Contents

# mkl_?getrfnp

Computes the LU factorization of a general m-by-n matrix without pivoting.

## Syntax

Include Files
• mkl.h
Description
The routine computes the
LU
factorization of a general
m
-by-
n
matrix
A
as
`A = L*U,`
where
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 does not use pivoting.
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.
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 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 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.