Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

mkl_?getrfnp

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

Syntax

lapack_int
LAPACKE_mkl_sgetrfnp
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_mkl_dgetrfnp
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_mkl_cgetrfnp
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_mkl_zgetrfnp
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
);
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
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.
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 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.