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CGBEQUB

Section: LAPACK routine (version 3.2) (1)
Updated: April 2011
Index

NAME

LAPACK-3 - 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 )
: IMPLICITNONE
: INTEGERINFO, KL, KU, LDAB, M, N
: REALAMAX, COLCND, ROWCND
: REALC( * ), R( * )
: COMPLEXAB( LDAB, * )

PURPOSE

CGBEQUB computes row and column scalings intended to equilibrate anM-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 entriesaq 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

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