F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF01VKF (ZTPTTF)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F01VKF (ZTPTTF) copies a complex triangular matrix stored in packed format to Rectangular Full Packed (RFP) format. The RFP storage format is described in Section 3.3.3 in the F07 Chapter Introduction and the packed storage format is described in Section 3.3.2 in the F07 Chapter Introduction.

## 2  Specification

 SUBROUTINE F01VKF ( TRANSR, UPLO, N, AP, ARF, INFO)
 INTEGER N, INFO COMPLEX (KIND=nag_wp) AP(N*(N+1)/2), ARF(N*(N+1)/2) CHARACTER(1) TRANSR, UPLO
The routine may be called by its LAPACK name ztpttf.

## 3  Description

F01VKF (ZTPTTF) copies a complex $n$ by $n$ triangular matrix, $A$, stored packed format, to RFP format. This routine is intended for possible use in conjunction with routines from Chapters F06 and F07 where some routines that use triangular matrices store them in RFP format.
None.

## 5  Parameters

1:     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 matrix $A$ is stored in normal RFP format.
${\mathbf{TRANSR}}=\text{'C'}$
The conjugate transpose of the RFP representation of the matrix $A$ is stored.
Constraint: ${\mathbf{TRANSR}}=\text{'N'}$ or $\text{'C'}$.
2:     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:     N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 0$.
4:     AP(${\mathbf{N}}×\left({\mathbf{N}}+1\right)/2$) – 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:     ARF(${\mathbf{N}}×\left({\mathbf{N}}+1\right)/2$) – COMPLEX (KIND=nag_wp) arrayOutput
On exit: the triangular matrix $A$ in RFP format, as described in Section 3.3.3 in the F07 Chapter Introduction.
6:     INFO – INTEGEROutput
On exit: ${\mathbf{INFO}}=0$ unless the routine detects an error (see Section 6).

## 6  Error Indicators and Warnings

Errors or warnings detected by the routine:
${\mathbf{INFO}}<0$
If ${\mathbf{INFO}}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

Not applicable.

None.

## 9  Example

This example reads in a triangular matrix in packed format and copies it to RFP format.

### 9.1  Program Text

Program Text (f01vkfe.f90)

### 9.2  Program Data

Program Data (f01vkfe.d)

### 9.3  Program Results

Program Results (f01vkfe.r)