zlaqsb.f (3) - Linux Manuals
subroutine zlaqsb (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, characterEQUED)
ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
ZLAQSB 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 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 is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
S is DOUBLE PRECISION array, dimension (N) The scale factors for A.
SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).
AMAX is DOUBLE PRECISION 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).
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
- September 2012
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