# dppequ.f(3) [centos man page]

```dppequ.f(3)							      LAPACK							       dppequ.f(3)

NAME
dppequ.f -

SYNOPSIS
Functions/Subroutines
subroutine dppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
DPPEQU

Function/Subroutine Documentation
subroutine dppequ (characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )S, double precisionSCOND,
double precisionAMAX, integerINFO)
DPPEQU

Purpose:

DPPEQU computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A in packed storage 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.

Parameters:
UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A.  N >= 0.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array.  The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

S

S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

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.

AMAX

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.

INFO

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.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Definition at line 117 of file dppequ.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dppequ.f(3)```

## Check Out this Related Man Page

```DPPEQU(l)								 )								 DPPEQU(l)

NAME
DPPEQU  -  compute  row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its
condition number (with respect to the two-norm)

SYNOPSIS
SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )

CHARACTER	  UPLO

INTEGER	  INFO, N

DOUBLE	  PRECISION AMAX, SCOND

DOUBLE	  PRECISION AP( * ), S( * )

PURPOSE
DPPEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed  storage  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 small-
est possible condition number over all possible diagonal scalings.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The  upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the
array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i	+  (j-1)*(2n-j)/2)  =  A(i,j)  for
j<=i<=n.

S       (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND   (output) 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.

AMAX    (output) 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.

INFO    (output) 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.

LAPACK version 3.0						   15 June 2000 							 DPPEQU(l)```
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