Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  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)

```

#### 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 smallest 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 routine (version 3.2)               April 2011                            SPPEQU(3lapack)
```