NAME¶

CLAQSB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

SYNOPSIS¶

SUBROUTINE CLAQSB(

UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

CHARACTER EQUED, UPLO INTEGER KD, LDAB, N REAL AMAX, SCOND REAL S( * ) COMPLEX AB( LDAB, * )

PURPOSE¶

CLAQSB 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 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 (input) REAL array, dimension (N)

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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.