F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF01VLF (DTFTTP)

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

F01VLF (DTFTTP) copies a real triangular matrix stored in a Rectangular Full Packed (RFP) format to packed 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 F01VLF ( TRANSR, UPLO, N, ARF, AP, INFO)
 INTEGER N, INFO REAL (KIND=nag_wp) ARF(N*(N+1)/2), AP(N*(N+1)/2) CHARACTER(1) TRANSR, UPLO
The routine may be called by its LAPACK name dtfttp.

## 3  Description

F01VLF (DTFTTP) packs a real $n$ by $n$ triangular matrix $A$ stored in RFP format to packed 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 RFP representation of $A$ is normal or transposed.
${\mathbf{TRANSR}}=\text{'N'}$
The matrix $A$ is stored in normal RFP format.
${\mathbf{TRANSR}}=\text{'T'}$
The matrix $A$ is stored in transposed RFP format.
Constraint: ${\mathbf{TRANSR}}=\text{'N'}$ or $\text{'T'}$.
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:     ARF(${\mathbf{N}}×\left({\mathbf{N}}+1\right)/2$) – REAL (KIND=nag_wp) arrayInput
On entry: the triangular matrix $A$ in RFP format, as described in Section 3.3.3 in the F07 Chapter Introduction.
5:     AP(${\mathbf{N}}×\left({\mathbf{N}}+1\right)/2$) – REAL (KIND=nag_wp) arrayOutput
On exit: the $n$ by $n$ triangular matrix $A$, packed by columns.
More precisely,
• if ${\mathbf{UPLO}}=\text{'U'}$, the upper triangle of $A$ is 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 $A$ is stored with element ${A}_{ij}$ in ${\mathbf{AP}}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.
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 RFP format and copies it to packed format.

### 9.1  Program Text

Program Text (f01vlfe.f90)

### 9.2  Program Data

Program Data (f01vlfe.d)

### 9.3  Program Results

Program Results (f01vlfe.r)