Developer Reference

Contents

?gemqrt

Multiplies a general matrix by the orthogonal/unitary matrix Q of the QR factorization formed by
?geqrt
.

Syntax

lapack_int
LAPACKE_sgemqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
nb
,
const
float
*
v
,
lapack_int
ldv
,
const
float
*
t
,
lapack_int
ldt
,
float
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_dgemqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
nb
,
const
double
*
v
,
lapack_int
ldv
,
const
double
*
t
,
lapack_int
ldt
,
double
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_cgemqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
nb
,
const
lapack_complex_float
*
v
,
lapack_int
ldv
,
const
lapack_complex_float
*
t
,
lapack_int
ldt
,
lapack_complex_float
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_zgemqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
nb
,
const
lapack_complex_double
*
v
,
lapack_int
ldv
,
const
lapack_complex_double
*
t
,
lapack_int
ldt
,
lapack_complex_double
*
c
,
lapack_int
ldc
);
Include Files
  • mkl.h
Description
The
?gemqrt
routine overwrites the general real or complex
m
-by-
n
matrix
C
with
side
='L'
side
='R'
trans
= 'N':
Q
*
C
C
*
Q
trans
= 'T':
Q
T
*
C
C
*
Q
T
trans
= 'C':
Q
H
*
C
C
*
Q
H
where
Q
is a real orthogonal (complex unitary) matrix defined as the product of
k
elementary reflectors
Q
=
H
(1)
H
(2)...
H
(
k
) =
I
-
V
*
T
*
V
T
for real flavors, and
Q
=
H
(1)
H
(2)...
H
(
k
) =
I
-
V
*
T
*
V
H
for complex flavors,
generated using the compact WY representation as returned by geqrt.
Q
is of order
m
if
side
= 'L' and of order
n
if
side
= 'R'.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
='L': apply
Q
,
Q
T
, or
Q
H
from the left.
='R': apply
Q
,
Q
T
, or
Q
H
from the right.
trans
='N', no transpose, apply
Q
.
='T', transpose, apply
Q
T
.
='C', transpose, apply
Q
H
.
m
The number of rows in the matrix
C
,
(
m
≥ 0)
.
n
The number of columns in the matrix
C
, (
n
≥ 0).
k
The number of elementary reflectors whose product defines the matrix
Q
. Constraints:
If
side
= 'L',
m
k
≥0
If
side
= 'R',
n
k
≥0.
nb
The block size used for the storage of
t
,
k
nb
≥ 1. This must be the same value of
nb
used to generate
t
in geqrt.
v
Array of size max(1,
ldv
*
k
) for column major layout, max(1,
ldv
*
m
) for row major layout and
side
= 'L', and max(1,
ldv
*
n
) for row major layout and
side
= 'R'.
The
i
th column must contain the vector which defines the elementary reflector
H
(
i
), for
i
= 1,2,...,
k
, as returned by geqrt in the first
k
columns of its array argument
a
.
ldv
The leading dimension of the array
v
.
if
side
= 'L',
ldv
must be at least max(1,
m
)
for column major layout and max(1,
k
) for row major layout
;
if
side
= 'R',
ldv
must be at least max(1,
n
)
for column major layout and max(1,
k
) for row major layout
.
t
Array, size max(1,
ldt
*min(
m
,
n
)) for column major layout and max(1,
ldt
*
nb
) for row major layout.
The upper triangular factors of the block reflectors as returned by geqrt.
ldt
The leading dimension of the array
t
.
ldt
must be at least
nb
for column major layout and max(1,
k
) for row major layout
.
c
The
m
-by-
n
matrix
C
.
ldc
The leadi
n
ng dimension of the array
c
.
ldc
must be at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
c
Overwritten by the product
Q
*
C
,
C
*
Q
,
Q
T
*
C
,
C
*
Q
T
,
Q
H
*
C
, or
C
*
Q
H
as specified by
side
and
trans
.
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.

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