F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF01VEF (DTRTTF)

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

F01VEF (DTRTTF) copies a real triangular matrix, stored in a full format array, to a Rectangular Full Packed (RFP) format array.

## 2  Specification

 SUBROUTINE F01VEF ( TRANSR, UPLO, N, A, LDA, AR, INFO)
 INTEGER N, LDA, INFO REAL (KIND=nag_wp) A(LDA,*), AR(N*(N+1)/2) CHARACTER(1) TRANSR, UPLO
The routine may be called by its LAPACK name dtrttf.

## 3  Description

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.

## 4  References

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

## 5  Parameters

1:     $\mathrm{TRANSR}$ – 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:     $\mathrm{UPLO}$ – 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:     $\mathrm{A}\left({\mathbf{LDA}},*\right)$ – 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:     $\mathrm{LDA}$ – 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:     $\mathrm{AR}\left({\mathbf{N}}×\left({\mathbf{N}}+1\right)/2\right)$ – 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:     $\mathrm{INFO}$ – INTEGEROutput
On exit: ${\mathbf{INFO}}=0$ unless the routine detects an error (see Section 6).

## 6  Error 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.

Not applicable.

None.

## 10  Example

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

### 10.1  Program Text

Program Text (f01vefe.f90)

### 10.2  Program Data

Program Data (f01vefe.d)

### 10.3  Program Results

Program Results (f01vefe.r)