.TH "TESTING/MATGEN/zlahilb.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/MATGEN/zlahilb.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlahilb\fP (n, nrhs, a, lda, x, ldx, b, ldb, work, info, path)"
.br
.RI "\fBZLAHILB\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBZLAHILB\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The dimension of the matrix A\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The requested number of right-hand sides\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension (LDA, N)
!>          The generated scaled Hilbert matrix\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= N\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX array, dimension (LDX, NRHS)
!>          The generated exact solutions\&.  Currently, the first NRHS
!>          columns of the inverse Hilbert matrix\&.
!> 
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
!>          LDX is INTEGER
!>          The leading dimension of the array X\&.  LDX >= N\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= N\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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
!> 
.fi
.PP
.br
\fIPATH\fP 
.PP
.nf
!>          PATH is CHARACTER*3
!>          The LAPACK path name\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB132\fP of file \fBzlahilb\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.