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template<typename T>
void unmtr(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 complex m-by-n matrix c with side = 'L' side = 'R' trans = 'N': Q * C C * Q trans = 'C': Q**H * C C * Q**H where Q is a complex unitary 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 CHETRD: 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**H from the Left;
= ‘R’: apply Q or Q**H from the Right.uplo – [in]
uplo is char*
= ‘U’: Upper triangle of a contains elementary reflectors from CHETRD;
= ‘L’: Lower triangle of a contains elementary reflectors from CHETRD.trans – [in]
trans is char*
= ‘N’: No transpose, apply Q;
= ‘C’: Transpose, apply Q**C.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 COMPLEX/COMPLEX*16 array, dimension
(lda,m) if side = ‘L’
(lda,n) if side = ‘R’
The vectors which define the elementary reflectors, as returned by CHETRD.
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 COMPLEX/COMPLEX*16 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 CHETRD.
c – [inout]
c is COMPLEX/COMPLEX*16 array, dimension (ldc,n)
On entry, the m-by-n matrix c.
On exit, c is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.ldc – [in]
ldc is integer*
The leading dimension of the array c. ldc >= fla_max(1,m).
WORK – [out]
WORK is COMPLEX 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