Developer Reference

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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.