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
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.