zlaqgb(3)

NAME

ZLAQGB - equilibrate a general M by N band matrix A with

KL subdiagonals and KU superdiagonals using the row and scaling

factors in the vectors R and C

SYNOPSIS

SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R,  C,  ROWCND,
COLCND, AMAX, EQUED )
    CHARACTER      EQUED
    INTEGER        KL, KU, LDAB, M, N
    DOUBLE         PRECISION AMAX, COLCND, ROWCND
    DOUBLE         PRECISION C( * ), R( * )
    COMPLEX*16     AB( LDAB, * )

PURPOSE

ZLAQGB equilibrates a general M by N band matrix A with KL

subdiagonals and KU superdiagonals using the row and scaling fac

tors in the vectors R and C.

ARGUMENTS

M (input) INTEGER

The number of rows of the matrix A. M >= 0.

N (input) INTEGER

The number of columns of the matrix A. N >= 0.

KL (input) INTEGER

The number of subdiagonals within the band of A.

KL >= 0.

KU (input) INTEGER

The number of superdiagonals within the band of A.

KU >= 0.

AB (input/output) COMPLEX*16 array, dimension

(LDAB,N)

On entry, the matrix A in band storage, in rows 1

to KL+KU+1. The j-th column of A is stored in the j-th column of

the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j

ku)<=i<=min(m,j+kl)

On exit, the equilibrated matrix, in the same

storage format as A. See EQUED for the form of the equilibrated

matrix.

LDAB (input) INTEGER

The leading dimension of the array AB. LDA >=

KL+KU+1.

R (output) DOUBLE PRECISION array, dimension (M)

The row scale factors for A.

C (output) DOUBLE PRECISION array, dimension (N)

The column scale factors for A.

ROWCND (output) DOUBLE PRECISION

Ratio of the smallest R(i) to the largest R(i).

COLCND (output) DOUBLE PRECISION

Ratio of the smallest C(i) to the largest C(i).

AMAX (input) DOUBLE PRECISION

Absolute value of largest matrix entry.

EQUED (output) CHARACTER*1

Specifies the form of equilibration that was done.

= 'N': No equilibration
= 'R': Row equilibration, i.e., A has been pre

multiplied by diag(R). = 'C': Column equilibration, i.e., A has

been postmultiplied by diag(C). = 'B': Both row and column

equilibration, i.e., A has been replaced by diag(R) * A * di

ag(C).

PARAMETERS

THRESH is a threshold value used to decide if row or col

umn scaling should be done based on the ratio of the row or col

umn scaling factors. If ROWCND < THRESH, row scaling is done,

and if COLCND < THRESH, column scaling is done.

LARGE and SMALL are threshold values used to decide if row

scaling should be done based on the absolute size of the largest

matrix element. If AMAX > LARGE or AMAX < SMALL, row scaling is

done.

LAPACK version 3.0 15 June 2000

ZLAQGB(3)