---
name: "dlaqgb"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlaqgb/3lapack"
---

# dlaqgb(3lapack)

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

## NAME

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

## 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 (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 = 'B':  Both row and column equilibration, i.e., A has been replaced by diag(R) \* A \* diag(C).

## 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.