NAG Library Routine Document

f01zaf (real_tri_pack)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{job}$ – Character(1)Input

On entry: specifies whether the triangular matrix is to be packed or unpacked.

$\mathbf{job}=\text{'P'}$ (Pack)

The matrix is to be packed into array b.

$\mathbf{job}=\text{'U'}$ (Unpack)

The matrix is to be unpacked into array a.

Constraint: $\mathbf{job}=\text{'P'}$ or $\text{'U'}$.

2:     $\mathbf{uplo}$ – Character(1)Input

On entry: specifies the type of the matrix to be copied

$\mathbf{uplo}=\text{'L'}$ (Lower)

The matrix is lower triangular. In this case the packed vector holds, or will hold on exit, the matrix elements in the following order: $\left(1,1\right),\left(2,1\right),\dots ,\left(\mathbf{n},1\right),\left(2,2\right),\left(3,2\right),\dots ,\left(\mathbf{n},2\right)$, etc..

$\mathbf{uplo}=\text{'U'}$ (Upper)

The matrix is upper triangular. In this case the packed vector holds, or will hold on exit, the matrix elements in the following order: $\left(1,1\right)$, $\left(1,2\right)$, $\left(2,2\right)$, $\left(1,3\right)$, $\left(2,3\right)$, $\left(3,3\right)$, $\left(1,4\right)$, etc..

Constraint: $\mathbf{uplo}=\text{'L'}$ or $\text{'U'}$.

3:     $\mathbf{diag}$ – Character(1)Input

On entry: must specify whether the diagonal elements of the matrix are to be copied.

$\mathbf{diag}=\text{'B'}$ (Blank)

The diagonal elements of the matrix are not referenced and not copied.

$\mathbf{diag}=\text{'U'}$ (Unit diagonal)

The diagonal elements of the matrix are not referenced, but are assumed all to be unity, and are copied as such.

$\mathbf{diag}=\text{'N'}$ (Non-unit diagonal)

The diagonal elements of the matrix are referenced and copied.

Constraint: $\mathbf{diag}=\text{'B'}$, $\text{'U'}$ or $\text{'N'}$.

4:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of rows and columns of the triangular matrix.

Constraint: $\mathbf{n}>0$.

5:     $\mathbf{a}\left(\mathbf{lda},\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: if $\mathbf{job}=\text{'P'}$, the leading n by n part of a must contain the matrix to be copied, stored in unpacked form, in the upper or lower triangle depending on argument uplo. The opposite triangle of a is not referenced and need not be assigned.

On exit: if $\mathbf{job}=\text{'U'}$, the leading n by n part of array a contains the copied matrix, stored in unpacked form, in the upper or lower triangle depending on argument uplo. The opposite triangle of a is not referenced.

6:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f01zaf is called.

Constraint: $\mathbf{lda}\ge \mathbf{n}$.

7:     $\mathbf{b}\left(\left(\mathbf{n}\times \left(\mathbf{n}+1\right)\right)/2\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: if $\mathbf{job}=\text{'U'}$, b must contain the triangular matrix packed by column.

On exit: if $\mathbf{job}=\text{'P'}$, b contains the triangular matrix packed by column.

Note that b must have space for the diagonal elements of the matrix, even if these are not stored.

8:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{job}\ne \text{'P'}$ or $\text{'U'}$: $\mathbf{job}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

On entry, $\mathbf{uplo}\ne \text{'U'}$ or $\text{'L'}$: $\mathbf{uplo}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=3$

On entry, $\mathbf{diag}\ne \text{'N'}$, $\text{'U'}$ or $\text{'B'}$: $\mathbf{diag}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=4$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=5$

On entry, $\mathbf{lda}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lda}\ge \mathbf{n}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f01zafe.f90)

10.2

Program Data

Program Data (f01zafe.d)

10.3

Program Results

Program Results (f01zafe.r)