cgbtrs.f

          SUBROUTINE CGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
         $                   INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          TRANS
          INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX            AB( LDAB, * ), B( LDB, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGBTRS 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 CGBTRF.
    *
    *  Arguments
    *  =========
    *
    *  TRANS   (input) 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)
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  KL      (input) INTEGER
    *          The number of subdiagonals within the band of A.  KL >= 0.
    *
    *  KU      (input) INTEGER
    *          The number of superdiagonals within the band of A.  KU >= 0.
    *
    *  NRHS    (input) INTEGER
    *          The number of right hand sides, i.e., the number of columns
    *          of the matrix B.  NRHS >= 0.
    *
    *  AB      (input) COMPLEX array, dimension (LDAB,N)
    *          Details of the LU factorization of the band matrix A, as
    *          computed by CGBTRF.  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.
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    *
    *  IPIV    (input) INTEGER array, dimension (N)
    *          The pivot indices; for 1 <= i <= N, row i of the matrix was
    *          interchanged with row IPIV(i).
    *
    *  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
    *          On entry, the right hand side matrix B.
    *          On exit, the solution matrix X.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(1,N).
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ONE
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LNOTI, NOTRAN
          INTEGER            I, J, KD, L, LM
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGEMV, CGERU, CLACGV, CSWAP, CTBSV, 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( 'CGBTRS', -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 CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
                   CALL CGERU( 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 CTBSV( '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 CTBSV( '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 CGEMV( '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 CSWAP( 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 CTBSV( '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 CLACGV( NRHS, B( J, 1 ), LDB )
                   CALL CGEMV( 'Conjugate transpose', LM, NRHS, -ONE,
         $                     B( J+1, 1 ), LDB, AB( KD+1, J ), 1, ONE,
         $                     B( J, 1 ), LDB )
                   CALL CLACGV( NRHS, B( J, 1 ), LDB )
                   L = IPIV( J )
                   IF( L.NE.J )
         $            CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
       60       CONTINUE
             END IF
          END IF
          RETURN
    *
    *     End of CGBTRS
    *
          END