NAG Library Routine Document

C06GSF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

On entry: $m$, the number of Hermitian sequences to be converted into complex form.

Constraint: $\mathbf{M}\ge 1$.

2:     N – INTEGERInput

On entry: $n$, the number of data values in each Hermitian sequence.

Constraint: $\mathbf{N}\ge 1$.

3:     X($\mathbf{M}\times \mathbf{N}$) – REAL (KIND=nag_wp) arrayInput

On entry: the data must be stored in X as if in a two-dimensional array of dimension $\left(1:\mathbf{M},0:\mathbf{N}-1\right)$; each of the $m$ sequences is stored in a row of the array in Hermitian form. If the $n$ data values $z_j^p$ are written as $x_j^p+i{y}_j^p$, then for $0\le j\le n/2$, $x_j^p$ is contained in $\mathbf{X}\left(p,j\right)$, and for $1\le j\le \left(n-1\right)/2$, $y_j^p$ is contained in $\mathbf{X}\left(p,n-j\right)$. (See also Section 2.1.2 in the C06 Chapter Introduction.)

4:     U($\mathbf{M}\times \mathbf{N}$) – REAL (KIND=nag_wp) arrayOutput

5:     V($\mathbf{M}\times \mathbf{N}$) – REAL (KIND=nag_wp) arrayOutput

On exit: the real and imaginary parts of the $m$ sequences of length $n$, are stored in U and V respectively, as if in two-dimensional arrays of dimension $\left(1:\mathbf{M},0:\mathbf{N}-1\right)$; each of the $m$ sequences is stored as if in a row of each array. In other words, if the real parts of the $p$th sequence are denoted by $x_{\mathit{j}}^p$, for $\mathit{j}=0,1,\dots ,n-1$ then the $mn$ elements of the array U contain the values

$$x_0^1,x_0^2,\dots ,x_0^m,x_1^1,x_1^2,\dots ,x_1^m,\dots ,x_{n-1}^1,x_{n-1}^2,\dots ,x_{n-1}^m$$

6:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,

$\mathbf{M}<1$.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{N}<1$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (c06gsfe.f90)

9.2  Program Data

Program Data (c06gsfe.d)

9.3  Program Results

Program Results (c06gsfe.r)