subroutine dgbtrs	(	character	TRANS,
		integer	N,
		integer	KL,
		integer	KU,
		integer	NRHS,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

DGBTRS

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Purpose:

 DGBTRS solves a system of linear equations
    A * X = B  or  A**T * X = B
 with a general band matrix A using the LU factorization computed
 by DGBTRF.

Parameters

[in]	TRANS	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**T* X = B (Conjugate transpose = Transpose)
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KL	KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
[in]	KU	KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	AB	AB is DOUBLE PRECISION array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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.
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
[in]	IPIV	IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2011

Definition at line 140 of file dgbtrs.f.

*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          trans
      INTEGER            info, kl, ku, ldab, ldb, n, nrhs
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      DOUBLE PRECISION   ab( ldab, * ), b( ldb, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   one
      parameter                ( one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            lnoti, notran
      INTEGER            i, j, kd, l, lm
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemv, dger, dswap, dtbsv, xerbla
*     ..
*     .. 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( 'DGBTRS', -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 dswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
               CALL dger( 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 dtbsv( 'Upper', 'No transpose', 'Non-unit', n, kl+ku,
     $                  ab, ldab, b( 1, i ), 1 )
   20    CONTINUE
*
      ELSE
*
*        Solve A**T*X = B.
*
         DO 30 i = 1, nrhs
*
*           Solve U**T*X = B, overwriting B with X.
*
            CALL dtbsv( '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 dgemv( '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 dswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
   40       CONTINUE
         END IF
      END IF
      RETURN
*
*     End of DGBTRS
*

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