# sppequ(3) [centos man page]

```sppequ.f(3)							      LAPACK							       sppequ.f(3)

NAME
sppequ.f -

SYNOPSIS
Functions/Subroutines
subroutine sppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
SPPEQU

Function/Subroutine Documentation
subroutine sppequ (characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )S, realSCOND, realAMAX, integerINFO)
SPPEQU

Purpose:

SPPEQU 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 REAL 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 REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

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.

AMAX

AMAX is REAL
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 sppequ.f.

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

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

## Check Out this Related Man Page

```SPPEQU(l)								 )								 SPPEQU(l)

NAME
SPPEQU  -  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 SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )

CHARACTER	  UPLO

INTEGER	  INFO, N

REAL 	  AMAX, SCOND

REAL 	  AP( * ), S( * )

PURPOSE
SPPEQU 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) REAL 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) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND   (output) 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.

AMAX    (output) REAL
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 							 SPPEQU(l)```
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