?opmtr
?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 , where . Use this routine after a call to
C
by Q
or Q
T
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
?sptrd
.Depending on the parameters , *, , or (overwriting the result on
side
and trans
, the routine can form one of the matrix products Q
*C
Q
T
C
C
*Q
C
*Q
T
C
).Input Parameters
In the descriptions below,
r
denotes the order of Q
: If , ; if , .
side
= 'L'
r
= m
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'QorQis applied toTCfrom the left.If,side='R'QorQis applied toTCfrom the right.
- uplo
- Must be'U'or'L'.Use the sameuploas supplied to?sptrd.
- trans
- Must be either'N'or'T'.If, the routine multipliestrans='N'CbyQ.If, the routine multipliestrans='T'CbyQ.T
- m
- The number of rows in the matrixC().m≥0
- n
- The number of columns inC().n≥0
- ap,tau,c
- apandtauare the arrays returned by?sptrd.The dimension ofapmust be at least max(1,r(r+1)/2).The dimension oftaumust be at least max(1,r-1).c(size max(1,contains the matrixldc*n) for column major layout and max(1,ldc*m) for row major layout)C.
- ldc
- The leading dimension ofc;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*TC, orC*Q(as specified byC*QTsideandtrans).
Return Values
This function returns a value
info
.If , the execution is successful.
info
=0If , the
info
= -i
i
-th parameter had an illegal value.Application Notes
The computed product differs from the exact product by a matrix
E
such that ||
, where E
||2
= O
(ε
) ||C
||2
ε
is the machine precision.The total number of floating-point operations is approximately , or .
2*
if m
2
*n
side
= 'L'
2*
if n
2
*m
side
= 'R'
The complex counterpart of this routine is upmtr.