# sgeequ.f - Man Page

SRC/sgeequ.f

## Synopsis

### Functions/Subroutines

subroutine sgeequ (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)
SGEEQU

## Function/Subroutine Documentation

### subroutine sgeequ (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

SGEEQU

Purpose:

``` SGEEQU 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 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.```

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.

Definition at line 137 of file sgeequ.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK