NAG Library Function Document

nag_dorgqr (f08afc)

1  Purpose

2  Specification

3  Description

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

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

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

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

4  References

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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     m – IntegerInput

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

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

3:     n – IntegerInput

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

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

4:     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:     a[$\mathit{dim}$] – doubleInput/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_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc).

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:     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:     tau[$\mathit{dim}$] – const doubleInput

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_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc).

8:     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 $⟨\mathit{\text{value}}⟩$ 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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f08afce.c)

10.2  Program Data

Program Data (f08afce.d)

10.3  Program Results

Program Results (f08afce.r)