!-----------------------------------------------------------------
!
! Purpose
! =======
!
! LA_PBSV computes the solution to a system of linear equations
!    A * X = B,
! where A is either a symmetric positive definite or hermitian band
! matrix and X and B are either retriangular matrices or vectors.
! The Cholesky decomposition is used to factor A as
!    A = U**T * U,  if UPLO = 'U', or
!    A = L * L**T,  if UPLO = 'L',
! where U is an upper triangular band matrix, and L is a lower
! triangular band matrix, with the same number of superdiagonals or
! subdiagonals as A.  The factored form of A is then used to solve the
! system of equations A * X = B.
!
! Arguments
! =========
!
!  SUBROUTINE LA_PBSV( AB, B, UPLO, INFO )
!    <type>(<wp>), INTENT(INOUT) :: AB(:,:), <rhs>
!    CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
!    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 upper or lower triangle of the symmetric band
!      matrix A, stored in the first kd+1 rows of the array.  The
!      j-th column of A is stored in the j-th column of the array AB
!      as follows:
!      if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!      if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!      See below for further details.
!      On exit, if INFO = 0, the triangular factor U or L from the
!      Cholesky factorization A = U**T*U or A = L*L**T of the band
!      matrix A, in the same storage format as A.
!      Where kd = SIZE(AB,1)-1 and n = SIZE(AB,2).
!
! 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.
!
! UPLO    Optional, (input) CHARACTER*1
!         If UPLO is present then:
!            = 'U':  Upper triangle of A is stored;
!            = 'L':  Lower triangle of A is stored.
!         otherwise UPLO = 'U' is assumed.
!
! 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, the leading minor of order i of A is not
!              positive definite, so the factorization could not be
!              completed, and the solution has not been 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
!  N = 6, KD = 2, and UPLO = 'U':
!
!  On entry:                       On exit:
!
!      *    *   a13  a24  a35  a46      *    *   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
!
!  Similarly, if UPLO = 'L' the format of A is as follows:
!
!  On entry:                       On exit:
!
!     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
!     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
!     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
!
!  Array elements marked * are not used by the routine.
!-------------------------------------

.