Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?gerqf

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

Syntax

lapack_int
LAPACKE_sgerqf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
float
*
tau
);
lapack_int
LAPACKE_dgerqf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
double
*
tau
);
lapack_int
LAPACKE_cgerqf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_complex_float
*
tau
);
lapack_int
LAPACKE_zgerqf
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_complex_double
*
tau
);
Include Files
  • mkl.h
Description
The routine forms the
RQ
factorization of a general
m
-by-
n
matrix
A
No pivoting is performed.
The routine does not form the matrix
Q
explicitly. Instead,
Q
is represented as a product of min(
m
,
n
) elementary reflectors. Routines are provided to work with
Q
in this representation.
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
a
of size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout
contains the
m
-by-
n
matrix
A
.
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten on exit by the factorization data as follows:
if
m
n
, the upper triangle of the subarray
a
(1:
m
,
n
-
m
+1:
n
) contains the
m
-by-
m
upper triangular matrix
R
;
if
m
n
, the elements on and above the (
m
-
n
)th subdiagonal contain the
m
-by-
n
upper trapezoidal matrix
R
;
in both cases, the remaining elements, with the array
tau
, represent the orthogonal/unitary matrix
Q
as a product of min(
m
,
n
) elementary reflectors.
tau
Array, size at least max (1, min(
m
,
n
)). (See Orthogonal Factorizations.)
Contains scalar factors of the elementary reflectors for the matrix
Q
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
Application Notes
Related routines include:
to generate matrix Q (for real matrices);
to generate matrix Q (for complex matrices);
to apply matrix Q (for real matrices);
to apply matrix Q (for complex matrices).

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