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template<typename T>
void ormtr(char *side, char *uplo, char *trans, integer *m, integer *n, T *a, integer *lda, T *tau, T *c, integer *ldc, T *work, integer *lwork, integer *info)# Apply Q or Q’ from tridiagonal reduction.
Purpose:
Apply Q or Q' from tridiagonal reduction. Overwrite the general real m-by-n matrix c with side = 'L' side = 'R' trans = 'N': Q * C C * Q trans = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix of order nq, with nq = m if side = 'L' and nq = n if side = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD: if uplo = 'U', Q = H(nq-1) . . . H(2) H(1); if uplo = 'L', Q = H(1) H(2) . . . H(nq-1).
- Parameters:
side – [in]
side is char*
= ‘L’: apply Q or Q**T from the Left;
= ‘R’: apply Q or Q**T from the Right.uplo – [in]
uplo is char*
= ‘U’: Upper triangle of a contains elementary reflectors from SSYTRD;
= ‘L’: Lower triangle of a contains elementary reflectors from SSYTRD.trans – [in]
trans is char*
= ‘N’: No transpose, apply Q;
= ‘T’: Transpose, apply Q**T.m – [in]
m is integer*
The number of rows of the matrix c. m >= 0.
n – [in]
n is integer*
The number of columns of the matrix c. n >= 0.
a – [in]
a is float/double array, dimension
(lda,m) if side = ‘L’
(lda,n) if side = ‘R’
The vectors which define the elementary reflectors, as returned by SSYTRD.
lda – [in]
lda is integer*
The leading dimension of the array a.
lda >= fla_max(1,m) if side = ‘L’; lda >= fla_max(1,n) if side = ‘R’.tau – [in]
tau is float/double array, dimension
(m-1) if side = ‘L’
(n-1) if side = ‘R’
tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.
c – [inout]
c is float/double array, dimension (ldc,n)
On entry, the m-by-n matrix c.
On exit, c is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.ldc – [in]
ldc is integer*
The leading dimension of the array c. ldc >= fla_max(1,m).
WORK – [out]
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK – [in]
LWORK is INTEGER
The dimension of the array WORK.
If SIDE = ‘L’, LWORK >= fla_max(1,N);
if SIDE = ‘R’, LWORK >= fla_max(1,M).
For optimum performance LWORK >= N*NB if SIDE = ‘L’, and LWORK >= M*NB if SIDE = ‘R’, where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value