NAG Library Function Document

nag_complex_form_q (f01rec)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     wheret – Nag_WhereElementsInput

On entry: the elements of $\theta$ are to be found as follows:

• $\mathbf{wheret}=\mathrm{Nag\_ElementsIn}$, the elements of $\theta$ are in $A$.
• $\mathbf{wheret}=\mathrm{Nag\_ElementsSeparate}$, the elements of $\theta$ are separate from $A$, in theta.

Constraint: wheret must be one of $\mathrm{Nag\_ElementsIn}$ or $\mathrm{Nag\_ElementsSeparate}$.

2:     m – IntegerInput

On entry: $m$, the number of rows of $A$.

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

3:     n – IntegerInput

On entry: $n$, the number of columns of $A$.

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

4:     ncolq – IntegerInput

On entry: $\mathit{ncolq}$, the required number of columns of $Q$.

When $\mathbf{ncolq}=0$ then an immediate return is effected.

Constraint: $0\le \mathbf{ncolq}\le \mathbf{m}$.

5:     a[$\mathbf{m}\times \mathbf{tda}$] – ComplexInput/Output

On entry: the leading $m$ by $n$ strictly lower triangular part of the array a must contain details of the matrix $Q$. In addition, when $\mathbf{wheret}=\mathrm{Nag\_ElementsIn}$, then the diagonal elements of a must contain the elements of $\theta$ as described under the argument theta.

On exit: the first ncolq columns of the array a are overwritten by the first ncolq columns of the $m$ by $m$ unitary matrix $Q$. When $\mathbf{n}=0$ then the first ncolq columns of a are overwritten by the first ncolq columns of the unit matrix.

6:     tda – IntegerInput

On entry: the stride separating matrix column elements in the array a.

Constraint: $\mathbf{tda}\ge \max \left(\mathbf{n},\mathbf{ncolq}\right)$.

7:     theta[n] – const ComplexInput

On entry: if $\mathbf{wheret}=\mathrm{Nag\_ElementsSeparate}$, the array theta must contain the elements of $\theta$. If $\mathbf{theta}\left[k-1\right]=0.0$ then $T_k$ is assumed to be $I$; if $\mathbf{theta}\left[k-1\right]=\alpha$, with $\mathrm{Re}\alpha <0.0$, then $T_k$ is assumed to be of the form

$$T_k=\left(\begin{array}{cc}\alpha & 0\\ 0& I\end{array}\right)\text{; }$$

otherwise $\mathbf{theta}\left[k-1\right]$ is assumed to contain ${\theta }_k$ given by ${\theta }_k=\left({\zeta }_k,\mathrm{Im}{\gamma }_k\right)$.

When $\mathbf{wheret}=\mathrm{Nag\_ElementsIn}$, the array theta is not referenced and may be NULL.

8:     fail – NagError *Input/Output

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

6  Error Indicators and Warnings

NE_2_INT_ARG_GT

On entry, $\mathbf{ncolq}=⟨\mathit{\text{value}}⟩$ while $\mathbf{m}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{ncolq}\le \mathbf{m}$.

NE_2_INT_ARG_LT

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$ while $\mathbf{n}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{m}\ge \mathbf{n}$.

On entry, $\mathbf{tda}=⟨\mathit{\text{value}}⟩$ while $\max \left(\mathbf{n},\mathbf{ncolq}\right)=\mathbf{ncolq}$. These arguments must satisfy $\mathbf{tda}\ge \mathbf{n}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument wheret had an illegal value.

NE_INT_ARG_LT

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

On entry, $\mathbf{ncolq}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ncolq}\ge 0$.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f01rece.c)

10.2  Program Data

Program Data (f01rece.d)

10.3  Program Results

Program Results (f01rece.r)