Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?getrf

Computes the LU factorization of a general m-by-n matrix.

Syntax

lapack_int
LAPACKE_sgetrf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
);
lapack_int
LAPACKE_dgetrf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
);
lapack_int
LAPACKE_cgetrf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zgetrf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
);
Include Files
  • mkl.h
Description
The routine computes the
LU
 factorization of a general
m
-by-
n
 matrix
A
 as 

					A = P*L*U,
where
P
 is a permutation matrix,
L
 is lower triangular with unit diagonal elements (lower trapezoidal if
m
 >
n
) and
U
 is upper triangular (upper trapezoidal if
m
 <
n
). The routine uses partial pivoting, with row interchanges.
This routine supports the Progress Routine feature. See Progress Function for details.
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 in the matrix
A
 (
m
≥
 0
).
n
The number of columns in
A
;
n
≥
 0
.
a
Array, size at least max(1,
lda
*
n
) for column-major layout or max(1,
lda
*
m
) for row-major layout. Contains the matrix
A
.
lda
The leading dimension of array
a
, which must be at least max(1,
m
) for column-major layout or max(1,
n
) for row-major layout.
Output Parameters
a
Overwritten by
L
 and
U
. The unit diagonal elements of
L
 are not stored.
ipiv
Array, size at least
max(1,min(
m
,
n
))
. Contains the pivot indices; for
1
≤
i
≤
 min(
m
,
n
)
, row
i
 was interchanged with row
ipiv
(
i
)
.
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
,
u
i
i
 is 0. The factorization has been completed, but
U
 is exactly singular. Division by 0 will occur if you use the factor
U
 for solving a system of linear equations.
Application Notes
The computed
L
 and
U
 are the exact factors of a perturbed matrix
A
 +
E
, where 
|E| ≤
					c(min(m,n))ε
					P|L||U|
c
(
n
)
 is a modest linear function of
n
, and
ε
 is the machine precision.
The approximate number of floating-point operations for real flavors is
(2/3)
n
3
If
m
 =
n
,
(1/3)
n
2
(3
m
-
n
)
If
m
>
n
,
(1/3)
m
2
(3
n
-
m
)
If
m
<
n
.
The number of operations for complex flavors is four times greater.
After calling this routine with
m
 =
n
, you can call the following:
to solve
A
*
X
 =
B
 or
A
T
X
 =
B
 or
A
H
X
 =
B
to estimate the condition number of
A
to compute the inverse of
A
.

Product and Performance Information

1

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