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 dormlq.
3 Description
F08AKF (DORMLQ) is intended to be used after a call to F08AHF (DGELQF), which performs an factorization of a real matrix . The orthogonal matrix is represented as a product of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on (which may be any real rectangular matrix).
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 or is to be applied to .
or is applied to from the left.
or is applied to from the right.
Constraint:
or .
2: TRANS – CHARACTER(1)Input
On entry: indicates whether or is to be applied to .
is applied to .
is applied to .
Constraint:
or .
3: M – INTEGERInput
On entry: , the number of rows of the matrix .
Constraint:
.
4: N – INTEGERInput
On entry: , the number of columns of the matrix .
Constraint:
.
5: K – INTEGERInput
On entry: , the number of elementary reflectors whose product defines the matrix .
Note: the second dimension of the array C
must be at least
.
On entry: the by matrix .
On exit: C is overwritten by or or or as specified by SIDE and TRANS.
10: LDC – INTEGERInput
On entry: the first dimension of the array C as declared in the (sub)program from which F08AKF (DORMLQ) is called.
Constraint:
.
11: WORK() – REAL (KIND=nag_wp) arrayWorkspace
On exit: if , 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 F08AKF (DORMLQ) is called.
If , 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, if and at least if , where is the optimal block size.
Constraints:
if , or ;
if , or .
13: INFO – INTEGEROutput
On exit: unless the routine detects an error (see Section 6).
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
If , argument 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 such that
where is the machine precision.
8 Further Comments
The total number of floating point operations is approximately if and if .