!>
!> ZLAHILB generates an N by N scaled Hilbert matrix in A along with
!> NRHS right-hand sides in B and solutions in X such that A*X=B.
!>
!> The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all
!> entries are integers.  The right-hand sides are the first NRHS
!> columns of M * the identity matrix, and the solutions are the
!> first NRHS columns of the inverse Hilbert matrix.
!>
!> The condition number of the Hilbert matrix grows exponentially with
!> its size, roughly as O(e ** (3.5*N)).  Additionally, the inverse
!> Hilbert matrices beyond a relatively small dimension cannot be
!> generated exactly without extra precision.  Precision is exhausted
!> when the largest entry in the inverse Hilbert matrix is greater than
!> 2 to the power of the number of bits in the fraction of the data type
!> used plus one, which is 24 for single precision.
!>
!> In single, the generated solution is exact for N <= 6 and has
!> small componentwise error for 7 <= N <= 11.
!> 

N

!>          N is INTEGER
!>          The dimension of the matrix A.
!> 

NRHS

!>          NRHS is INTEGER
!>          The requested number of right-hand sides.
!> 

A

!>          A is COMPLEX array, dimension (LDA, N)
!>          The generated scaled Hilbert matrix.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= N.
!> 

X

!>          X is COMPLEX array, dimension (LDX, NRHS)
!>          The generated exact solutions.  Currently, the first NRHS
!>          columns of the inverse Hilbert matrix.
!> 

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= N.
!> 

B

!>          B is REAL array, dimension (LDB, NRHS)
!>          The generated right-hand sides.  Currently, the first NRHS
!>          columns of LCM(1, 2, ..., 2*N-1) * the identity matrix.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= N.
!> 

WORK

!>          WORK is REAL array, dimension (N)
!> 

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          = 1: N is too large; the data is still generated but may not
!>               be not exact.
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 

PATH

!>          PATH is CHARACTER*3
!>          The LAPACK path name.
!> 

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