Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?opmtr

Multiplies a real matrix by the real orthogonal matrix Q determined by
?sptrd
.

Syntax

lapack_int
LAPACKE_sopmtr
(
int
matrix_layout
,
char
side
,
char
uplo
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
const
float
*
ap
,
const
float
*
tau
,
float
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_dopmtr
(
int
matrix_layout
,
char
side
,
char
uplo
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
const
double
*
ap
,
const
double
*
tau
,
double
*
c
,
lapack_int
ldc
);
Include Files
  • mkl.h
Description
The routine multiplies a real matrix
C
 by
Q
 or
Q
T
, where
Q
 is the orthogonal matrix
Q
 formed by sptrd when reducing a packed real symmetric matrix
A
 to tridiagonal form:
A
 =
Q
*
T
*
Q
T
. Use this routine after a call to
?sptrd
.
Depending on the parameters
side
 and
trans
, the routine can form one of the matrix products
Q
*
C
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
 (overwriting the result on
C
).
Input Parameters
In the descriptions below,
r
 denotes the order of
Q
:
If
side
 =
'L'
,
r
 =
m
; if
side
 =
'R'
,
r
 =
n
.
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
Must be either
'L'
 or
'R'
.
If
side
 =
'L'
,
Q
 or
Q
T
 is applied to
C
 from the left.
If
side
 =
'R'
,
Q
 or
Q
T
 is applied to
C
 from the right.
uplo
Must be
'U'
 or
'L'
.
Use the same
uplo
 as supplied to
?sptrd
.
trans
Must be either
'N'
 or
'T'
.
If
trans
 =
'N'
, the routine multiplies
C
 by
Q
.
If
trans
 =
'T'
, the routine multiplies
C
 by
Q
T
.
m
The number of rows in the matrix
C
 (
m
≥
 0
).
n
The number of columns in
C
 (
n
≥
 0
).
ap
,
tau
,
c
ap
 and
tau
 are the arrays returned by
?sptrd
.
The dimension of
ap
 must be at least max(1,
r
(
r
+1)/2).
The dimension of
tau
 must be at least max(1,
r
-1).
c
(size max(1,
ldc
*
n
) for column major layout and max(1,
ldc
*
m
) for row major layout)
 contains the matrix
C
.
ldc
The leading dimension of
c
;
ldc
≥
 max(1,
n
)
for column major layout and
ldc
≥
 max(1,
m
) for row major layout
 .
Output Parameters
c
Overwritten by the product
Q
*
C
,
Q
T
*
C
,
C
*
Q
, or
C
*
Q
T
 (as specified by
side
 and
trans
).
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.
Application Notes
The computed product differs from the exact product by a matrix
E
 such that
||
E
||
2
 =
O
(
ε
) ||
C
||
2
, where
ε
 is the machine precision.
The total number of floating-point operations is approximately
2*
m
2
*
n
 if
side
 =
'L'
, or
2*
n
2
*
m
 if
side
 =
'R'
.
The complex counterpart of this routine is upmtr.

Product and Performance Information

1

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