Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?geequb

Computes row and column scaling factors restricted to a power of radix to equilibrate a general matrix and reduce its condition number.

Syntax

lapack_int LAPACKE_sgeequb
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
const float*
a
,
lapack_int
lda
,
float*
r
,
float*
c
,
float*
rowcnd
,
float*
colcnd
,
float*
amax
);
lapack_int LAPACKE_dgeequb
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
const double*
a
,
lapack_int
lda
,
double*
r
,
double*
c
,
double*
rowcnd
,
double*
colcnd
,
double*
amax
);
lapack_int LAPACKE_cgeequb
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
const lapack_complex_float*
a
,
lapack_int
lda
,
float*
r
,
float*
c
,
float*
rowcnd
,
float*
colcnd
,
float*
amax
);
lapack_int LAPACKE_zgeequb
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
const lapack_complex_double*
a
,
lapack_int
lda
,
double*
r
,
double*
c
,
double*
rowcnd
,
double*
colcnd
,
double*
amax
);
Include Files
  • mkl.h
Description
The routine computes row and column scalings intended to equilibrate an
m
-by-
n
 general matrix
A
 and reduce its condition number. The output array
r
 returns the row scale factors and the array
c
 - the column scale factors. These factors are chosen to try to make the largest element in each row and column of the matrix
B
 with elements
b
i
,
j
 =
r
[i-1]*
a
i
,
j
*
c
[j-1]
 have an absolute value of at most the radix.
r
[i-1]
 and
c
[j-1]
 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.
SMLNUM
 and
BIGNUM
 are parameters representing machine precision. You can use the
?lamch
 routines to compute them. For example, compute single precision values of
SMLNUM
 and
BIGNUM
 as follows: 
SMLNUM = slamch ('s')
BIGNUM = 1 / SMLNUM
This routine differs from
?geequ
 by restricting the scaling factors to a power of the radix. Except for over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitudes are no longer equal to approximately 1 but lie between
sqrt(radix)
 and
1/sqrt(radix)
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The number of rows of the matrix
A
;
m
≥
 0
.
n
The number of columns of the matrix
A
;
n
≥
 0
.
a
Array: size
max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout
.
Contains the
m
-by-
n
 matrix
A
 whose equilibration factors are to be computed.
lda
The leading dimension of
a
;
lda
≥
 max(1,
m
)
.
Output Parameters
r
,
c
Arrays:
r
(
m
)
,
c
(
n
)
.
If
info
 = 0
, or
info
>
m
, the array
r
 contains the row scale factors for the matrix
A
.
If
info
 = 0
, the array
c
 contains the column scale factors for the matrix
A
.
rowcnd
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
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
Absolute value of the largest element of the matrix
A
. If
amax
 is very close to
SMLNUM
 or very close to
BIGNUM
, the matrix should be scaled.
Return Values
This function returns a value
info
.
If
info
 = 0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.
If
info
 =
i
,
i
 > 0
, and
i
≤
m
, the
i
-th row of
A
 is exactly zero;
i
>
m
, the (
i
-
m
)-th column of
A
 is exactly zero.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.