NAG FL Interface
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: $(1,1),(2,1),\dots ,(\mathbf{n},1),(2,2),(3,2),\dots ,(\mathbf{n},2)$, 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: $(1,1)$, $(1,2)$, $(2,2)$, $(1,3)$, $(2,3)$, $(3,3)$, $(1,4)$, 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: $\mathbf{n}$ – Integer Input

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

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

5: $\mathbf{a}(\mathbf{lda},\mathbf{n})$ – Real (Kind=nag_wp) array Input/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: $\mathbf{lda}$ – Integer Input

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: $\mathbf{b}\left((\mathbf{n}\times (\mathbf{n}+1))/2\right)$ – Real (Kind=nag_wp) array Input/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: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results