Developer Reference

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

?geqlf

Computes the QL factorization of a general m-by-n matrix.

Syntax

call sgeqlf
(
m
,
n
,
a
,
lda
,
tau
,
work
,
lwork
,
info
)
call dgeqlf
(
m
,
n
,
a
,
lda
,
tau
,
work
,
lwork
,
info
)
call cgeqlf
(
m
,
n
,
a
,
lda
,
tau
,
work
,
lwork
,
info
)
call zgeqlf
(
m
,
n
,
a
,
lda
,
tau
,
work
,
lwork
,
info
)
call geqlf
(
a
[
,
tau
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine forms the
QL
factorization of a general
m
-by-
n
matrix
A
(see Orthogonal Factorizations). No pivoting is performed.
The routine does not form the matrix
Q
explicitly. Instead,
Q
is represented as a product of min(
m
,
n
) elementary reflectors. Routines are provided to work with
Q
in this representation.
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
m
INTEGER
.
The number of rows in the matrix
A
(
m
0
).
n
INTEGER
.
The number of columns in
A
(
n
0
).
a
,
work
REAL
for
sgeqlf
DOUBLE PRECISION
for
dgeqlf
COMPLEX
for
cgeqlf
DOUBLE COMPLEX
for
zgeqlf
.
Arrays:
Array
a
(
lda
,*)
contains the matrix
A
.
The second dimension of
a
must be at least max(1,
n
).
work
is a workspace array, its dimension
max(1,
lwork
)
.
lda
INTEGER
.
The leading dimension of
a
; at least max(1,
m
).
lwork
INTEGER
.
The size of the
work
array; at least max(1,
n
).
If
lwork
= -1
, then a workspace query is assumed; the routine only calculates the optimal size of the
work
array, returns this value as the first entry of the
work
array, and no error message related to
lwork
is issued by xerbla.
See
Application Notes
for the suggested value of
lwork
.
Output Parameters
a
Overwritten on exit by the factorization data as follows:
if
m
n
, the lower triangle of the subarray
a
(
m
-
n
+1:
m
, 1:
n
) contains the
n
-by-
n
lower triangular matrix
L
; if