- SUBROUTINE ZGBEQUB(
- M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )
- IMPLICIT NONE
- INTEGER INFO, KL, KU, LDAB, M, N
- DOUBLE PRECISION AMAX, COLCND, ROWCND
- DOUBLE PRECISION C( * ), R( * )
- COMPLEX*16 AB( LDAB, * )
PURPOSEZGBEQUB 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 ZGEEQU 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-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