CXML
        	    
LAPACK version 3.0
cgbsv(3)

PURPOSE
  CGBSV - compute the solution to a complex system of linear equations A * X
  = B, where A is a band matrix of order N with KL subdiagonals and KU
  superdiagonals, and X and B are N-by-NRHS matrices

SYNTAX
  SUBROUTINE CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )

      INTEGER	    INFO, KL, KU, LDAB, LDB, N, NRHS

      INTEGER	    IPIV( * )

      COMPLEX	    AB( LDAB, * ), B( LDB, * )

DESCRIPTION
  CGBSV computes the solution to a complex system of linear equations A * X =
  B, where A is a band matrix of order N with KL subdiagonals and KU
  superdiagonals, and X and B are N-by-NRHS matrices.  The LU decomposition
  with partial pivoting and row interchanges is used to factor A as A = L *
  U, where L is a product of permutation and unit lower triangular matrices
  with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals.
  The factored form of A is then used to solve the system of equations A * X
  = B.

ARGUMENTS
  N	  (input) INTEGER
	  The number of linear equations, i.e., 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/output) COMPLEX array, dimension (LDAB,N)
	  On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1;
	  rows 1 to KL of the array need not be set.  The j-th column of A is
	  stored in the j-th column of the array AB as follows:
	  AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) On exit,
	  details of the factorization: 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.	 See below for further details.

  LDAB	  (input) INTEGER
	  The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

  IPIV	  (output) INTEGER array, dimension (N)
	  The pivot indices that define the permutation matrix P; row i of
	  the matrix was interchanged with row IPIV(i).

  B	  (input/output) COMPLEX array, dimension (LDB,NRHS)
	  On entry, the N-by-NRHS right hand side matrix B.  On exit, if INFO
	  = 0, the N-by-NRHS 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
	  > 0:	if INFO = i, U(i,i) is exactly zero.  The factorization has
	  been completed, but the factor U is exactly singular, and the
	  solution has not been computed.

FURTHER DETAILS
  The band storage scheme is illustrated by the following example, when M = N
  = 6, KL = 2, KU = 1:

  On entry:			  On exit:

      *	   *	*    +	  +    +       *    *	 *   u14  u25  u36
      *	   *	+    +	  +    +       *    *	u13  u24  u35  u46
      *	  a12  a23  a34	 a45  a56      *   u12	u23  u34  u45  u56
     a11  a22  a33  a44	 a55  a66     u11  u22	u33  u44  u55  u66
     a21  a32  a43  a54	 a65   *      m21  m32	m43  m54  m65	*
     a31  a42  a53  a64	  *    *      m31  m42	m53  m64   *	*

  Array elements marked * are not used by the routine; elements marked + need
  not be set on entry, but are required by the routine to store elements of U
  because of fill-in resulting from the row interchanges.