ZLAQHB - equilibrate a symmetric band matrix A using the
scaling factors in the vector S
SYNOPSIS
SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX,
EQUED )
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION S( * )
COMPLEX*16 AB( LDAB, * )
PURPOSE
ZLAQHB equilibrates a symmetric band matrix A using the
scaling factors in the vector S.
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular
part of the symmetric matrix A is stored. = 'U':
Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) 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 (input/output) COMPLEX*16 array, dimension
(LDAB,N)
On entry, the upper or lower triangle of the sym
metric 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'*U or A =
L*L' of the band matrix A, in the same storage
format as A.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >=
S (output) DOUBLE PRECISION array, dimension (N)
The scale factors for A.
SCOND (input) DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) 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= 'Y': Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).
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.
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