Contents

?geqlf

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

Syntax

Include Files
• mkl.h
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
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
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
).
a
Array
a
of size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout
contains the 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 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
m
n
, the elements on and below the (
n
-
m
)-th superdiagonal contain the
m
-by-
n
lower trapezoidal matrix
L
; in both cases, the remaining elements, 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 for the matrix
Q
(see Orthogonal Factorizations).
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.
Application Notes
Related routines include:
to generate matrix Q (for real matrices);
to generate matrix Q (for complex matrices);
to apply matrix Q (for real matrices);
to apply matrix Q (for complex matrices).

Product and Performance Information

1

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