NAG Library Function Document

nag_zungqr (f08atc)

1

Purpose

2

Specification

3

Description

nag_zungqr(order,m,m,p,a,pda,tau,&fail)

nag_zungqr(order,m,p,p,a,pda,tau,&fail)

nag_zungqr(order,m,m,k,a,pda,tau,&fail)

nag_zungqr(order,m,k,k,a,pda,tau,&fail)

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:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the order of the unitary matrix $Q$.

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

3:    $\mathbf{n}$ – IntegerInput

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

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

4:    $\mathbf{k}$ – IntegerInput

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

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

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

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

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

On entry: details of the vectors which define the elementary reflectors, as returned by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc).

On exit: the $m$ by $n$ matrix $Q$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

6:    $\mathbf{pda}$ – IntegerInput

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

Constraints:

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

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

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

On entry: further details of the elementary reflectors, as returned by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc).

8:    $\mathbf{fail}$ – 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_INT

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

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

NE_INT_2

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

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

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

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

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

10.1

Program Text

Program Text (f08atce.c)

10.2

Program Data

Program Data (f08atce.d)

10.3

Program Results

Program Results (f08atce.r)