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 zppequ.f(3) LAPACK zppequ.f(3)

zppequ.f -

SYNOPSIS

Functions/Subroutines

subroutine zppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)

ZPPEQU

Function/Subroutine Documentation

subroutine zppequ (characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)

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
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 118 of file zppequ.f.

Author

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