# sppequ.f (3) - Linux Manuals

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