NAG Library Function Document

nag_zunmrz (f08bxc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – 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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{side}$ – Nag_SideTypeInput

On entry: indicates how $Z$ or $Z^{\mathrm{H}}$ is to be applied to $C$.

$\mathbf{side}=\mathrm{Nag\_LeftSide}$

$Z$ or $Z^{\mathrm{H}}$ is applied to $C$ from the left.

$\mathbf{side}=\mathrm{Nag\_RightSide}$

$Z$ or $Z^{\mathrm{H}}$ is applied to $C$ from the right.

Constraint: $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or $\mathrm{Nag\_RightSide}$.

3:    $\mathbf{trans}$ – Nag_TransTypeInput

On entry: indicates whether $Z$ or $Z^{\mathrm{H}}$ is to be applied to $C$.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

$Z$ is applied to $C$.

$\mathbf{trans}=\mathrm{Nag\_ConjTrans}$

$Z^{\mathrm{H}}$ is applied to $C$.

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ or $\mathrm{Nag\_ConjTrans}$.

4:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $C$.

Constraint: $\mathbf{m}\ge 0$.

5:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $C$.

Constraint: $\mathbf{n}\ge 0$.

6:    $\mathbf{k}$ – IntegerInput

On entry: $k$, the number of elementary reflectors whose product defines the matrix $Z$.

Constraints:

• if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{m}\ge \mathbf{k}\ge 0$;
• if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{n}\ge \mathbf{k}\ge 0$.

7:    $\mathbf{l}$ – IntegerInput

On entry: $l$, the number of columns of the matrix $A$ containing the meaningful part of the Householder reflectors.

Constraints:

• if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{m}\ge \mathbf{l}\ge 0$;
• if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{n}\ge \mathbf{l}\ge 0$.

8:    $\mathbf{a}\left[\mathit{dim}\right]$ – const ComplexInput

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

• $\max \left(1,\mathbf{pda}\times \mathbf{m}\right)$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{k}\times \mathbf{pda}\right)$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$;
• $\max \left(1,\mathbf{pda}\times \mathbf{n}\right)$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{k}\times \mathbf{pda}\right)$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $A$ is stored in

• $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $\mathit{i}$th row of a must contain the vector which defines the elementary reflector $H_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,k$, as returned by nag_ztzrzf (f08bvc).

9:    $\mathbf{pda}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$,
  • if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{m}\right)$;
  • if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

10:  $\mathbf{tau}\left[\mathit{dim}\right]$ – const ComplexInput

Note: the dimension, dim, of the array tau must be at least $\max \left(1,\mathbf{k}\right)$.

On entry: $\mathbf{tau}\left[i-1\right]$ must contain the scalar factor of the elementary reflector $H_i$, as returned by nag_ztzrzf (f08bvc).

11:  $\mathbf{c}\left[\mathit{dim}\right]$ – ComplexInput/Output

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

• $\max \left(1,\mathbf{pdc}\times \mathbf{n}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{m}\times \mathbf{pdc}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $C$ is stored in

• $\mathbf{c}\left[\left(j-1\right)\times \mathbf{pdc}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{c}\left[\left(i-1\right)\times \mathbf{pdc}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $m$ by $n$ matrix $C$.

On exit: c is overwritten by $ZC$ or $Z^{\mathrm{H}}C$ or $CZ$ or $Z^{\mathrm{H}}C$ as specified by side and trans.

12:  $\mathbf{pdc}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdc}\ge \max \left(1,\mathbf{m}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdc}\ge \max \left(1,\mathbf{n}\right)$.

13:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_INT_3

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{k}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{m}\ge \mathbf{k}\ge 0$;
if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{n}\ge \mathbf{k}\ge 0$.

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$ and $\mathbf{l}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{m}\ge \mathbf{l}\ge 0$;
if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{n}\ge \mathbf{l}\ge 0$.

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{m}\right)$;
if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

NE_INT

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}>0$.

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}>0$.

NE_INT_2

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$ and $\mathbf{k}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}\ge \max \left(1,\mathbf{k}\right)$.

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}\ge \max \left(1,\mathbf{n}\right)$.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example