OpenBLAS/lapack-netlib/SRC/cgtsv.f

*> \brief <b> CGTSV computes the solution to system of linear equations A * X = B for GT matrices </b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CGTSV  solves the equation
*>
*>    A*X = B,
*>
*> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
*> partial pivoting.
*>
*> Note that the equation  A**T *X = B  may be solved by interchanging the
*> order of the arguments DU and DL.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          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] DL
*> \verbatim
*>          DL is COMPLEX array, dimension (N-1)
*>          On entry, DL must contain the (n-1) subdiagonal elements of
*>          A.
*>          On exit, DL is overwritten by the (n-2) elements of the
*>          second superdiagonal of the upper triangular matrix U from
*>          the LU factorization of A, in DL(1), ..., DL(n-2).
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is COMPLEX array, dimension (N)
*>          On entry, D must contain the diagonal elements of A.
*>          On exit, D is overwritten by the n diagonal elements of U.
*> \endverbatim
*>
*> \param[in,out] DU
*> \verbatim
*>          DU is COMPLEX array, dimension (N-1)
*>          On entry, DU must contain the (n-1) superdiagonal elements
*>          of A.
*>          On exit, DU is overwritten by the (n-1) elements of the first
*>          superdiagonal of U.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*>          B is COMPLEX 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, U(i,i) is exactly zero, and the solution
*>                has not been computed.  The factorization has not been
*>                completed unless i = N.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexGTsolve
*
*  =====================================================================
      SUBROUTINE CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
*  -- LAPACK driver routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ZERO
      PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            J, K
      COMPLEX            MULT, TEMP, ZDUM
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, AIMAG, MAX, REAL
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     ..
*     .. Statement Functions ..
      REAL               CABS1
*     ..
*     .. Statement Function definitions ..
      CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
*     ..
*     .. Executable Statements ..
*
      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CGTSV ', -INFO )
         RETURN
      END IF
*
      IF( N.EQ.0 )
     $   RETURN
*
      DO 30 K = 1, N - 1
         IF( DL( K ).EQ.ZERO ) THEN
*
*           Subdiagonal is zero, no elimination is required.
*
            IF( D( K ).EQ.ZERO ) THEN
*
*              Diagonal is zero: set INFO = K and return; a unique
*              solution can not be found.
*
               INFO = K
               RETURN
            END IF
         ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
*
*           No row interchange required
*
            MULT = DL( K ) / D( K )
            D( K+1 ) = D( K+1 ) - MULT*DU( K )
            DO 10 J = 1, NRHS
               B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
   10       CONTINUE
            IF( K.LT.( N-1 ) )
     $         DL( K ) = ZERO
         ELSE
*
*           Interchange rows K and K+1
*
            MULT = D( K ) / DL( K )
            D( K ) = DL( K )
            TEMP = D( K+1 )
            D( K+1 ) = DU( K ) - MULT*TEMP
            IF( K.LT.( N-1 ) ) THEN
               DL( K ) = DU( K+1 )
               DU( K+1 ) = -MULT*DL( K )
            END IF
            DU( K ) = TEMP
            DO 20 J = 1, NRHS
               TEMP = B( K, J )
               B( K, J ) = B( K+1, J )
               B( K+1, J ) = TEMP - MULT*B( K+1, J )
   20       CONTINUE
         END IF
   30 CONTINUE
      IF( D( N ).EQ.ZERO ) THEN
         INFO = N
         RETURN
      END IF
*
*     Back solve with the matrix U from the factorization.
*
      DO 50 J = 1, NRHS
         B( N, J ) = B( N, J ) / D( N )
         IF( N.GT.1 )
     $      B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
         DO 40 K = N - 2, 1, -1
            B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
     $                  B( K+2, J ) ) / D( K )
   40    CONTINUE
   50 CONTINUE
*
      RETURN
*
*     End of CGTSV
*
      END