DLAQGB
November 2006
Purpose
DLAQGB equilibrates a general M by N band matrix A with KL
subdiagonals and KU superdiagonals using the row and scaling factors
in the vectors R and C.
subdiagonals and KU superdiagonals using the row and scaling factors
in the vectors R and C.
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/output) 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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix. |
| LDAB |
(input) INTEGER
The leading dimension of the array AB. LDA >= KL+KU+1.
|
| R |
(input) DOUBLE PRECISION array, dimension (M)
The row scale factors for A.
|
| C |
(input) DOUBLE PRECISION array, dimension (N)
The column scale factors for A.
|
| ROWCND |
(input) DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).
|
| COLCND |
(input) DOUBLE PRECISION
Ratio of the smallest C(i) to the largest C(i).
|
| AMAX |
(input) DOUBLE PRECISION
Absolute value of largest matrix entry.
|
| EQUED |
(output) CHARACTER*1
Specifies the form of equilibration that was done.
= 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C). |
Internal Parameters
THRESH is a threshold value used to decide if row or column scaling
should be done based on the ratio of the row or column scaling
factors. If ROWCND < THRESH, row scaling is done, and if
COLCND < THRESH, column scaling is done.
LARGE and SMALL are threshold values used to decide if row scaling
should be done based on the absolute size of the largest matrix
element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
should be done based on the ratio of the row or column scaling
factors. If ROWCND < THRESH, row scaling is done, and if
COLCND < THRESH, column scaling is done.
LARGE and SMALL are threshold values used to decide if row scaling
should be done based on the absolute size of the largest matrix
element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.