CGBEQUB(1) LAPACK routine (version 3.2) CGBEQUB(1)NAME
CGBEQUB - computes row and column scalings intended to equilibrate an
M-by-N matrix A and reduce its condition number
SYNOPSIS
SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
INFO )
IMPLICIT NONE
INTEGER INFO, KL, KU, LDAB, M, N
REAL AMAX, COLCND, ROWCND
REAL C( * ), R( * )
COMPLEX AB( LDAB, * )
PURPOSE
CGBEQUB computes row and column scalings intended to equilibrate an M-
by-N 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 an absolute value of at most the radix.
R(i) and C(j) are restricted to be a power of the radix 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.
This routine differs from CGEEQU by restricting the scaling factors to
a power of the radix. Baring over- and underflow, scaling by these
factors introduces no additional rounding errors. However, the scaled
entries' magnitured are no longer approximately 1 but lie between
sqrt(radix) and 1/sqrt(radix).
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) DOUBLE PRECISION 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(N,j+kl)
LDAB (input) INTEGER
The leading dimension of the array A. LDAB >= max(1,M).
R (output) REAL array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors for
A.
C (output) REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND (output) REAL
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) REAL
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) REAL
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) November 2008 CGBEQUB(1)
