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

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

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

.PP
.nf
!>
!> DPOEQUB computes row and column scalings intended to equilibrate a
!> symmetric 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 DPOEQU 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 DOUBLE PRECISION array, dimension (LDA,N)
!>          The N-by-N symmetric 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 \fB117\fP of file \fBdpoequb\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.