# sgeequb.f man page

sgeequb.f —

## Synopsis

### Functions/Subroutines

subroutinesgeequb(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)SGEEQUB

## Function/Subroutine Documentation

### subroutine sgeequb (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO)

**SGEEQUB**

**Purpose:**

```
SGEEQUB 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. Baring over- and underflow, scaling by
these factors introduces no additional rounding errors. However, the
scaled entries' magnitured 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.
```

*A*

```
A is REAL array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are
to be computed.
```

*LDA*

```
LDA is INTEGER
The leading dimension of the array A. LDA >= 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.

**Date:**

November 2011

Definition at line 146 of file sgeequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK