MAN page from OpenSuSE 12.X lapack-man-3.3.1-15.1.noarch.rpm
Section: LAPACK routine (version 3.2) (1)
Updated: April 2011Index
LAPACK-3 - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number
- SUBROUTINE CGBEQU(
- M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,AMAX, INFO )
- INTEGERINFO, KL, KU, LDAB, M, N
- REALAMAX, COLCND, ROWCND
- REALC( * ), R( * )
- COMPLEXAB( LDAB, * )
CGBEQU computes row and column scalings intended to equilibrate anM-by-N band 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 absolute value 1.
R(i) and C(j) are restricted to be 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.
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) COMPLEX array, dimension (LDAB,N)
The band matrix A, stored 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
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
R (output) REAL array, dimension (M)
If INFO = 0, or INFO > M, R contains the row scale factors
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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