# sgeequb.f man page

sgeequb.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine sgeequb (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) R, real, dimension( * ) C, real ROWCND, real COLCND, real AMAX, integer INFO)

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

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
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

NAG Ltd.

Date:

December 2016

Definition at line 148 of file sgeequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgeequb(3) is an alias of sgeequb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK