Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

p?larzc

Applies (multiplies by) the conjugate transpose of an elementary reflector as returned by
p?tzrzf
 to a general matrix.

Syntax

void
pclarzc
(
char
*side
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*l
,
MKL_Complex8
*v
,
MKL_INT
*iv
,
MKL_INT
*jv
,
MKL_INT
*descv
,
MKL_INT
*incv
,
MKL_Complex8
*tau
,
MKL_Complex8
*c
,
MKL_INT
*ic
,
MKL_INT
*jc
,
MKL_INT
*descc
,
MKL_Complex8
*work
);
void
pzlarzc
(
char
*side
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*l
,
MKL_Complex16
*v
,
MKL_INT
*iv
,
MKL_INT
*jv
,
MKL_INT
*descv
,
MKL_INT
*incv
,
MKL_Complex16
*tau
,
MKL_Complex16
*c
,
MKL_INT
*ic
,
MKL_INT
*jc
,
MKL_INT
*descc
,
MKL_Complex16
*work
);
Include Files
  • mkl_scalapack.h
Description
The
p?larzc
function
applies a complex elementary reflector
Q
H
 to a complex
m
-by-
n
 distributed matrix
sub(
C
) =
C
(
ic
:
ic
+
m
-1
,
jc
:
jc
+
n
-1)
, from either the left or the right.
Q
 is represented in the form
Q
 =
i
-
tau
*
v
*
v'
,
where
tau
 is a complex scalar and
v
 is a complex vector.
If
tau
 = 0
, then
Q
 is taken to be the unit matrix.
Q
 is a product of
k
 elementary reflectors as returned by
p?tzrzf
.
Input Parameters
side
(global)
if
side
 =
'L'
: form
Q
H
*sub(
C
)
;
if
side
 =
'R'
: form
sub(
C
)*Q
H
 .
m
(global)
The number of rows in the distributed matrix sub(
C
).
(
m
≥
 0)
.
n
(global)
The number of columns in the distributed matrix sub(
C
).
(
n
≥
 0)
.
l
(global)
The columns of the distributed matrix sub(
A
) containing the meaningful part of the Householder reflectors.
If
side
 =
'L'
,
m
≥
l
≥
 0,
if
side
 =
'R'
,
n
≥
l
≥
 0
.
v
(local).
Pointer into the local memory to an array of size
lld_v
 *
LOCc
(
n_v
)
 containing the local pieces of the global distributed matrix
V
representing the Householder transformation
Q
,
V
(
iv
:
iv
+l-1,
jv
)
 if
side
 =
'L'
 and
incv
 = 1
,
V
(
iv
,
jv
:
jv
+
l
-1)
 if
side
 =
'L'
 and
incv
 =
m_v
,
V
(
iv
:
iv
+
l
-1,
jv
)
 if
side
 =
'R'
 and
incv
 = 1
,
V
(
iv
,
jv
:
jv
+
l
-1)
 if
side
 =
'R'
 and
incv
 =
m_v
.
The vector
v
 in the representation of
Q
.
v
 is not used if
tau
 = 0
.
iv
,
jv
(global)
The row and column indices in the global matrix
V
indicating the first row and the first column of the matrix sub(
V
), respectively.
descv
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
V
.
incv
(global)
The global increment for the elements of
V
. Only two values of
incv
 are supported in this version, namely 1 and
m_v
.
incv
 must not be zero.
tau
(local)
Array of size
LOCc
(
jv
) if
incv
 = 1
, and
LOCr
(
iv
) otherwise. This array contains the Householder scalars related to the Householder vectors.
tau
 is tied to the distributed matrix
V
.
c
(local).
Pointer into the local memory to an array of size
lld_c
 *
LOCc
(
jc
+
n
-1)
, containing the local pieces of sub(
C
).
ic
,
jc
(global)
The row and column indices in the global matrix
C
 indicating the first row and the first column of the matrix sub(
C
), respectively.
descc
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
C
.
work
(local).
If incv = 1,
  if side = 'L' ,
    if ivcol = iccol,
      lwork ≥ nqc0
    else
      lwork ≥ mpc0 + max(1, nqc0)
    end if
  else if side = 'R' ,
    lwork ≥ nqc0 + max(max(1, mpc0), numroc(numroc(n+icoffc, nb_v, 0, 0, npcol),
           nb_v, 0, 0, lcmq))  end if
else if incv = m_v,
  if side = 'L' ,
    lwork ≥ mpc0 + max(max(1, nqc0), numroc(numroc(m+iroffc, mb_v, 0, 0, nprow),
           mb_v, 0, 0, lcmp))
  else if side = 'R',
    if ivrow = icrow,
      lwork ≥ mpc0
    else
      lwork ≥ nqc0 + max(1, mpc0)
    end if
  end if
         end if
Here
lcm
 is the least common multiple of
nprow
 and
npcol
;
lcm
 =
ilcm
(
nprow
,
npcol
)
,
lcmp
 =
lcm
/
nprow
,
lcmq
=
lcm
/
npcol
,
iroffc
 =
mod
(
ic
-1,
mb_c
),
icoffc
=
mod
(
jc
-1,
nb_c
)
,
icrow
 =
indxg2p
(
ic
,
mb_c
,
myrow
,
rsrc_c
,
nprow
)
,
iccol
 =
indxg2p
(
jc
,
nb_c
,
mycol
,
csrc_c
,
npcol
)
,
mpc0
 =
numroc
(
m
+
iroffc
,
mb_c
,
myrow
,
icrow
,
nprow
)
,
nqc0
 =
numroc
(
n
+
icoffc
,
nb_c
,
mycol
,
iccol
,
npcol
)
,
ilcm
,
indxg2p
, and
numroc
 are ScaLAPACK tool functions;
myrow
,
mycol
,
nprow
, and
npcol
 can be determined by calling the
function
blacs_gridinfo
.
Output Parameters
c
(local).
On exit, sub(
C
) is overwritten by the
Q
H
*sub(
C
)
 if
side
 =
'L'
, or
sub(
C
)*
Q
H
 if
side
 =
'R'
.

Product and Performance Information

1

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