Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?tpmqrt

Applies a real or complex orthogonal matrix obtained from a "triangular-pentagonal" complex block reflector to a general real or complex matrix, which consists of two blocks.

Syntax

lapack_int
LAPACKE_stpmqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
lapack_int
nb
,
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_dtpmqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
lapack_int
nb
,
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_ctpmqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
lapack_int
nb
,
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_ztpmqrt
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_int
l
,
lapack_int
nb
,
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 columns of the pentagonal matrix
V
 contain the elementary reflectors
H
(1),
H
(2), ...,
H
(
k
);
V
 is composed of a rectangular block
V1
 and a trapezoidal block
V2
:
Equation
The size of the trapezoidal block
V2
 is determined by the parameter
l
, where 0 ≤
l
 ≤
k
.
V2
 is upper trapezoidal, consisting of the first
l
 rows of a
k
-by-
k
 upper triangular matrix.
If
l
=
k
,
V2
 is upper triangular;
If
l
=0, there is no trapezoidal block, so
V
 =
V1
 is rectangular.
If
side
 = 'L':
Equation
where
A
 is
k
-by-
n
,
B
 is
m
-by-
n
 and
V
 is
m
-by-
k
.
If
side
 = 'R':
Equation
where
A
 is
m
-by-
k
,
B
 is
m
-by-
n
 and
V
 is
n
-by-
k
.
The real/complex orthogonal matrix
Q
 is formed from
V
 and
T
.
If
trans
='N' and
side
='L',
c
 contains
Q
 *
C
 on exit.
If
trans
='T' and
side
='L',
C
 contains
Q
T
 *
C
 on exit.
If
trans
='C' and
side
='L',
C
 contains
Q
H
 *
C
 on exit.
If
trans
='N' and
side
='R',
C
 contains
C
 *
Q
 on exit.
If
trans
='T' and
side
='R',
C
 contains
C
 *
Q
T
 on exit.
If
trans
='C' and
side
='R',
C
 contains
C
 *
Q
H
 on exit.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
=
'L'
: apply
Q
,
Q
T
, or
Q
H
 from the left.
=
'R'
: apply
Q
,
Q
T
, or
Q
H
 from the right.
trans
=
'N'
, no transpose, apply
Q
.
=
'T'
, transpose, apply
Q
T
.
=
'C'
, transpose, apply
Q
H
.
m
The number of rows in the matrix
B
,
(
m
 ≥ 0)
.
n
The number of columns in the matrix
B
,
(
n
 ≥ 0)
.
k
The number of elementary reflectors whose product defines the matrix
Q
,
(
k
 ≥ 0)
.
l
The order of the trapezoidal part of
V
 (
k
 ≥
l
 ≥ 0).
nb
The block size used for the storage of
t
,
k
 ≥
nb
 ≥ 1. This must be the same value of
nb
 used to generate
t
 in
tpqrt
.
v
Size
ldv
*
k
 for column major layout;
ldv
*
m
 for row major layout and
side
 = 'L',
ldv
*
n
 for row major layout and
side
 = 'R'.
The
i
th column must contain the vector which defines the elementary reflector
H
(
i
), for
i
 = 1,2,...,
k
, as returned by
tpqrt
 in array argument
b
.
ldv
The leading dimension of the array
v
.
If
side
 = 'L',
ldv
 must be at least max(1,
m
)
for column major layout and max(1,
k
 for row major layout
;
If
side
 = 'R',
ldv
 must be at least max(1,
n
)
for column major layout and max(1,
k
 for row major layout
.
t
Array, size
ldt
*
k
 for column major layout and
ldt
*
nb
 for row major layout
.
The upper triangular factors of the block reflectors as returned by
tpqrt
ldt
The leading dimension of the array
t
.
ldt
 must be at least
nb
for column major layout and max(1,
k
 for row major layout
.
a
If
side
 = 'L', size
lda
*
n
 for column major layout and
lda
*
k
 for row major layout .
.
If
side
 = 'R', size
lda
*
k
 for column major layout and
lda
*
m
 for row major layout .
.
The
k
-by-
n
 or
m
-by-
k
 matrix
A
.
lda
The leading dimension of the array
a
.
If
side
 = 'L',
lda
 must be at least max(1,
k
)
for column major layout and max(1,
n
 for row major layout
.
If
side
 = 'R',
lda
 must be at least max(1,
m
)
for column major layout and max(1,
k
 for row major layout
.
b
Size
ldb
*
n
 for column major layout and
ldb
*
m
 for row major layout
.
The
m
-by-
n
 matrix
B
.
ldb
The leading dimension of the array
b
.
ldb
 must be at least max(1,
m
)
for column major layout and max(1,
n
 for row major layout
.
Output Parameters
a
Overwritten by the corresponding block of the product
Q
*
C
,
C
*
Q
,
Q
T
*
C
,
C
*
Q
T
,
Q
H
*
C
, or
C
*
Q
H
.
b
Overwritten by the corresponding block of the product
Q
*
C
,
C
*
Q
,
Q
T
*
C
,
C
*
Q
T
,
Q
H
*
C
, or
C
*
Q
H
.
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.

Product and Performance Information

1

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