zgbequ(3)

NAME

ZGBEQU - compute row and column scalings intended to equi

librate an M-by-N band matrix A and reduce its condition number

SYNOPSIS

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

PURPOSE

ZGBEQU computes row and column scalings intended to equi

librate an M-by-N band matrix A and reduce its condition number.

R returns the row scale factors and C the column scale factors,

chosen to try to make the largest element in each row and column

of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have abso

lute value 1.

R(i) and C(j) are restricted to be between SMLNUM = small

est safe number and BIGNUM = largest safe number. Use of these

scaling factors is not guaranteed to reduce the condition number

of A but works well in practice.

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) COMPLEX*16 array, dimension (LDAB,N)

The band matrix A, stored 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).

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >=

KL+KU+1.

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

If INFO = 0, or INFO > M, R contains the row scale

factors for A.

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

If INFO = 0, C contains the column scale factors

for A.

ROWCND (output) DOUBLE PRECISION

If INFO = 0 or INFO > M, ROWCND contains the ratio

of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and

AMAX is neither too large nor too small, it is not worth scaling

by R.

COLCND (output) DOUBLE PRECISION

If INFO = 0, COLCND contains the ratio of the

smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not

worth scaling by C.

AMAX (output) DOUBLE PRECISION

Absolute value of largest matrix element. If AMAX

is very close to overflow or very close to underflow, the matrix

should be scaled.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero

LAPACK version 3.0 15 June 2000

ZGBEQU(3)