LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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zlaqsb.f File Reference

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Functions/Subroutines

subroutine zlaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
 ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Function/Subroutine Documentation

subroutine zlaqsb ( 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 
)

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Download ZLAQSB + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 ZLAQSB equilibrates a symmetric band matrix A using the scaling
 factors in the vector S.
Parameters:
[in]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
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]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.
[in,out]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.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
[in]S
          S is DOUBLE PRECISION array, dimension (N)
          The scale factors for A.
[in]SCOND
          SCOND is DOUBLE PRECISION
          Ratio of the smallest S(i) to the largest S(i).
[in]AMAX
          AMAX is DOUBLE PRECISION
          Absolute value of largest matrix entry.
[out]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 142 of file zlaqsb.f.

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