TESTING/MATGEN/clahilb.f(3)                           Library Functions Manual

NAME
       TESTING/MATGEN/clahilb.f

SYNOPSIS
   Functions/Subroutines
       subroutine clahilb (n, nrhs, a, lda, x, ldx, b, ldb, work, info, path)
           CLAHILB

Function/Subroutine Documentation
   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
           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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 132 of file clahilb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0     TESTING/MATGEN/clahilb.f(3)