equations.
*>          On exit, the solution vectors, X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date June 2016
*
*> \ingroup complexPTcomputational
*
*  =====================================================================
      SUBROUTINE cptts2( IUPLO, N, NRHS, D, E, B, LDB )
*
*  -- LAPACK computational routine (version 3.6.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      INTEGER            IUPLO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      REAL               D( * )
      COMPLEX            B( ldb, * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            I, J
*     ..
*     .. External Subroutines ..
      EXTERNAL           csscal
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          conjg
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.LE.1 ) THEN
         IF( n.EQ.1 )
     $      CALL csscal( nrhs, 1. / d( 1 ), b, ldb )
         RETURN
      END IF
*
      IF( iuplo.EQ.1 ) THEN
*
*        Solve A * X = B using the factorization A = U**H *D*U,
*        overwriting each right hand side vector with its solution.
*
         IF( nrhs.LE.2 ) THEN
            j = 1
    5       CONTINUE
*
*           Solve U**H * x = b.
*
            DO 10 i = 2, n
               b( i, j ) = b( i, j ) - b( i-1, j )*conjg( e( i-1 ) )
   10       CONTINUE
*
*           Solve D * U * x = b.
*
            DO 20 i = 1, n
               b( i, j ) = b( i, j ) / d( i )
   20       CONTINUE
            DO 30 i = n - 1, 1, -1
               b( i, j ) = b( i, j ) - b( i+1, j )*e( i )
   30       CONTINUE
            IF( j.LT.nrhs ) THEN
               j = j + 1
               GO TO 5
            END IF
         ELSE
            DO 60 j = 1, nrhs
*
*              Solve U**H * x = b.
*
               DO 40 i = 2, n
                  b( i, j ) = b( i, j ) - b( i-1, j )*conjg( e( i-1 ) )
   40          CONTINUE
*
*              Solve D * U * x = b.
*
               b( n, j ) = b( n, j ) / d( n )
               DO 50 i = n - 1, 1, -1
                  b( i, j ) = b( i, j ) / d( i ) - b( i+1, j )*e( i )
   50          CONTINUE
   60       CONTINUE
         END IF
      ELSE
*
*        Solve A * X = B using the factorization A = L*D*L**H,
*        overwriting each right hand side vector with its solution.
*
         IF( nrhs.LE.2 ) THEN
            j = 1
   65       CONTINUE
*
*           Solve L * x = b.
*
            DO 70 i = 2, n
               b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
   70       CONTINUE
*
*           Solve D * L**H * x = b.
*
            DO 80 i = 1, n
               b( i, j ) = b( i, j ) / d( i )
   80       CONTINUE
            DO 90 i = n - 1, 1, -1
               b( i, j ) = b( i, j ) - b( i+1, j )*conjg( e( i ) )
   90       CONTINUE
            IF( j.LT.nrhs ) THEN
               j = j + 1
               GO TO 65
            END IF
         ELSE
            DO 120 j = 1, nrhs
*
*              Solve L * x = b.
*
               DO 100 i = 2, n
                  b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
  100          CONTINUE
*
*              Solve D * L**H * x = b.
*
               b( n, j ) = b( n, j ) / d( n )
               DO 110 i = n - 1, 1, -1
                  b( i, j ) = b( i, j ) / d( i ) -
     $                        b( i+1, j )*conjg( e( i ) )
  110          CONTINUE
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of CPTTS2
*
      END