!>
!> SGBSV computes the solution to a real 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.
!> 

N

!>          N is INTEGER
!>          The number of linear equations, i.e., the order of the
!>          matrix A.  N >= 0.
!> 

KL

!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!> 

KU

!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!> 

AB

!>          AB is REAL 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

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
!> 

IPIV

!>          IPIV is 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

!>          B is REAL 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

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!> 

INFO

!>          INFO is 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.
!> 

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!>
!>  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.
!>