# NAG Library Routine Document

## 1Purpose

f01vef (dtrttf) copies a real triangular matrix, stored in a full format array, to a Rectangular Full Packed (RFP) format array.

## 2Specification

Fortran Interface
 Subroutine f01vef ( uplo, n, a, lda, ar, info)
 Integer, Intent (In) :: n, lda Integer, Intent (Out) :: info Real (Kind=nag_wp), Intent (In) :: a(lda,*) Real (Kind=nag_wp), Intent (Out) :: ar(n*(n+1)/2) Character (1), Intent (In) :: transr, uplo
#include nagmk26.h
 void f01vef_ (const char *transr, const char *uplo, const Integer *n, const double a[], const Integer *lda, double ar[], Integer *info, const Charlen length_transr, const Charlen length_uplo)
The routine may be called by its LAPACK name dtrttf.

## 3Description

f01vef (dtrttf) packs a real $n$ by $n$ triangular matrix $A$, stored conventionally in a full format array, into RFP format. This routine is intended for possible use in conjunction with routines from Chapters F06, F07 and F16 where some routines that use triangular matrices store them in RFP format. The RFP storage format is described in Section 3.3.3 in the F07 Chapter Introduction.
Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

## 5Arguments

1:     $\mathbf{transr}$ – Character(1)Input
On entry: specifies whether the normal RFP representation of $A$ or its transpose is stored.
${\mathbf{transr}}=\text{'N'}$
The RFP representation of the matrix $A$ is stored.
${\mathbf{transr}}=\text{'T'}$
The transpose of the RFP representation of the matrix $A$ is stored.
Constraint: ${\mathbf{transr}}=\text{'N'}$ or $\text{'T'}$.
2:     $\mathbf{uplo}$ – 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:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
4:     $\mathbf{a}\left({\mathbf{lda}},*\right)$ – Real (Kind=nag_wp) arrayInput
Note: the second dimension of the array a must be at least ${\mathbf{n}}$.
On entry: the triangular matrix $A$.
• If ${\mathbf{uplo}}=\text{'U'}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{uplo}}=\text{'L'}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
5:     $\mathbf{lda}$ – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f01vef (dtrttf) is called.
Constraint: ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
6:     $\mathbf{ar}\left({\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right)$ – Real (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.
7:     $\mathbf{info}$ – IntegerOutput
On exit: ${\mathbf{info}}=0$ unless the routine detects an error (see Section 6).

## 6Error Indicators and Warnings

${\mathbf{info}}<0$
If ${\mathbf{info}}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

Not applicable.

## 8Parallelism and Performance

f01vef (dtrttf) is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (f01vefe.f90)

### 10.2Program Data

Program Data (f01vefe.d)

### 10.3Program Results

Program Results (f01vefe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017