clahilb()

subroutine clahilb	(	integer	N,
		integer	NRHS,
		complex, dimension(lda,n)	A,
		integer	LDA,
		complex, dimension(ldx, nrhs)	X,
		integer	LDX,
		complex, dimension(ldb, nrhs)	B,
		integer	LDB,
		real, dimension(n)	WORK,
		integer	INFO,
		character*3	PATH
	)

CLAHILB

Purpose:

 CLAHILB 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.

Parameters

[in]	N	N is INTEGER The dimension of the matrix A.
[in]	NRHS	NRHS is INTEGER The requested number of right-hand sides.
[out]	A	A is COMPLEX array, dimension (LDA, N) The generated scaled Hilbert matrix.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= N.
[out]	X	X is COMPLEX array, dimension (LDX, NRHS) The generated exact solutions. Currently, the first NRHS columns of the inverse Hilbert matrix.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= N.
[out]	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.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= N.
[out]	WORK	WORK is REAL array, dimension (N)
[out]	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
[in]	PATH	PATH is CHARACTER*3 The LAPACK path name.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.