# zlaqsp.f - Man Page

SRC/zlaqsp.f

## Synopsis

### Functions/Subroutines

subroutine zlaqsp (uplo, n, ap, s, scond, amax, equed)
ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

## Function/Subroutine Documentation

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

ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:

``` ZLAQSP equilibrates a symmetric matrix A using the scaling factors
in the vector S.```
Parameters

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U':  Upper triangular
= 'L':  Lower triangular```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

AP

```          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, 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.

On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
the same storage format as A.```

S

```          S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.```

SCOND

```          SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).```

AMAX

```          AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.```

EQUED

```          EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N':  No equilibration.
= 'Y':  Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).```

Internal Parameters:

```  THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors.  If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file zlaqsp.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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