Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • 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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804