Contents

# ?getrf2

Computes LU factorization using partial pivoting with row interchanges.

## Syntax

Include Files
• mkl.h
Description
?getrf2
computes an LU factorization of a general
m
-by-
n
matrix
A
using partial pivoting with row interchanges.
The factorization has the form
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
).
This is the recursive version of the algorithm. It divides the matrix into four submatrices: where
A11
is
n1
by
n1
and
A22
is
n2
by
n2
with
n1
= min(
m
,
n
), and
n2
=
n
-
n1
.
The subroutine calls itself to factor ,
do the swaps on , solve
A12
, update
A22
, then it calls itself to factor
A22
and do the swaps on
A21
.
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
lda
*
n
.
On entry, the
m
-by-
n
matrix to be factored.
lda
The leading dimension of the array
a
.
lda
>= max(1,
m
).
Output Parameters
a
On exit, the factors
L
and
U
from the factorization
A
=
P
*
L
*
U
; the unit diagonal elements of
L
are not stored.
ipiv
Array, size (min(
m
,
n
)).
The pivot indices; for 1 <=
i
<= min(
m
,
n
), row
i
of the matrix was interchanged with row
ipiv
[
i
- 1]
.
Return Values
This function returns a value
info
.
= 0: successful exit
< 0: if info = -
i
, the
i
-th argument had an illegal value.
> 0: if info =
i
,
U
i
,
i
is exactly zero. The factorization has been completed, but the factor
U
is exactly singular, and division by zero will occur if it is used to solve a system of equations.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804