!-----------------------------------------------------------------
!
!  Purpose
!  =======
!
!  LA_GBSV computes the solution to either a real or complex system of
!  linear equations A * X = B, where A is a band matrix and X and B are
!  either rectangular matrices or vectors.
!  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, and U is upper triangular. The
!  factored form of A is then used to solve the system of equations
!  A * X = B.
!
!  Arguments
!  =========
!
!   SUBROUTINE LA_GBSV( AB, B, KL, IPIV, INFO )
!     <type>(<wp>), INTENT(INOUT) :: AB(:,:), <rhs>
!     INTEGER, INTENT(IN), OPTIONAL :: KL
!     INTEGER, INTENT(OUT), OPTIONAL :: IPIV(:)
!     INTEGER, INTENT(OUT), OPTIONAL :: INFO
!     <type> ::= REAL | COMPLEX
!     <wp>   ::= KIND(1.0) | KIND(1.0D0)
!     <rhs>  ::= B(:,:) | B(:)
!
!  =====================
!
!  AB   (input/output) either REAL or COMPLEX rectangular array,
!       shape (:,:).
!       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.
!       Description KL see below, while KU = SIZE(A,1)-2*KL-1 and
!       SIZE(A,2) is the order of the banded matrix (n).
!
!  B    (input/output) either REAL or COMPLEX rectangular array,
!       shape either (:,:) or (:), size(B,1) or size(B) == size(A,2).
!       On entry, the right hand side vector(s) of matrix B for the
!       system of equations AX = B.
!       On exit, if there is no error, the matrix of solution
!       vector(s) X.
!
!  KL   Optional (input) INTEGER
!       If KL is present it indicates the number of subdiagonals
!       within the band of A.  KL >= 0. If it is not present the
!       system assumes equal numbers of subdiagonals and superdiagonals.
!       The number of superdiagonals is SIZE(A,1)-2*KL-1.
!
!  IPIV Optional (output) INTEGER array, shape (:),
!       size(IPIV) == size(AB,2). If IPIV is present it indices
!       define the permutation matrix P; row i of the matrix was
!       interchanged with row IPIV(i).
!
!  INFO Optional (output) INTEGER.
!       If INFO is present
!          = 0: successful exit
!          < 0: if INFO = -k, the k-th argument had an illegal value
!          > 0: if INFO = k, U(k,k) is exactly zero.  The factorization
!               has been completed, but the factor U is exactly
!               singular, so the solution could not be computed.
!       If INFO is not present and an error occurs, then the program is
!          terminated with an error message.
!
!  Further Details
!  ===============
!
!  The band storage scheme is illustrated by the following example, when
!  SIZE(A,1) = SIZE(A,2) = 6, KL = 2, KU SIZE(A,1)-2*KL-1 = 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.
!
!-------------------------------------

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