slaqsb.f man page

slaqsb.f —



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

Function/Subroutine Documentation

subroutine slaqsb (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND, realAMAX, characterEQUED)

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


 SLAQSB equilibrates a symmetric band matrix A using the scaling
 factors in the vector S.


          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 is INTEGER
          The order of the matrix A.  N >= 0.


          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 is REAL 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**T*U or A = L*L**T of the band
          matrix A, in the same storage format as A.


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


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


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


          AMAX is REAL
          Absolute value of largest matrix entry.


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          = 'Y':  Equilibration was done, i.e., A has been replaced by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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


September 2012

Definition at line 141 of file slaqsb.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

slaqsb(3) is an alias of slaqsb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK