Contents

# ?geqrt

Computes a blocked QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Syntax

Include Files
• mkl.h
Description
The strictly lower triangular matrix
V
contains the elementary reflectors
H
(
i
) in the
i
th column below the diagonal. For example, if
m
=5 and
n
=3, the matrix
V
is
where
v
i
represents one of the vectors that define
H
(
i
). The vectors are returned in the lower triangular part of array
a
.
The 1s along the diagonal of
V
are not stored in
a
.
Let
k
= min(
m
,
n
)
. The number of blocks is
b
= ceiling(
k
/
nb
)
, where each block is of order
nb
except for the last block, which is of order
ib
=
k
- (
b
-1)*
nb
. For each of the
b
blocks, a upper triangular block reflector factor is computed:
t1
,
t2
, ...,
tb
. The
nb
-by-
nb
(and
ib
-by-
ib
for the last block)
t
s are stored in the
nb
-by-
n
array
t
as
t
= (
t1
t2
...
tb
)
.
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).
nb
The block size to be used in the blocked QR (min(
m
,
n
) ≥
nb
≥ 1).
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
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
ldt
t
; at least
nb
for column major layout and max(1, min(
m
,
n
)) for row major layout
.
Output Parameters
a
Overwritten by the factorization data as follows:
The elements on and above the diagonal of the array contain the min(
m
,
n
)-by-
n
upper trapezoidal matrix
R
(
R
is upper triangular if
m
n
); the elements below the diagonal, with the array
t
, present the orthogonal matrix
Q
as a product of min(
m
,
n
) elementary reflectors (see Orthogonal Factorizations).
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 block reflector's factors stored as a sequence of upper triangular blocks.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
< 0 and
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