F01 Chapter Contents
F01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF01VCF (DTPTTR)

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

F01VCF (DTPTTR) unpacks a real triangular matrix, stored in packed format in a one-dimensional array, to full format in a two-dimensional array. Packed storage format is described in Section 3.3.2 in the F07 Chapter Introduction.

## 2  Specification

 SUBROUTINE F01VCF ( UPLO, N, AP, A, LDA, INFO)
 INTEGER N, LDA, INFO REAL (KIND=nag_wp) AP(N*(N+1)/2), A(LDA,*) CHARACTER(1) UPLO
The routine may be called by its LAPACK name dtpttr.

## 3  Description

F01VCF (DTPTTR) unpacks a real $n$ by $n$ triangular matrix $A$, stored in a one-dimensional array of length $n\left(n+1\right)/2$ to conventional storage in a two-dimensional array. This routine is intended for possible use in conjunction with routines from Chapters F06, F07 and F08 where some routines use triangular matrices stored in the packed form.

None.

## 5  Parameters

1:     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 $\text{'L'}$.
2:     N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 1$.
3:     AP(${\mathbf{N}}×\left({\mathbf{N}}+1\right)/2$) – REAL (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 $i\ge j$.
4:     A(LDA,$*$) – REAL (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.
5:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F01VCF (DTPTTR) is called.
Constraint: ${\mathbf{LDA}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
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 packed by columns and unpacks it to full format.

### 9.1  Program Text

Program Text (f01vcfe.f90)

### 9.2  Program Data

Program Data (f01vcfe.d)

### 9.3  Program Results

Program Results (f01vcfe.r)