*DECK STBSV
      SUBROUTINE STBSV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
C***BEGIN PROLOGUE  STBSV
C***PURPOSE  Solve a real triangular banded system of linear equations.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B4
C***TYPE      SINGLE PRECISION (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  STBSV  solves one of the systems of equations
C
C     A*x = b,   or   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'   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      - REAL             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      - REAL             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  STBSV