Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?latrz

Factors an upper trapezoidal matrix by means of orthogonal/unitary transformations.

Syntax

call slatrz
(
m
,
n
,
l
,
a
,
lda
,
tau
,
work
)
call dlatrz
(
m
,
n
,
l
,
a
,
lda
,
tau
,
work
)
call clatrz
(
m
,
n
,
l
,
a
,
lda
,
tau
,
work
)
call zlatrz
(
m
,
n
,
l
,
a
,
lda
,
tau
,
work
)
Include Files
  • mkl.fi
Description
The routine
?latrz
factors the
m
-by-(
m
+
l
) real/complex upper trapezoidal matrix
[
A
1
A
2] = [
A
(1:
m
,1:
m
)
A
(1:
m
,
n
-
l
+1:
n
)]
as (
R
0 )*
Z
, by means of orthogonal/unitary transformations.
Z
is an (
m+l
)-by-(
m+l
) orthogonal/unitary matrix and
R
and
A
1 are
m
-by -
m
upper triangular matrices.
Input Parameters
m
INTEGER
. The number of rows of the matrix
A
.
m
0
.
n
INTEGER
. The number of columns of the matrix
A
.
n
0
.
l
INTEGER
. The number of columns of the matrix
A
containing the meaningful part of the Householder vectors.
n
-
m
l
0
.
a
REAL
for
slatrz
DOUBLE PRECISION
for
dlatrz
COMPLEX
for
clatrz
DOUBLE COMPLEX
for
zlatrz
.
Array,
DIMENSION
(
lda
,
n
).
On entry, the leading
m
-by-
n
upper trapezoidal part of the array
a
must contain the matrix to be factorized.
lda
INTEGER
. The leading dimension of the array
a
.
lda
max(1,
m
)
.
work
REAL
for
slatrz
DOUBLE PRECISION
for
dlatrz
COMPLEX
for
clatrz
DOUBLE COMPLEX
for
zlatrz
.
Workspace array,
DIMENSION
(
m
).
Output Parameters
a
On exit, the leading
m
-by-
m
upper triangular part of
a
contains the upper triangular matrix
R
, and elements
n
-
l
+1 to
n
of the first
m
rows of
a
, with the array
tau
, represent the orthogonal/unitary matrix
Z
as a product of
m
elementary reflectors.