Contents

# ?geqr2

Computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

## Syntax

Include Files
• mkl.h
Description
The routine computes a
QR
factorization of a real/complex
m
-by-
n
matrix
A
as
A
=
Q
*
R
.
The routine does not form the matrix
Q
Q
is represented as a product of min(
m
,
n
) elementary reflectors :
Q
=
H
(1)
*H
(2)* ...
*H
(k)
, where
k
= min(
m
,
n
)
Each
H
(i) has the form
H
(i) =
I
-
tau
*
v
*
v
T
for real flavors, or
H
(i) =
I
-
tau
*
v
*
v
H
for complex flavors
where
tau
is a real/complex scalar stored in
tau
[
i
]
, and
v
is a real/complex vector with
v
1:i-1
= 0
and
v
i
= 1
.
On exit,
v
i+1:
m
is stored in
a
(i+1:
m
, i)
.
Input Parameters
A
<datatype>
placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
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 and
max(1,
lda
*
m
)
for row major layout. Array
a
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
.
Output Parameters
a
Overwritten by the factorization data as follows:
on exit, the elements on and above the diagonal of the array
a
contain the min(
n
,
m
)-by-
n
upper trapezoidal matrix
R
(
R
is upper triangular if
m
n
); the elements below the diagonal, with the array
tau
, represent the orthogonal/unitary matrix
Q
as a product of elementary reflectors.
tau
Array, size at least
max(1, min(
m
,
n
))
.
Contains scalar factors of the elementary reflectors.
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.
If
info
= -1011
, memory allocation error occurred.

#### 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