
 
 Purpose
 =======
 
      LA_GBSV computes the solution to a real or complex linear system
 of equations A*X = B, where A is a square band matrix and X and B are
 rectangular matrices or vectors. The LU decomposition with 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 above system.
 
 =========
 
       SUBROUTINE LA_GBSV( AB, B, KL=kl, IPIV=ipiv, INFO=info )
             <type>(<wp>), INTENT(INOUT) :: AB(:,:), <rhs>
             INTEGER, INTENT(IN), OPTIONAL :: KL
             INTEGER, INTENT(OUT), OPTIONAL :: IPIV(:)
             INTEGER, INTENT(OUT), OPTIONAL :: INFO
       where
             <type> ::= REAL | COMPLEX
             <wp>   ::= KIND(1.0) | KIND(1.0D0)
             <rhs>  ::= B(:,:) | B(:)
 
 Arguments
 =========
 
 AB      (input/output) REAL or COMPLEX rectangular array, shape (:,:)
         with size(AB,1) = 2*kl+ku+1 and size(AB,2) = n, where kl and ku
         are, respectively, the numbers of subdiagonals and 
         superdiagonals in the band of A, and n is the order of A.
         On entry, the matrix A in band storage. The (kl + ku + 1) 
 	  diagonals of A are stored in rows (kl + 1) to (2*kl + ku + 1) 
 	  of AB, so that the j-th column of A is stored in the j-th 
 	  column of AB as follows:
 	  AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl)
 	                                 1<=j<=n
         The remaining elements in AB need not be set.
         On exit, details of the factorization. U is an upper triangular 
         band matrix with (kl + ku + 1) diagonals. These are stored in
 	  the first (kl + ku + 1) rows of AB. The multipliers that arise
         during the factorization are stored in the remaining rows.
 B       (input/output) REAL or COMPLEX array, shape (:,:) with 
         size(B,1) = n or shape (:) with size(B) = n.
         On entry, the matrix B.
         On exit, the solution matrix X.
 KL      Optional (input) INTEGER.
         The number of subdiagonals in the band of A (KL = kl).
         The number of superdiagonals in the band is given by
 	  ku = size(AB,1) - 2 * kl - 1.
         Default value: (size(AB,1)-1)/3.
 IPIV    Optional (output) INTEGER array, shape (:) with size(IPIV) = n.
         The pivot indices that define the row interchanges; row i of the
         matrix was interchanged with row IPIV(i).
 INFO    Optional (output) INTEGER
         = 0: successful exit.
         < 0: if INFO = -i, the i-th argument had an illegal value.
         > 0: if INFO = i, U(i,i) = 0. The factorization has been 
         completed, but the factor U is 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.

