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

# dgbequ(3lapack)

computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

## NAME

DGBEQU - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

## SYNOPSIS

- SUBROUTINE DGBEQU(

  M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )

- INTEGER

  INFO, KL, KU, LDAB, M, N

- DOUBLE

  PRECISION AMAX, COLCND, ROWCND

- DOUBLE

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

## PURPOSE

DGBEQU computes row and column scalings intended to equilibrate an M-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.\

## 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) DOUBLE PRECISION 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 follows: 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) 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