zlaqsp.f man page

subroutine zlaqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED)
ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

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          = 'Y':  Equilibration was done, i.e., A has been replaced by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

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 127 of file zlaqsp.f.