Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?tprfb

Applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks.

Syntax

lapack_int
LAPACKE_stprfb
(
int
matrix_layout
,
char
side
,
char
trans
,
char
direct
,
char
storev
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
const
float
*
v
,
lapack_int
ldv
,
const
float
*
t
,
lapack_int
ldt
,
float
*
a
,
lapack_int
lda
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dtprfb
(
int
matrix_layout
,
char
side
,
char
trans
,
char
direct
,
char
storev
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
const
double
*
v
,
lapack_int
ldv
,
const
double
*
t
,
lapack_int
ldt
,
double
*
a
,
lapack_int
lda
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_ctprfb
(
int
matrix_layout
,
char
side
,
char
trans
,
char
direct
,
char
storev
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
const
lapack_complex_float
*
v
,
lapack_int
ldv
,
const
lapack_complex_float
*
t
,
lapack_int
ldt
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_ztprfb
(
int
matrix_layout
,
char
side
,
char
trans
,
char
direct
,
char
storev
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
const
lapack_complex_double
*
v
,
lapack_int
ldv
,
const
lapack_complex_double
*
t
,
lapack_int
ldt
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The
?tprfb
 routine applies a real or complex "triangular-pentagonal" block reflector
H
,
H
T
, or
H
H
 from either the left or the right to a real or complex matrix
C
, which is composed of two blocks
A
 and
B
.
The block
B
 is
m
-by-
n
. If
side
 = 'R',
A
 is
m
-by-
k
, and if
side
 = 'L',
A
 is of size
k
-by-
n
.
Table
The pentagonal matrix
V
 is composed of a rectangular block
V1
 and a trapezoidal block
V2
. The size of the trapezoidal block is determined by the parameter
l
, where 0≤
l
≤
k
. if
l
=
k
, the
V2
 block of
V
 is triangular; if
l
=0, there is no trapezoidal block, thus
V
 =
V1
 is rectangular.
direct
='F'
direct
='B'
storev
='C'
Equation
V2
 is upper trapezoidal (first
l
 rows of
k
-by-
k
 upper triangular)
Equation
V2
 is lower trapezoidal (last
l
 rows of
k
-by-
k
 lower triangular matrix)
storev
='R'
Equation
V2
 is lower trapezoidal (first
l
 columns of
k
-by-
k
 lower triangular matrix)
Equation
V2
 is upper trapezoidal (last
l
 columns of
k
-by-
k
 upper triangular matrix)
side
='L'
side
='R'
storev
='C'
V
 is
m
-by-
k
V2
 is
l
-by-
k
V
 is
n
-by-
k
V2
 is
l
-by-
k
storev
='R'
V
 is
k
-by-
m
V2
 is
k
-by-
l
V
 is
k
-by-
n
V2
 is
k
-by-
l
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
 ).
side
= 'L': apply
H
,
H
T
, or
H
H
 from the left,
= 'R': apply
H
,
H
T
, or
H
H
 from the right.
trans
= 'N': apply
H
 (no transpose),
= 'T': apply
H
T
 (transpose),
= 'C': apply
H
H
 (conjugate transpose).
direct
Indicates how
H
 is formed from a product of elementary reflectors:
= 'F':
H
 =
H
(1)
H
(2) . . .
H
(
k
) (Forward),
= 'B':
H
 =
H
(
k
) . . .
H
(2)
H
(1) (Backward).
storev
Indicates how the vectors that define the elementary reflectors are stored:
= 'C': Columns,
= 'R': Rows.
m
The total number of rows in the matrix
B
 (
m
 ≥ 0).
n
The number of columns in
B
 (
n
 ≥ 0).
k
The order of the matrix
T
, which is the number of elementary reflectors whose product defines the block reflector. (
k
 ≥ 0)
l
The order of the trapezoidal part of
V
. (
k
 ≥
l
 ≥ 0).
v
An array containing the pentagonal matrix
V
 (the elementary reflectors
H
(1),
H
(2), …,
H
(k)
. The size limitations depend on values of parameters
storev
 and
side
 as described in the following table
storev
 =
C
storev
 =
R
side
 =
L
side
 =
R
side
 =
L
side
 =
R
Column major
max(1,
ldv
*
k
)
max(1,
ldv
*
k
)
max(1,
ldv
*
m
)
max(1,
ldv
*
n
)
Row major
max(1,
ldv
*
m
)
max(1,
ldv
*
n
)
max(1,
ldv
*
k
)
max(1,
ldv
*
k
)
ldv
The leading dimension of the array
v
.It should satisfy the following conditions:
storev
 =
C
storev
 =
R
side
 =
L
side
 =
R
side
 =
L
side
 =
R
Column major
max(1,
m
)
max(1,
n
)
max(1,
k
)
max(1,
k
)
Row major
max(1,
k
)
max(1,
k
)
max(1,
m
)
max(1,
n
)
t
Array size
max(1,
ldt
 *
k
)
. The triangular
k
-by-
k
 matrix
T
 in the representation of the block reflector.
ldt
The leading dimension of the array
t
 (
ldt
 ≥
k
).
a
size should satisfy the following conditions:
k
 if
side
 = 'R'.
side
 =
L
side
 =
R
Column major
max(1,
lda
*
n
)
max(1,
lda
*
k
)
Row major
max(1,
lda
*
k
)
max(1,
lda
*
m
)
The
k
-by-
n
 or
m
-by-
k
 matrix
A
.
lda
The leading dimension of the array
a
 should satisfy the following conditions:
side
 =
L
side
 =
R
Column major
max(1,
k
)
max(1,
m
)
Row major
max(1,
n
)
max(1,
k
)
b
Array size
at least max(1,
ldb
 *
n
) for column major layout and max(1,
ldb
 *
m
) for row major layout
, the
m
-by-
n
 matrix
B
.
ldb
The leading dimension of the array
b
 (
ldb
 ≥ max(1,
m
)
for column major layout and
ldb
 ≥ max(1,
n
) for row major layout
).
Output Parameters
a
Contains the corresponding block of
H
*
C
,
H
T
*
C
,
H
H
*
C
,
C
*
H
,
C
*
H
T
, or
C
*
H
H
.
b
Contains the corresponding block of
H
*
C
,
H
T
*
C
,
H
H
*
C
,
C
*
H
,
C
*
H
T
, or
C
*