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

.in +1c
.ti -1c
.RI "subroutine \fBcheequb\fP (uplo, n, a, lda, s, scond, amax, work, info)"
.br
.RI "\fBCHEEQUB\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine cheequb (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, complex, dimension( * ) work, integer info)"

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

.PP
.nf
 CHEEQUB computes row and column scalings intended to equilibrate a
 Hermitian matrix A (with respect to the Euclidean norm) and reduce
 its condition number\&. The scale factors S are computed by the BIN
 algorithm (see references) so that the scaled matrix B with elements
 B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
 the smallest possible condition number over all possible diagonal
 scalings\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
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.nf
          N is INTEGER
          The order of the matrix A\&. N >= 0\&.
.fi
.PP
.br
\fIA\fP 
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.nf
          A is COMPLEX array, dimension (LDA,N)
          The N-by-N Hermitian matrix whose scaling factors are to be
          computed\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,N)\&.
.fi
.PP
.br
\fIS\fP 
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.nf
          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
          SCOND is REAL
          If INFO = 0, S contains the ratio of the smallest S(i) to
          the largest S(i)\&. If SCOND >= 0\&.1 and AMAX is neither too
          large nor too small, it is not worth scaling by S\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          AMAX is REAL
          Largest absolute value of any matrix element\&. If AMAX is
          very close to overflow or very close to underflow, the
          matrix should be scaled\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (2*N)
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, the i-th diagonal element is nonpositive\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', 
.br
 Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. 
.br
 DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 
.br
 Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 
.RE
.PP

.PP
Definition at line \fB131\fP of file \fBcheequb\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.