# sgbequ.f man page

sgbequ.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine sgbequ (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO)

**SGBEQU**

**Purpose:**

```
SGBEQU 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.
```

**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)
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*

```
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
```

*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.

**Date:**

November 2011

Definition at line 153 of file sgbequ.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

sgbequ(3) is an alias of sgbequ.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK