Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • 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

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