# ctbsv.f

          SUBROUTINE CTBSV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
    C***BEGIN PROLOGUE  CTBSV
    C***PURPOSE  Solve a complex triangular banded system of equations.
    C***LIBRARY   SLATEC (BLAS)
    C***CATEGORY  D1B4
    C***TYPE      COMPLEX (STBSV-S, DTBSV-D, CTBSV-C)
    C***KEYWORDS  LEVEL 2 BLAS, LINEAR ALGEBRA
    C***AUTHOR  Dongarra, J. J., (ANL)
    C           Du Croz, J., (NAG)
    C           Hammarling, S., (NAG)
    C           Hanson, R. J., (SNLA)
    C***DESCRIPTION
    C
    C  CTBSV  solves one of the systems of equations
    C
    C     A*x = b,   or   A'*x = b,   or   conjg( A')*x = b,
    C
    C  where b and x are n element vectors and A is an n by n unit, or
    C  non-unit, upper or lower triangular band matrix, with ( k + 1 )
    C  diagonals.
    C
    C  No test for singularity or near-singularity is included in this
    C  routine. Such tests must be performed before calling this routine.
    C
    C  Parameters
    C  ==========
    C
    C  UPLO   - CHARACTER*1.
    C           On entry, UPLO specifies whether the matrix is an upper or
    C           lower triangular matrix as follows:
    C
    C              UPLO = 'U' or 'u'   A is an upper triangular matrix.
    C
    C              UPLO = 'L' or 'l'   A is a lower triangular matrix.
    C
    C           Unchanged on exit.
    C
    C  TRANS  - CHARACTER*1.
    C           On entry, TRANS specifies the equations to be solved as
    C           follows:
    C
    C              TRANS = 'N' or 'n'   A*x = b.
    C
    C              TRANS = 'T' or 't'   A'*x = b.
    C
    C              TRANS = 'C' or 'c'   conjg( A' )*x = b.
    C
    C           Unchanged on exit.
    C
    C  DIAG   - CHARACTER*1.
    C           On entry, DIAG specifies whether or not A is unit
    C           triangular as follows:
    C
    C              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
    C
    C              DIAG = 'N' or 'n'   A is not assumed to be unit
    C                                  triangular.
    C
    C           Unchanged on exit.
    C
    C  N      - INTEGER.
    C           On entry, N specifies the order of the matrix A.
    C           N must be at least zero.
    C           Unchanged on exit.
    C
    C  K      - INTEGER.
    C           On entry with UPLO = 'U' or 'u', K specifies the number of
    C           super-diagonals of the matrix A.
    C           On entry with UPLO = 'L' or 'l', K specifies the number of
    C           sub-diagonals of the matrix A.
    C           K must satisfy  0 .le. K.
    C           Unchanged on exit.
    C
    C  A      - COMPLEX          array of DIMENSION ( LDA, n ).
    C           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
    C           by n part of the array A must contain the upper triangular
    C           band part of the matrix of coefficients, supplied column by
    C           column, with the leading diagonal of the matrix in row
    C           ( k + 1 ) of the array, the first super-diagonal starting at
    C           position 2 in row k, and so on. The top left k by k triangle
    C           of the array A is not referenced.
    C           The following program segment will transfer an upper
    C           triangular band matrix from conventional full matrix storage
    C           to band storage:
    C
    C                 DO 20, J = 1, N
    C                    M = K + 1 - J
    C                    DO 10, I = MAX( 1, J - K ), J
    C                       A( M + I, J ) = matrix( I, J )
    C              10    CONTINUE
    C              20 CONTINUE
    C
    C           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
    C           by n part of the array A must contain the lower triangular
    C           band part of the matrix of coefficients, supplied column by
    C           column, with the leading diagonal of the matrix in row 1 of
    C           the array, the first sub-diagonal starting at position 1 in
    C           row 2, and so on. The bottom right k by k triangle of the
    C           array A is not referenced.
    C           The following program segment will transfer a lower
    C           triangular band matrix from conventional full matrix storage
    C           to band storage:
    C
    C                 DO 20, J = 1, N
    C                    M = 1 - J
    C                    DO 10, I = J, MIN( N, J + K )
    C                       A( M + I, J ) = matrix( I, J )
    C              10    CONTINUE
    C              20 CONTINUE
    C
    C           Note that when DIAG = 'U' or 'u' the elements of the array A
    C           corresponding to the diagonal elements of the matrix are not
    C           referenced, but are assumed to be unity.
    C           Unchanged on exit.
    C
    C  LDA    - INTEGER.
    C           On entry, LDA specifies the first dimension of A as declared
    C           in the calling (sub) program. LDA must be at least
    C           ( k + 1 ).
    C           Unchanged on exit.
    C
    C  X      - COMPLEX          array of dimension at least
    C           ( 1 + ( n - 1 )*abs( INCX ) ).
    C           Before entry, the incremented array X must contain the n
    C           element right-hand side vector b. On exit, X is overwritten
    C           with the solution vector x.
    C
    C  INCX   - INTEGER.
    C           On entry, INCX specifies the increment for the elements of
    C           X. INCX must not be zero.
    C           Unchanged on exit.
    C
    C***REFERENCES  Dongarra, J. J., Du Croz, J., Hammarling, S., and
    C                 Hanson, R. J.  An extended set of Fortran basic linear
    C                 algebra subprograms.  ACM TOMS, Vol. 14, No. 1,
    C                 pp. 1-17, March 1988.
    C***ROUTINES CALLED  LSAME, XERBLA
    C***REVISION HISTORY  (YYMMDD)
    C   861022  DATE WRITTEN
    C   910605  Modified to meet SLATEC prologue standards.  Only comment
    C           lines were modified.  (BKS)
    C***END PROLOGUE  CTBSV