Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.10
  • 10/21/2020
  • Public Content
Contents

?upmtr

Multiplies a complex matrix by the unitary matrix Q determined by
?hptrd
.

Syntax

lapack_int
LAPACKE_cupmtr
(
int
matrix_layout
,
char
side
,
char
uplo
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
const
lapack_complex_float
*
ap
,
const
lapack_complex_float
*
tau
,
lapack_complex_float
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_zupmtr
(
int
matrix_layout
,
char
side
,
char
uplo
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
const
lapack_complex_double
*
ap
,
const
lapack_complex_double
*
tau
,
lapack_complex_double
*
c
,
lapack_int
ldc
);
Include Files
  • mkl.h
Description
The routine multiplies a complex matrix
C
 by
Q
 or
Q
H
, where
Q
 is the unitary matrix formed by hptrd when reducing a packed complex Hermitian matrix
A
 to tridiagonal form:
A
 =
Q*T*Q
H
. Use this routine after a call to
?hptrd
.
Depending on the parameters
side
 and
trans
, the routine can form one of the matrix products
Q*C
,
Q
H
*C
,
C*Q
, or
C*Q
H
 (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
H
 is applied to
C
 from the left.
If
side
 =
'R'
,
Q
 or
Q
H
 is applied to
C
 from the right.
uplo
Must be
'U'
 or
'L'
.
Use the same
uplo
 as supplied to
?hptrd
.
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
H
.
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
?hptrd
.
The size of
ap
 must be at least max(1,
r
(
r
+1)/2).
The size 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,
m
)
for column major layout and
ldc
≥
 max(1,
n
) for row major layout
 .
Output Parameters
c
Overwritten by the product
Q*C
,
Q
H
*C
,
C*Q
, or
C*Q
H
 (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
8*
m
2
*
n
 if
side
 =
'L'
 or
8*
n
2
*
m
 if
side
 =
'R'
.
The real counterpart of this routine is opmtr.

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 reserverd 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