Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  - computes row and column scalings intended to equilibrate 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 equilibrate 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 absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest 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 illegal 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 routine (version 3.2)               April 2011                            ZGBEQU(3lapack)