Contents

?getrf

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

Syntax

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
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
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))εP|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

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