NAG Library Function Document

nag_zunmlq (f08axc)

void	nag_zunmlq (Nag_OrderType order, Nag_SideType side, Nag_TransType trans, Integer m, Integer n, Integer k, const Complex a[], Integer pda, const Complex tau[], Complex c[], Integer pdc, NagError *fail)

3 Description

nag_zunmlq (f08axc) is intended to be used after a call to nag_zgelqf (f08avc), which performs an

L Q

factorization of a complex matrix

A

. The unitary matrix

Q

is represented as a product of elementary reflectors.

This function may be used to form one of the matrix products

Q C, Q^{H} C, C Q ​ or ​ C Q^{H},

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 Arguments

1: order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by

order = Nag_RowMajor

. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint:

order = Nag_RowMajor

or Nag_ColMajor.

2: side – Nag_SideTypeInput

On entry: indicates how

Q

Q^{H}

is to be applied to

C

$side = Nag_LeftSide$: $Q$ or $Q^{H}$ is applied to $C$ from the left.
$side = Nag_RightSide$: $Q$ or $Q^{H}$ is applied to $C$ from the right.

Constraint:

side = Nag_LeftSide

Nag_RightSide

3: trans – Nag_TransTypeInput

On entry: indicates whether

Q

Q^{H}

is to be applied to

C

$trans = Nag_NoTrans$: $Q$ is applied to $C$ .
$trans = Nag_ConjTrans$: $Q^{H}$ is applied to $C$ .

Constraint:

trans = Nag_NoTrans

Nag_ConjTrans

4: m – IntegerInput

On entry:

m

, the number of rows of the matrix

C

Constraint:

m \geq 0

5: n – IntegerInput

On entry:

n

, the number of columns of the matrix

C

Constraint:

n \geq 0

6: k – IntegerInput

On entry:

k

, the number of elementary reflectors whose product defines the matrix

Q

Constraints:

if $side = Nag_LeftSide$ , $m \geq k \geq 0$ ;
if $side = Nag_RightSide$ , $n \geq k \geq 0$ .

7: a[ $\dim$ ] – const ComplexInput

Note: the dimension, dim, of the array a must be at least

$\max (1, pda \times m)$ when $side = Nag_LeftSide$ and $order = Nag_ColMajor$ ;
$\max (1, k \times pda)$ when $side = Nag_LeftSide$ and $order = Nag_RowMajor$ ;
$\max (1, pda \times n)$ when $side = Nag_RightSide$ and $order = Nag_ColMajor$ ;
$\max (1, k \times pda)$ when $side = Nag_RightSide$ and $order = Nag_RowMajor$ .

On entry: details of the vectors which define the elementary reflectors, as returned by nag_zgelqf (f08avc).

8: pda – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

Constraints:

if $order = Nag_ColMajor$ , $pda \geq \max (1, k)$ ;
if order=Nag_RowMajor,
- if $side = Nag_LeftSide$ , $pda \geq \max (1, m)$ ;
- if $side = Nag_RightSide$ , $pda \geq \max (1, n)$ .

9: tau[ $\dim$ ] – const ComplexInput

Note: the dimension, dim, of the array tau must be at least

\max (1, k)

On entry: further details of the elementary reflectors as returned by nag_zgelqf (f08avc).

10: c[ $\dim$ ] – ComplexInput/Output

Note: the dimension, dim, of the array c must be at least

$\max (1, pdc \times n)$ when $order = Nag_ColMajor$ ;
$\max (1, m \times pdc)$ when $order = Nag_RowMajor$ .

The

(i, j)

th element of the matrix

C

is stored in

$c [(j - 1) \times pdc + i - 1]$ when $order = Nag_ColMajor$ ;
$c [(i - 1) \times pdc + j - 1]$ when $order = Nag_RowMajor$ .

On entry: the

m

n

matrix

C

On exit: c is overwritten by

Q C

Q^{H} C

C Q

C Q^{H}

as specified by side and trans.

11: pdc – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array c.

Constraints:

if $order = Nag_ColMajor$ , $pdc \geq \max (1, m)$ ;
if $order = Nag_RowMajor$ , $pdc \geq \max (1, n)$ .

12: fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_ENUM_INT_3: On entry, $side = 〈value〉$ , $m = 〈value〉$ , $n = 〈value〉$ and $k = 〈value〉$ .
Constraint: if $side = Nag_LeftSide$ , $m \geq k \geq 0$ ;
if $side = Nag_RightSide$ , $n \geq k \geq 0$ .; On entry, $side = 〈value〉$ , $pda = 〈value〉$ , $m = 〈value〉$ and $n = 〈value〉$ .
Constraint: if $side = Nag_LeftSide$ , $pda \geq \max (1, m)$ ;
if $side = Nag_RightSide$ , $pda \geq \max (1, n)$ .
NE_INT: On entry, $m = 〈value〉$ .
Constraint: $m \geq 0$ .; On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .; On entry, $pda = 〈value〉$ .
Constraint: $pda > 0$ .; On entry, $pdc = 〈value〉$ .
Constraint: $pdc > 0$ .
NE_INT_2: On entry, $pda = 〈value〉$ and $k = 〈value〉$ .
Constraint: $pda \geq \max (1, k)$ .; On entry, $pdc = 〈value〉$ and $m = 〈value〉$ .
Constraint: $pdc \geq \max (1, m)$ .; On entry, $pdc = 〈value〉$ and $n = 〈value〉$ .
Constraint: $pdc \geq \max (1, n)$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7 Accuracy

The computed result differs from the exact result by a matrix

E

such that

{‖E‖}_{2} = O (ε) {‖C‖}_{2},

where

ε

is the machine precision.

8 Further Comments

The total number of real floating point operations is approximately

8 n k (2 m - k)

side = Nag_LeftSide

and

8 m k (2 n - k)

side = Nag_RightSide

The real analogue of this function is nag_dormlq (f08akc).

9 Example

See Section 9 in nag_zgelqf (f08avc).

nag_zunmlq (f08axc) (PDF version)

f08 Chapter Contents

f08 Chapter Introduction

NAG C Library Manual

NAG Library Function Documentnag_zunmlq (f08axc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Function Document

nag_zunmlq (f08axc)