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CTBSV(1)			 BLAS routine			      CTBSV(1)

NAME
       CTBSV  - solves one of the systems of equations	 A*x = b, or A'*x = b,
       or conjg( A' )*x = b,

SYNOPSIS
       SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)

	   INTEGER					  INCX,K,LDA,N

	   CHARACTER					  DIAG,TRANS,UPLO

	   COMPLEX					  A(LDA,*),X(*)

PURPOSE
       CTBSV  solves one of the systems of equations

       where b and x are n element vectors and A is an n by n  unit,  or  non-
       unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

       No  test	 for  singularity or near-singularity is included in this rou‐
       tine. Such tests must be performed before calling this routine.

ARGUMENTS
       UPLO   - CHARACTER*1.
	      On entry, UPLO specifies whether the matrix is an upper or lower
	      triangular matrix as follows:

	      UPLO = 'U' or 'u'	  A is an upper triangular matrix.

	      UPLO = 'L' or 'l'	  A is a lower triangular matrix.

	      Unchanged on exit.

       TRANS  - CHARACTER*1.
	      On entry, TRANS specifies the equations to be solved as follows:

	      TRANS = 'N' or 'n'   A*x = b.

	      TRANS = 'T' or 't'   A'*x = b.

	      TRANS = 'C' or 'c'   conjg( A' )*x = b.

	      Unchanged on exit.

       DIAG   - CHARACTER*1.
	      On  entry, DIAG specifies whether or not A is unit triangular as
	      follows:

	      DIAG = 'U' or 'u'	  A is assumed to be unit triangular.

	      DIAG = 'N' or 'n'	  A is not assumed to be unit triangular.

	      Unchanged on exit.

       N      - INTEGER.
	      On entry, N specifies the order of the matrix A.	N must	be  at
	      least zero.  Unchanged on exit.

       K      - INTEGER.
	      On  entry	 with  UPLO  =	'U'  or 'u', K specifies the number of
	      super-diagonals of the matrix A.	On entry with UPLO  =  'L'  or
	      'l', K specifies the number of sub-diagonals of the matrix A.  K
	      must satisfy  0 .le. K.  Unchanged on exit.

       A      - COMPLEX		 array of DIMENSION ( LDA, n ).
	      Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by  n
	      part  of the array A must contain the upper triangular band part
	      of the matrix of coefficients, supplied column by	 column,  with
	      the  leading  diagonal  of  the  matrix  in row ( k + 1 ) of the
	      array, the first super-diagonal starting at position 2 in row k,
	      and  so  on.  The top left k by k triangle of the array A is not
	      referenced.  The following  program  segment  will  transfer  an
	      upper triangular band matrix from conventional full matrix stor‐
	      age to band storage:

	      DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M
	      + I, J ) = matrix( I, J ) 10    CONTINUE 20 CONTINUE

	      Before  entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n
	      part of the array A must contain the lower triangular band  part
	      of  the  matrix of coefficients, supplied column by column, with
	      the leading diagonal of the matrix in row 1 of  the  array,  the
	      first  sub-diagonal  starting at position 1 in row 2, and so on.
	      The bottom right k by k triangle of the array A  is  not	refer‐
	      enced.  The following program segment will transfer a lower tri‐
	      angular band matrix from conventional  full  matrix  storage  to
	      band storage:

	      DO  20,  J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M +
	      I, J ) = matrix( I, J ) 10    CONTINUE 20 CONTINUE

	      Note that when DIAG = 'U' or 'u' the elements  of	 the  array  A
	      corresponding  to	 the  diagonal	elements of the matrix are not
	      referenced, but are assumed to be unity.	Unchanged on exit.

       LDA    - INTEGER.
	      On entry, LDA specifies the first dimension of A as declared  in
	      the  calling  (sub)  program.  LDA  must	be at least ( k + 1 ).
	      Unchanged on exit.

       X      - COMPLEX		 array of dimension at least
	      ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
	      array  X must contain the n element right-hand side vector b. On
	      exit, X is overwritten with the solution vector x.

       INCX   - INTEGER.
	      On entry, INCX specifies the increment for the  elements	of  X.
	      INCX must not be zero.  Unchanged on exit.

FURTHER DETAILS
       Level 2 Blas routine.

       -- Written on 22-October-1986.
	  Jack Dongarra, Argonne National Lab.
	  Jeremy Du Croz, Nag Central Office.
	  Sven Hammarling, Nag Central Office.
	  Richard Hanson, Sandia National Labs.

BLAS routine			 November 2008			      CTBSV(1)
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