Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

p?tzrzf

Reduces the upper trapezoidal matrix
A
 to upper triangular form.

Syntax

void
pstzrzf
(
MKL_INT
*m
,
MKL_INT
*n
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*tau
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdtzrzf
(
MKL_INT
*m
,
MKL_INT
*n
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*tau
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pctzrzf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex8
*tau
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pztzrzf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex16
*tau
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
p?tzrzf
function
reduces the
m
-by-
n
 (
m
 ≤
n
) real/complex upper trapezoidal matrix sub(
A
)=
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1) to upper triangular form by means of orthogonal/unitary transformations. The upper trapezoidal matrix
A
 is factored as
A
 = (
R
 0)*
Z
,
where
Z
 is an
n
-by-
n
 orthogonal/unitary matrix and
R
 is an
m
-by-
m
 upper triangular matrix.
Input Parameters
m
(global) The number of rows in the matrix sub(
A
);
(
m
≥
0)
.
n
(global) The number of columns in the matrix sub(
A
)
(
n
≥
0)
.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
n
-1)
. Contains the local pieces of the
m
-by-
n
 distributed matrix sub (
A
) to be factored.
ia
,
ja
(global) The row and column indices in the global matrix
A
 indicating the first row and the first column of the submatrix
A
, respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
work
(local)
Workspace array of size of
lwork
.
lwork
(local or global) size of
work
, must be at least
lwork
≥
mb_a*
(
mp
0+
nq
0+
mb_a
)
, where
iroff
 =
mod
(
ia
-1,
mb_a
)
,
icoff
 =
mod
(
ja
-1,
nb_a
)
,
iarow
 =
indxg2p
(
ia
,
mb_a
,
MYROW
,
rsrc_a
,
NPROW
)
,
iacol
 =
indxg2p
(
ja
,
nb_a
,
MYCOL
,
csrc_a
,
NPCOL
)
,
mp
0 =
numroc
 (
m
+
iroff
,
mb_a
,
MYROW
,
iarow
,
NPROW
)
,
nq
0 =
numroc
 (
n
+
icoff
,
nb_a
,
MYCOL
,
iacol
,
NPCOL
)
mod(
x
,
y
)
 is the integer remainder of
x
/
y
.
indxg2p
 and
numroc
 are ScaLAPACK tool functions;
MYROW
,
MYCOL
,
NPROW
 and
NPCOL
 can be determined by calling the
function
blacs_gridinfo
.
If
lwork
 = -1
, then
lwork
 is global input and a workspace query is assumed; the
function
only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
Output Parameters
a
On exit, the leading
m
-by-
m
 upper triangular part of sub(
A
) contains the upper triangular matrix
R
, and elements
m
+1 to
n
 of the first
m
 rows of sub (
A
), with the array
tau
, represent the orthogonal/unitary matrix
Z
 as a product of
m
 elementary reflectors.
work
[0]
On exit
work
[0]
 contains the minimum value of
lwork
 required for optimum performance.
tau
(local)
Array of size
LOCr
(
ia
+
m
-1)
.
Contains the scalar factor of elementary reflectors.
tau
 is tied to the distributed matrix
A
.
info
(global)
= 0
: the execution is successful.
< 0
:if the
i
-th argument is an array and the
j-
th entry
, indexed
j
 - 1,
 had an illegal value, then
info
 = -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
 =
-i
.
Application Notes
The factorization is obtained by the Householder's method.
The
k
-th transformation matrix,
Z
(
k
), which is or whose conjugate transpose is used to introduce zeros into the
(
m
 -
k
 +1)
-th row of sub(
A
), is given in the form
Equation
where
T
(
k
) =
i
 -
tau
*
u
(
k
)*
u
(
k
)',
Equation
tau
 is a scalar and
Z
(
k
) is an (
n
 -
m
) element vector.
tau
 and
Z
(
k
) are chosen to annihilate the elements of the
k
-th row of sub(
A
). The scalar
tau
 is returned in the
k
-th element of
tau
, indexed
k
-1,
 and the vector
u
(
k
) in the
k
-th row of sub(
A
), such that the elements of
Z
(
k
) are in
a
(
k
,
m
 + 1),...,
a
(
k
,
n
)
. The elements of
R
 are returned in the upper triangular part of sub(
A
).
Z
 is given by
Z
 =
Z
(1) *
Z
(2) *... *
Z
(
m
).

Product and Performance Information

1

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