NAG Library Routine Document

F01VKF (ZTPTTF)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{TRANSR}$ – CHARACTER(1)Input

On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.

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

The RFP representation of the matrix $A$ is stored.

$\mathbf{TRANSR}=\text{'C'}$

The conjugate transpose of the RFP representation of the matrix $A$ is stored.

Constraint: $\mathbf{TRANSR}=\text{'N'}$ or $\text{'C'}$.

2:     $\mathrm{UPLO}$ – CHARACTER(1)Input

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{UPLO}=\text{'U'}$

$A$ is upper triangular.

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

$A$ is lower triangular.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

3:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the order of the matrix $A$.

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

4:     $\mathrm{AP}\left(\mathbf{N}\times \left(\mathbf{N}+1\right)/2\right)$ – COMPLEX (KIND=nag_wp) arrayInput

On entry: the $n$ by $n$ triangular matrix $A$, packed by columns.

More precisely,

• if $\mathbf{UPLO}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{AP}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{UPLO}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{AP}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

5:     $\mathrm{AR}\left(\mathbf{N}\times \left(\mathbf{N}+1\right)/2\right)$ – COMPLEX (KIND=nag_wp) arrayOutput

On exit: the upper or lower $n$ by $n$ triangular matrix $A$ (as specified by UPLO) in either normal or transposed RFP format (as specified by TRANSR). The storage format is described in Section 3.3.3 in the F07 Chapter Introduction.

6:     $\mathrm{INFO}$ – INTEGEROutput

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

6  Error Indicators and Warnings

$-999<\mathbf{INFO}<0$

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

$\mathbf{INFO}=-999$

Dynamic memory allocation failed.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f01vkfe.f90)

10.2  Program Data

Program Data (f01vkfe.d)

10.3  Program Results

Program Results (f01vkfe.r)