ZLAQHB equilibrates a Hermitian band matrix A 


 using the scaling factors in the vector S.

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.

KD

          KD is INTEGER


          The number of super-diagonals of the matrix A if UPLO = 'U',


          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

AB

          AB is COMPLEX*16 array, dimension (LDAB,N)


          On entry, the upper or lower triangle of the symmetric band


          matrix A, stored in the first KD+1 rows of the array.  The


          j-th column of A is stored in the j-th column of the array AB


          as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          On exit, if INFO = 0, the triangular factor U or L from the


          Cholesky factorization A = U**H *U or A = L*L**H of the band


          matrix A, in the same storage format as A.

LDAB

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

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          = 'Y':  Equilibration was done, i.e., A has been replaced by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

  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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012