F08BKF (DORMRZ) multiplies a general real
m by
n matrix
C by the real orthogonal matrix
Z from an
RZ factorization computed by
F08BHF (DTZRZF).
SUBROUTINE F08BKF ( |
SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
INTEGER |
M, N, K, L, LDA, LDC, LWORK, INFO |
REAL (KIND=nag_wp) |
A(LDA,*), TAU(*), C(LDC,*), WORK(max(1,LWORK)) |
CHARACTER(1) |
SIDE, TRANS |
|
F08BKF (DORMRZ) is intended to be used following a call to
F08BHF (DTZRZF), which performs an
RZ factorization of a real upper trapezoidal matrix
A and represents the orthogonal matrix
Z as a product of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
C, which may be any real rectangular
m by
n matrix.
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999)
LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia
http://www.netlib.org/lapack/lug- 1: SIDE – CHARACTER(1)Input
On entry: indicates how
Z or
ZT is to be applied to
C.
- SIDE='L'
- Z or ZT is applied to C from the left.
- SIDE='R'
- Z or ZT is applied to C from the right.
Constraint:
SIDE='L' or 'R'.
- 2: TRANS – CHARACTER(1)Input
On entry: indicates whether
Z or
ZT is to be applied to
C.
- TRANS='N'
- Z is applied to C.
- TRANS='T'
- ZT is applied to C.
Constraint:
TRANS='N' or 'T'.
- 3: M – INTEGERInput
On entry: m, the number of rows of the matrix C.
Constraint:
M≥0.
- 4: N – INTEGERInput
On entry: n, the number of columns of the matrix C.
Constraint:
N≥0.
- 5: K – INTEGERInput
On entry: k, the number of elementary reflectors whose product defines the matrix Z.
Constraints:
- if SIDE='L', M≥ K≥ 0 ;
- if SIDE='R', N≥ K≥ 0 .
- 6: L – INTEGERInput
On entry: l, the number of columns of the matrix A containing the meaningful part of the Householder reflectors.
Constraints:
- if SIDE='L', M≥ L≥ 0 ;
- if SIDE='R', N≥ L≥ 0 .
- 7: A(LDA,*) – REAL (KIND=nag_wp) arrayInput
-
Note: the second dimension of the array
A
must be at least
max1,M if
SIDE='L' and at least
max1,N if
SIDE='R'.
On entry: the
ith row of
A must contain the vector which defines the elementary reflector
Hi, for
i=1,2,…,k, as returned by
F08BHF (DTZRZF).
- 8: LDA – INTEGERInput
On entry: the first dimension of the array
A as declared in the (sub)program from which F08BKF (DORMRZ) is called.
Constraint:
LDA≥max1,K.
- 9: TAU(*) – REAL (KIND=nag_wp) arrayInput
-
Note: the dimension of the array
TAU
must be at least
max1,K.
On entry:
TAUi must contain the scalar factor of the elementary reflector
Hi, as returned by
F08BHF (DTZRZF).
- 10: C(LDC,*) – REAL (KIND=nag_wp) arrayInput/Output
-
Note: the second dimension of the array
C
must be at least
max1,N.
On entry: the m by n matrix C.
On exit:
C is overwritten by
ZC or
ZTC or
CZ or
ZTC as specified by
SIDE and
TRANS.
- 11: LDC – INTEGERInput
On entry: the first dimension of the array
C as declared in the (sub)program from which F08BKF (DORMRZ) is called.
Constraint:
LDC≥max1,M.
- 12: WORK(max1,LWORK) – REAL (KIND=nag_wp) arrayWorkspace
On exit: if
INFO=0,
WORK1 contains the minimum value of
LWORK required for optimal performance.
- 13: LWORK – INTEGERInput
On entry: the dimension of the array
WORK as declared in the (sub)program from which F08BKF (DORMRZ) is called.
If
LWORK=-1, 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.
Suggested value:
for optimal performance, LWORK≥N×nb if SIDE='L' and at least M×nb if SIDE='R', where nb is the optimal block size.
Constraints:
- if SIDE='L', LWORK≥max1,N or LWORK=-1;
- if SIDE='R', LWORK≥max1,M or LWORK=-1.
- 14: INFO – INTEGEROutput
On exit:
INFO=0 unless the routine detects an error (see
Section 6).
The computed result differs from the exact result by a matrix
E such that
where
ε is the
machine precision.
The complex analogue of this routine is
F08BXF (ZUNMRZ).