slaqsp.f man page

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

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

Purpose:

 SLAQSP 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 REAL 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 REAL array, dimension (N)
          The scale factors for A.

SCOND

          SCOND is REAL
          Ratio of the smallest S(i) to the largest S(i).

AMAX

          AMAX is REAL
          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          = 'Y':  Equilibration was done, i.e., A has been replaced by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 126 of file slaqsp.f.