DGBEQUB
Purpose
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-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).
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) 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 |