TESTING/MATGEN/zlahilb.f(3)

NAME
TESTING/MATGEN/zlahilb.f

SYNOPSIS

  Functions/Subroutines
subroutine zlahilb (n, nrhs, a, lda, x, ldx, b, ldb, work, info, path)
ZLAHILB

Function/Subroutine Documentation

  subroutine zlahilb (integer n, integer nrhs, complex*16, dimension(lda,n) a, integer lda, complex*16, dimension(ldx, nrhs) x, integer ldx, complex*16, dimension(ldb, nrhs) b, integer ldb, double precision, dimension(n) work, integer info, character*3 path)

ZLAHILB

Purpose:

     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.

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 zlahilb.f.

Author

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