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# dlaqgb

```
NAME
DLAQGB - equilibrate 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

SYNOPSIS
SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND,
COLCND, AMAX, EQUED )

CHARACTER      EQUED

INTEGER        KL, KU, LDAB, M, N

DOUBLE         PRECISION AMAX, COLCND, ROWCND

DOUBLE         PRECISION AB( LDAB, * ), C( * ), R( * )

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.

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       (output) DOUBLE PRECISION array, dimension (M)
The row scale factors for A.

C       (output) DOUBLE PRECISION array, dimension (N)
The column scale factors for A.

ROWCND  (output) DOUBLE PRECISION
Ratio of the smallest R(i) to the largest R(i).

COLCND  (output) 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 premul-
tiplied 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Both row and column equilibration, i.e., A has been
replaced by diag(R) * A * diag(C).

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.
```