man zlaqhb (Fonctions bibliothèques) - equilibrate a symmetric band matrix A using the scaling factors in the vector S
NAME
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 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'*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.
- 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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.