F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF01VHF (ZTFTTR)

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

F01VHF (ZTFTTR) unpacks a complex triangular matrix, stored in a Rectangular Full Packed (RFP) format array, to a full format array.

## 2  Specification

 SUBROUTINE F01VHF ( TRANSR, UPLO, N, AR, A, LDA, INFO)
 INTEGER N, LDA, INFO COMPLEX (KIND=nag_wp) AR(N*(N+1)/2), A(LDA,*) CHARACTER(1) TRANSR, UPLO
The routine may be called by its LAPACK name ztfttr.

## 3  Description

F01VHF (ZTFTTR) unpacks a complex $n$ by $n$ triangular matrix $A$, stored in RFP format to conventional storage in a full format array. 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 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:     $\mathrm{AR}\left({\mathbf{N}}×\left({\mathbf{N}}+1\right)/2\right)$ – COMPLEX (KIND=nag_wp) arrayInput
On entry: 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.
5:     $\mathrm{A}\left({\mathbf{LDA}},*\right)$ – COMPLEX (KIND=nag_wp) arrayOutput
Note: the second dimension of the array A must be at least ${\mathbf{N}}$.
On exit: 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.
6:     $\mathrm{LDA}$ – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F01VHF (ZTFTTR) is called.
Constraint: ${\mathbf{LDA}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
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 in RFP format and unpacks it to full format.

### 10.1  Program Text

Program Text (f01vhfe.f90)

### 10.2  Program Data

Program Data (f01vhfe.d)

### 10.3  Program Results

Program Results (f01vhfe.r)