zlaqsb (l)  Linux Man Pages
zlaqsb: equilibrates a symmetric band matrix A using the scaling factors in the vector S
NAME
ZLAQSB  equilibrates a symmetric band matrix A using the scaling factors in the vector SSYNOPSIS
 SUBROUTINE ZLAQSB(
 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
ZLAQSB 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.
= aqUaq: Upper triangular
= aqLaq: Lower triangular  N (input) INTEGER
 The order of the matrix A. N >= 0.
 KD (input) INTEGER
 The number of superdiagonals of the matrix A if UPLO = aqUaq, or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
 AB (input/output) 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 jth column of A is stored in the jth column of the array AB as follows: if UPLO = aqUaq, AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = aqLaq, AB(1+ij,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 = Uaq*U or A = L*Laq 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.
 S (input) 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.
= aqNaq: No equilibration.
= aqYaq: Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.