SLAQSB - equilibrate a symmetric band matrix A using the
scaling factors in the vector S
SYNOPSIS
SUBROUTINE SLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX,
EQUED )
CHARACTER EQUED, UPLO
INTEGER KD, LDAB, N
REAL AMAX, SCOND
REAL AB( LDAB, * ), S( * )
PURPOSE
SLAQSB 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) REAL 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 >=
KD+1.
The scale factors for A.
SCOND (input) REAL
Ratio of the smallest S(i) to the largest S(i).
AMAX (input) REAL
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= 'Y': Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).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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