zgbtrs.f

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*> \brief \b ZGBTRS
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
*                          INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANS
*       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZGBTRS solves a system of linear equations
*>    A * X = B,  A**T * X = B,  or  A**H * X = B
*> with a general band matrix A using the LU factorization computed
*> by ZGBTRF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Specifies the form of the system of equations.
*>          = 'N':  A * X = B     (No transpose)
*>          = 'T':  A**T * X = B  (Transpose)
*>          = 'C':  A**H * X = B  (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*>          KL is INTEGER
*>          The number of subdiagonals within the band of A.  KL >= 0.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*>          KU is INTEGER
*>          The number of superdiagonals within the band of A.  KU >= 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] AB
*> \verbatim
*>          AB is COMPLEX*16 array, dimension (LDAB,N)
*>          Details of the LU factorization of the band matrix A, as
*>          computed by ZGBTRF.  U is stored as an upper triangular band
*>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
*>          the multipliers used during the factorization are stored in
*>          rows KL+KU+2 to 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*>          LDAB is INTEGER
*>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          The pivot indices; for 1 <= i <= N, row i of the matrix was
*>          interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
*>          On entry, the right hand side matrix B.
*>          On exit, the 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
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gbtrs
*
*  =====================================================================
      SUBROUTINE zgbtrs( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B,
     $                   LDB,
     $                   INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         AB( LDAB, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER          ( ONE = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            LNOTI, NOTRAN
      INTEGER            I, J, KD, L, LM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zgemv, zgeru, zlacgv, zswap,
     $                   ztbsv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      notran = lsame( trans, 'N' )
      IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
     $    lsame( trans, 'C' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( kl.LT.0 ) THEN
         info = -3
      ELSE IF( ku.LT.0 ) THEN
         info = -4
      ELSE IF( nrhs.LT.0 ) THEN
         info = -5
      ELSE IF( ldab.LT.( 2*kl+ku+1 ) ) THEN
         info = -7
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZGBTRS', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 )
     $   RETURN
*
      kd = ku + kl + 1
      lnoti = kl.GT.0
*
      IF( notran ) THEN
*
*        Solve  A*X = B.
*
*        Solve L*X = B, overwriting B with X.
*
*        L is represented as a product of permutations and unit lower
*        triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
*        where each transformation L(i) is a rank-one modification of
*        the identity matrix.
*
         IF( lnoti ) THEN
            DO 10 j = 1, n - 1
               lm = min( kl, n-j )
               l = ipiv( j )
               IF( l.NE.j )
     $            CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
               CALL zgeru( lm, nrhs, -one, ab( kd+1, j ), 1, b( j,
     $                     1 ),
     $                     ldb, b( j+1, 1 ), ldb )
   10       CONTINUE
         END IF
*
         DO 20 i = 1, nrhs
*
*           Solve U*X = B, overwriting B with X.
*
            CALL ztbsv( 'Upper', 'No transpose', 'Non-unit', n,
     $                  kl+ku,
     $                  ab, ldab, b( 1, i ), 1 )
   20    CONTINUE
*
      ELSE IF( lsame( trans, 'T' ) ) THEN
*
*        Solve A**T * X = B.
*
         DO 30 i = 1, nrhs
*
*           Solve U**T * X = B, overwriting B with X.
*
            CALL ztbsv( 'Upper', 'Transpose', 'Non-unit', n, kl+ku,
     $                  ab,
     $                  ldab, b( 1, i ), 1 )
   30    CONTINUE
*
*        Solve L**T * X = B, overwriting B with X.
*
         IF( lnoti ) THEN
            DO 40 j = n - 1, 1, -1
               lm = min( kl, n-j )
               CALL zgemv( 'Transpose', lm, nrhs, -one, b( j+1, 1 ),
     $                     ldb, ab( kd+1, j ), 1, one, b( j, 1 ), ldb )
               l = ipiv( j )
               IF( l.NE.j )
     $            CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
   40       CONTINUE
         END IF
*
      ELSE
*
*        Solve A**H * X = B.
*
         DO 50 i = 1, nrhs
*
*           Solve U**H * X = B, overwriting B with X.
*
            CALL ztbsv( 'Upper', 'Conjugate transpose', 'Non-unit',
     $                  n,
     $                  kl+ku, ab, ldab, b( 1, i ), 1 )
   50    CONTINUE
*
*        Solve L**H * X = B, overwriting B with X.
*
         IF( lnoti ) THEN
            DO 60 j = n - 1, 1, -1
               lm = min( kl, n-j )
               CALL zlacgv( nrhs, b( j, 1 ), ldb )
               CALL zgemv( 'Conjugate transpose', lm, nrhs, -one,
     $                     b( j+1, 1 ), ldb, ab( kd+1, j ), 1, one,
     $                     b( j, 1 ), ldb )
               CALL zlacgv( nrhs, b( j, 1 ), ldb )
               l = ipiv( j )
               IF( l.NE.j )
     $            CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
   60       CONTINUE
         END IF
      END IF
      RETURN
*
*     End of ZGBTRS
*
      END