F08AXF (ZUNMLQ) (PDF version)
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F08AXF (ZUNMLQ)

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.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F08AXF (ZUNMLQ) multiplies an arbitrary complex matrix C by the complex unitary matrix Q from an LQ factorization computed by F08AVF (ZGELQF).

2  Specification

SUBROUTINE F08AXF ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
INTEGER  M, N, K, LDA, LDC, LWORK, INFO
COMPLEX (KIND=nag_wp)  A(LDA,*), TAU(*), C(LDC,*), WORK(max(1,LWORK))
CHARACTER(1)  SIDE, TRANS
The routine may be called by its LAPACK name zunmlq.

3  Description

F08AXF (ZUNMLQ) is intended to be used after a call to F08AVF (ZGELQF), which performs an LQ 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).

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: M0.
4:     N – INTEGERInput
On entry: n, the number of columns of the matrix C.
Constraint: N0.
5:     K – INTEGERInput
On entry: k, the number of elementary reflectors whose product defines the matrix Q.
Constraints:
  • if SIDE='L', MK0;
  • if SIDE='R', NK0.
6:     A(LDA,*) – COMPLEX (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: details of the vectors which define the elementary reflectors, as returned by F08AVF (ZGELQF).
7:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F08AXF (ZUNMLQ) is called.
Constraint: LDAmax1,K.
8:     TAU(*) – COMPLEX (KIND=nag_wp) arrayInput
Note: the dimension of the array TAU must be at least max1,K.
On entry: further details of the elementary reflectors as returned by F08AVF (ZGELQF).
9:     C(LDC,*) – COMPLEX (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 QC or QHC or CQ or CQH 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 F08AXF (ZUNMLQ) is called.
Constraint: LDCmax1,M.
11:   WORK(max1,LWORK) – COMPLEX (KIND=nag_wp) arrayWorkspace
12:   LWORK – INTEGERInput
On entry: the dimension of the array WORK as declared in the (sub)program from which F08AXF (ZUNMLQ) 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, LWORKN×nb if SIDE='L' and at least M×nb if SIDE='R', where nb is the optimal block size.
Constraints:
  • if SIDE='L', LWORKmax1,N or LWORK=-1;
  • if SIDE='R', LWORKmax1,M or LWORK=-1.
13:   INFO – INTEGEROutput

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 = Oε C2 ,
where ε is the machine precision.

8  Further Comments

The total number of real floating point operations is approximately 8nk 2m-k  if SIDE='L' and 8mk 2n-k  if SIDE='R'.
The real analogue of this routine is F08AKF (DORMLQ).

9  Example

See Section 9 in F08AVF (ZGELQF).

F08AXF (ZUNMLQ) (PDF version)
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011