# zppequ.f man page

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

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 119 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 14 2017 Version 3.8.0 LAPACK