cgttrs.f

Go to the documentation of this file.

*> \brief \b CGTTRS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> Download CGTTRS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgttrs.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgttrs.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgttrs.f">
*> [TXT]</a>
*
*  Definition:
*  ===========
*
*       SUBROUTINE CGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
*                          INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANS
*       INTEGER            INFO, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CGTTRS solves one of the systems of equations
*>    A * X = B,  A**T * X = B,  or  A**H * X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by CGTTRF.
*> \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.
*> \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] DL
*> \verbatim
*>          DL is COMPLEX array, dimension (N-1)
*>          The (n-1) multipliers that define the matrix L from the
*>          LU factorization of A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is COMPLEX array, dimension (N)
*>          The n diagonal elements of the upper triangular matrix U from
*>          the LU factorization of A.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*>          DU is COMPLEX array, dimension (N-1)
*>          The (n-1) elements of the first super-diagonal of U.
*> \endverbatim
*>
*> \param[in] DU2
*> \verbatim
*>          DU2 is COMPLEX array, dimension (N-2)
*>          The (n-2) elements of the second super-diagonal of U.
*> \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).  IPIV(i) will always be either
*>          i or i+1; IPIV(i) = i indicates a row interchange was not
*>          required.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX array, dimension (LDB,NRHS)
*>          On entry, the matrix of right hand side vectors B.
*>          On exit, B is overwritten by the solution vectors 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 = -k, the k-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 gttrs
*
*  =====================================================================
      SUBROUTINE cgttrs( TRANS, N, NRHS, DL, D, DU, DU2, 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, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            NOTRAN
      INTEGER            ITRANS, J, JB, NB
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgtts2, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
      info = 0
      notran = ( trans.EQ.'N' .OR. trans.EQ.'n' )
      IF( .NOT.notran .AND. .NOT.( trans.EQ.'T' .OR. trans.EQ.
     $    't' ) .AND. .NOT.( trans.EQ.'C' .OR. trans.EQ.'c' ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( nrhs.LT.0 ) THEN
         info = -3
      ELSE IF( ldb.LT.max( n, 1 ) ) THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CGTTRS', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 )
     $   RETURN
*
*     Decode TRANS
*
      IF( notran ) THEN
         itrans = 0
      ELSE IF( trans.EQ.'T' .OR. trans.EQ.'t' ) THEN
         itrans = 1
      ELSE
         itrans = 2
      END IF
*
*     Determine the number of right-hand sides to solve at a time.
*
      IF( nrhs.EQ.1 ) THEN
         nb = 1
      ELSE
         nb = max( 1, ilaenv( 1, 'CGTTRS', trans, n, nrhs, -1, -1 ) )
      END IF
*
      IF( nb.GE.nrhs ) THEN
         CALL cgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )
      ELSE
         DO 10 j = 1, nrhs, nb
            jb = min( nrhs-j+1, nb )
            CALL cgtts2( itrans, n, jb, dl, d, du, du2, ipiv, b( 1,
     $                   j ),
     $                   ldb )
   10    CONTINUE
      END IF
*
*     End of CGTTRS
*
      SUBROUTINE cgttrs( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, …
      END