LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine zlaqhb | ( | 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 | ||
) |
ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.
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ZLAQHB equilibrates a Hermitian band matrix A using the scaling factors in the vector S.
[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. |
[out] | 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). |
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.
Definition at line 143 of file zlaqhb.f.