Contents

# ?tpqrt2

Computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

## Syntax

Include Files
• mkl.h
Description
The input matrix
C
is an (
n
+
m
)-by-
n
matrix
where
A
is an
n
-by-
n
upper triangular matrix, and
B
is an
m
-by-
n
pentagonal matrix consisting of an (
m
-
l
)-by-
n
rectangular matrix
B1
on top of an
l
-by-
n
upper trapezoidal matrix
B2
:
The upper trapezoidal matrix
B2
consists of the first
l
rows of an
n
-by-
n
upper triangular matrix, where 0 ≤
l
≤ min(
m
,
n
). If
l
=0,
B
is an
m
-by-
n
rectangular matrix. If
m
=
l
=
n
,
B
is upper triangular. The matrix
W
contains the elementary reflectors
H(i)
in the
i
th column below the diagonal (of
A
) in the (
n
+
m
)-by-
n
input matrix
C
so that
W
can be represented as
Thus,
V
contains all of the information needed for
W
, and is returned in array
b
.
V
has the same form as
B
:
The columns of
V
represent the vectors which define the
H(i)
s.
The (
m
+
n
)-by-(
m
+
n
) block reflector
H
is then given by
H
= I -
W
*
T
*
W
T
for real flavors, and
H
= I -
W
*
T
*
W
H
for complex flavors
where
W
T
is the transpose of
W
,
W
H
is the conjugate transpose of
W
, and
T
is the upper triangular factor of the block reflector.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The total number of rows in the matrix
B
(
m
≥ 0).
n
The number of columns in
B
and the order of the triangular matrix
A
(
n
≥ 0).
l
The number of rows of the upper trapezoidal part of
B
(min(
m
,
n
) ≥
l
≥ 0).
a
,
b
Arrays:
a
, size
max(1,
lda
*
n
)
contains the
n
-by-
n
upper triangular matrix
A
.
b
, size
max(1,
ldb
*
n
) for column major and max(1,
ldb
*
m
) for row major
, the pentagonal
m
-by-
n
matrix
B
. The first (
m
-
l
) rows contain the rectangular
B1
matrix, and the next
l
rows contain the upper trapezoidal
B2
matrix.
lda
The leading dimension of
a
; at least max(1,
n
).
ldb
The leading dimension of
b
; at least max(1,
m
)
for column major and max(1,
n
) for row major
.
ldt
The leading dimension of
t
; at least max(1,
n
).
Output Parameters
a
The elements on and above the diagonal of the array contain the upper triangular matrix
R
.
b
The pentagonal matrix
V
.
t
Array, size
max(1,
ldt
*
n
)
.
The upper
n
-by-
n
upper triangular factor
T
of the block reflector.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
< 0 and
info
=
-i
, the
i
th argument had an illegal value.
If
info
= -1011
, memory allocation error occurred.

#### Product and Performance Information

1

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