zlaqhb.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

zlaqhb.f  

SYNOPSIS


 

Functions/Subroutines


subroutine zlaqhb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.  

Function/Subroutine Documentation

 

subroutine zlaqhb (character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED)

ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

Purpose:

 ZLAQHB equilibrates a Hermitian band 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.


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          = 'Y':  Equilibration was done, i.e., A has been replaced by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


 

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:

December 2016

Definition at line 143 of file zlaqhb.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine zlaqhb (character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED)
Author