Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?larft

Forms the triangular factor
T
 of a block reflector
H
 =
I
 -
V
*
T
*
V
**
H
.

Syntax

lapack_int
LAPACKE_slarft
(
int
matrix_layout
,
char
direct
,
char
storev
,
lapack_int
n
,
lapack_int
k
,
const
float
*
v
,
lapack_int
ldv
,
const
float
*
tau
,
float
*
t
,
lapack_int
ldt
);
lapack_int
LAPACKE_dlarft
(
int
matrix_layout
,
char
direct
,
char
storev
,
lapack_int
n
,
lapack_int
k
,
const
double
*
v
,
lapack_int
ldv
,
const
double
*
tau
,
double
*
t
,
lapack_int
ldt
);
lapack_int
LAPACKE_clarft
(
int
matrix_layout
,
char
direct
,
char
storev
,
lapack_int
n
,
lapack_int
k
,
const
lapack_complex_float
*
v
,
lapack_int
ldv
,
const
lapack_complex_float
*
tau
,
lapack_complex_float
*
t
,
lapack_int
ldt
);
lapack_int
LAPACKE_zlarft
(
int
matrix_layout
,
char
direct
,
char
storev
,
lapack_int
n
,
lapack_int
k
,
const
lapack_complex_double
*
v
,
lapack_int
ldv
,
const
lapack_complex_double
*
tau
,
lapack_complex_double
*
t
,
lapack_int
ldt
);
Include Files
  • mkl.h
Description
The routine
?larft
 forms the triangular factor
T
 of a real/complex block reflector
H
 of order
n
, which is defined as a product of
k
 elementary reflectors.
If
direct
 =
'F'
,
H
 =
H
(1)*
H
(2)* . . .*
H
(
k
)
 and
T
 is upper triangular;
If
direct
 =
'B'
,
H
 =
H
(
k
)*. . .*
H
(2)*
H
(1)
 and
T
 is lower triangular.
If
storev
 =
'C'
, the vector which defines the elementary reflector H(
i
) is stored in the
i
-th column of the array
v
, and
H
 =
I
 -
V
*
T
*
V
T
 (for real flavors) or
H
 =
I
 -
V
*
T
*
V
H
 (for complex flavors) .
If
storev
 =
'R'
, the vector which defines the elementary reflector H(
i
) is stored in the
i
-th row of the array
v
, and
H
 =
I
 -
V
T
*
T
*
V
 (for real flavors) or
H
 =
I
 -
V
H
*
T
*
V
 (for complex flavors).
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.
direct
Specifies the order in which the elementary reflectors are multiplied to form the block reflector:
=
'F'
:
H
 =
H
(1)*
H
(2)*. . . *
H
(
k
)
 (forward)
=
'B'
:
H
 =
H
(
k
)*. . .*
H
(2)*
H
(1)
 (backward)
storev
Specifies how the vectors which define the elementary reflectors are stored
(see also
Application Notes
 below)
:
=
'C'
: column-wise
=
'R'
: row-wise.
The order of the block reflector
H
.
n
≥
 0
.
k
The order of the triangular factor
T
 (equal to the number of elementary reflectors).
k
≥
 1
.
v
The size limitations depend on values of parameters
storev
 and
side
 as described in the following table:
storev
 =
C
storev
 =
R
Column major
max(1,
ldv
*
k
)
max(1,
ldv
*
n
)
Row major
max(1,
ldv
*
n
)
max(1,
ldv
*
k
)
The matrix
v
.
See
Application Notes
 below.
ldv
The leading dimension of the array
v
.
If
storev
 =
'C'
,
ldv
≥
 max(1,
n
)
for column major and
ldv
≥
max(1,
k
)
 for row major;
if
storev
 =
'R'
,
ldv
≥
k
for column major and
ldv
≥
max(1,
n
)
 for row major
.
tau
Array, size (
k
).
tau
[
i
-1]
 must contain the scalar factor of the elementary reflector
H
(
i
).
ldt
The leading dimension of the output array
t
.
ldt
≥
k
.
Output Parameters
t
Array, size
ldt
 *
k
. The
k
-by-
k
 triangular factor
T
 of the block reflector. If
direct
 =
'F'
,
T
 is upper triangular; if
direct
 =
'B'
,
T
 is lower triangular. The rest of the array is not used.
v
The matrix
V
.
Application Notes
The shape of the matrix
V
 and the storage of the vectors which define the
H
(
i
) is best illustrated by the following example with
n
 = 5
 and
k
 = 3
. The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.
Equation
Equation

Product and Performance Information

1

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Notice revision #20110804