NAG FL Interface
f08acf (dgemqrt)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{side}$ – Character(1) Input

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

$\mathbf{side}=\text{'L'}$

$Q$ or $Q^{\mathrm{T}}$ is applied to $C$ from the left.

$\mathbf{side}=\text{'R'}$

$Q$ or $Q^{\mathrm{T}}$ is applied to $C$ from the right.

Constraint: $\mathbf{side}=\text{'L'}$ or $\text{'R'}$.

2: $\mathbf{trans}$ – Character(1) Input

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

$\mathbf{trans}=\text{'N'}$

$Q$ is applied to $C$.

$\mathbf{trans}=\text{'T'}$

$Q^{\mathrm{T}}$ is applied to $C$.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

3: $\mathbf{m}$ – Integer Input

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

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

4: $\mathbf{n}$ – Integer Input

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

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

5: $\mathbf{k}$ – Integer Input

On entry: $k$, the number of elementary reflectors whose product defines the matrix $Q$. Usually $\mathbf{k}=\min (m_A,n_A)$ where $m_A$, $n_A$ are the dimensions of the matrix $A$ supplied in a previous call to f08abf.

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{m}\ge \mathbf{k}\ge 0$;
• if $\mathbf{side}=\text{'R'}$, $\mathbf{n}\ge \mathbf{k}\ge 0$.

6: $\mathbf{nb}$ – Integer Input

On entry: the block size used in the $QR$ factorization performed in a previous call to f08abf; this value must remain unchanged from that call.

Constraints:

• $\mathbf{nb}\ge 1$;
• if $\mathbf{k}>0$, $\mathbf{nb}\le \mathbf{k}$.

7: $\mathbf{v}(\mathbf{ldv},*)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array v must be at least $\max (1,\mathbf{k})$.

On entry: details of the vectors which define the elementary reflectors, as returned by f08abf in the first $k$ columns of its array argument a.

8: $\mathbf{ldv}$ – Integer Input

On entry: the first dimension of the array v as declared in the (sub)program from which f08acf is called.

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{ldv}\ge \max (1,\mathbf{m})$;
• if $\mathbf{side}=\text{'R'}$, $\mathbf{ldv}\ge \max (1,\mathbf{n})$.

9: $\mathbf{t}(\mathbf{ldt},*)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array t must be at least $\max (1,\mathbf{k})$.

On entry: further details of the orthogonal matrix $Q$ as returned by f08abf. The number of blocks is $b=\lceil \frac{k}{\mathbf{nb}}\rceil$, where $k=\min (m,n)$ and each block is of order nb except for the last block, which is of order $k-(b-1)\times \mathbf{nb}$. For the $b$ blocks the upper triangular block reflector factors ${\mathit{T}}_1,{\mathit{T}}_2,\dots ,{\mathit{T}}_b$ are stored in the $\mathbf{nb}\times n$ matrix $T$ as $\mathit{T}=\left[{\mathit{T}}_1\right|{\mathit{T}}_2|\cdots |{\mathit{T}}_b]$.

10: $\mathbf{ldt}$ – Integer Input

On entry: the first dimension of the array t as declared in the (sub)program from which f08acf is called.

Constraint: $\mathbf{ldt}\ge \mathbf{nb}$.

11: $\mathbf{c}(\mathbf{ldc},*)$ – Real (Kind=nag_wp) array Input/Output

Note: the second dimension of the array c must be at least $\max (1,\mathbf{n})$.

On entry: the $m\times n$ matrix $C$.

On exit: c is overwritten by $QC$ or $Q^{\mathrm{T}}C$ or $CQ$ or $C{Q}^{\mathrm{T}}$ as specified by side and trans.

12: $\mathbf{ldc}$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which f08acf is called.

Constraint: $\mathbf{ldc}\ge \max (1,\mathbf{m})$.

13: $\mathbf{work}\left(*\right)$ – Real (Kind=nag_wp) array Workspace

Note: the dimension of the array work must be at least $\mathbf{n}\times \mathbf{nb}$ if $\mathbf{side}=\text{'L'}$ and at least $\mathbf{m}\times \mathbf{nb}$ if $\mathbf{side}=\text{'R'}$.

14: $\mathbf{info}$ – Integer Output

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6 Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example