# zppequ.f - Man Page

SRC/zppequ.f

## Synopsis

### Functions/Subroutines

subroutine zppequ (uplo, n, ap, s, scond, amax, info)
ZPPEQU

## Function/Subroutine Documentation

### subroutine zppequ (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

ZPPEQU

Purpose:

``` ZPPEQU computes row and column scalings intended to equilibrate a
Hermitian 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 COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian 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.

Definition at line 116 of file zppequ.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zppequ(3) is an alias of zppequ.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK