Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
The routine may be called by its
LAPACK
name zunmqr.
3 Description
F08AUF (ZUNMQR) is intended to be used after a call to F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3), which perform a QR factorization of a complex matrix A. The unitary matrix Q is represented as a product of elementary reflectors.
This routine may be used to form one of the matrix products
QC,QHC,CQ or CQH,
overwriting the result on C (which may be any complex rectangular matrix).
A common application of this routine is in solving linear least squares problems, as described in the F08 Chapter Introduction and illustrated in Section 9 in F08ASF (ZGEQRF).
4 References
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
5 Parameters
1: SIDE – CHARACTER(1)Input
On entry: indicates how Q or QH is to be applied to C.
SIDE='L'
Q or QH is applied to C from the left.
SIDE='R'
Q or QH is applied to C from the right.
Constraint:
SIDE='L' or 'R'.
2: TRANS – CHARACTER(1)Input
On entry: indicates whether Q or QH is to be applied to C.
TRANS='N'
Q is applied to C.
TRANS='C'
QH is applied to C.
Constraint:
TRANS='N' or 'C'.
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 Q.
On exit: if INFO=0, the real part of WORK1 contains the minimum value of LWORK required for optimal performance.
12: LWORK – INTEGERInput
On entry: the dimension of the array WORK as declared in the (sub)program from which F08AUF (ZUNMQR) 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.
13: INFO – INTEGEROutput
On exit: INFO=0 unless the routine detects an error (see Section 6).
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
INFO<0
If INFO=-i, argument i had an illegal value. An explanatory message is output, and execution of the program is terminated.
7 Accuracy
The computed result differs from the exact result by a matrix E such that
E2=OεC2,
where ε is the machine precision.
8 Further Comments
The total number of real floating point operations is approximately 8nk2m-k if SIDE='L' and 8mk2n-k if SIDE='R'.