---
name: "sgbequb.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/sgbequb.f"
---

# sgbequb.f(3)

## NAME

SRC/sgbequb.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgbequb** (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)\
 **SGBEQUB**

## Function/Subroutine Documentation

### subroutine sgbequb (integer m, integer n, integer kl, integer ku, real, dimension( ldab, \* ) ab, integer ldab, real, dimension( \* ) r, real, dimension( \* ) c, real rowcnd, real colcnd, real amax, integer info)

**SGBEQUB**

**Purpose:**

```
!>
!> SGBEQUB computes row and column scalings intended to equilibrate an
!> M-by-N 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 an absolute value of at most
!> the radix.
!>
!> R(i) and C(j) are restricted to be a power of the radix 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.
!>
!> This routine differs from SGEEQU by restricting the scaling factors
!> to a power of the radix.  Barring over- and underflow, scaling by
!> these factors introduces no additional rounding errors.  However, the
!> scaled entries' magnitudes are no longer approximately 1 but lie
!> between sqrt(radix) and 1/sqrt(radix).
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
```

*KL*

```
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!>
```

*KU*

```
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>
```

*AB*

```
!>          AB is REAL 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(N,j+kl)
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array A.  LDAB >= max(1,M).
!>
```

*R*

```
!>          R is REAL array, dimension (M)
!>          If INFO = 0 or INFO > M, R contains the row scale factors
!>          for A.
!>
```

*C*

```
!>          C is REAL array, dimension (N)
!>          If INFO = 0,  C contains the column scale factors for A.
!>
```

*ROWCND*

```
!>          ROWCND is 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*

```
!>          COLCND is 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*

```
!>          AMAX is 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*

```
!>          INFO is 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
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **158** of file **sgbequb.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.