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

.in +1c
.ti -1c
.RI "subroutine \fBzpoequb\fP (n, a, lda, s, scond, amax, info)"
.br
.RI "\fBZPOEQUB\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zpoequb (integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)"

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

.PP
.nf
 ZPOEQUB computes row and column scalings intended to equilibrate a
 Hermitian positive definite matrix A and reduce its condition number
 (with respect to the two-norm)\&.  S contains the scale factors,
 S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
 elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal\&.  This
 choice of S puts the condition number of B within a factor N of the
 smallest possible condition number over all possible diagonal
 scalings\&.

 This routine differs from ZPOEQU by restricting the scaling factors
 to a power of the radix\&.  Barring over- and underflow, scaling by
 these factors introduces no additional rounding errors\&.  However, the
 scaled diagonal entries are no longer approximately 1 but lie
 between sqrt(radix) and 1/sqrt(radix)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          The N-by-N Hermitian positive definite matrix whose scaling
          factors are to be computed\&.  Only the diagonal elements of A
          are referenced\&.
.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 
.PP
.nf
          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
          SCOND is DOUBLE PRECISION
          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 DOUBLE PRECISION
          Absolute value of largest matrix element\&.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled\&.
.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 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB118\fP of file \fBzpoequb\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.