DGBEQUB(1) LAPACK routine (version 3.2) DGBEQUB(1)NAME
DGBEQUB - computes row and column scalings intended to equilibrate an
M-by-N matrix A and reduce its condition number
SUBROUTINE DGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
DGBEQUB 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 DGEEQU 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).
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-
LDAB (input) INTEGER
The leading dimension of the array A. LDAB >= max(1,M).
R (output) DOUBLE PRECISION array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors for
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
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
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
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 DGBEQUB(1)