Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
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

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