NAG FL Interface
f01zcf (real_​band_​pack)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

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

$\mathbf{job}=\text{'P'}$ (Pack)

The band matrix is to be packed into array b.

$\mathbf{job}=\text{'U'}$ (Unpack)

The band matrix is to be unpacked into array a.

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

2: $\mathbf{m}$ – Integer Input

3: $\mathbf{n}$ – Integer Input

On entry: $m$ and $n$, the number of rows and columns of the band matrix, respectively.

Constraints:

• $\mathbf{m}>0$;
• $\mathbf{n}>0$.

4: $\mathbf{kl}$ – Integer Input

On entry: $k_l$, the number of subdiagonals of the band matrix.

Constraint: $\mathbf{kl}\ge 0$.

5: $\mathbf{ku}$ – Integer Input

On entry: $k_u$, the number of superdiagonals of the band matrix.

Constraint: $\mathbf{ku}\ge 0$.

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

On entry: if $\mathbf{job}=\text{'P'}$, the leading $m$ by $n$ part of a must contain the band matrix stored in unpacked form. Elements of the array that lie outside the banded part of the matrix are not referenced and need not be assigned.

On exit: if $\mathbf{job}=\text{'U'}$, the leading $m$ by $n$ part of a contains the band matrix stored in unpacked form. Elements of the leading $m$ by $n$ part of a that are not within the banded part of the matrix are assigned the value zero.

7: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01zcf is called.

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

8: $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Real (Kind=nag_wp) array Input/Output

Note: the second dimension of the array b must be at least $\min \left(\mathbf{m}+\mathbf{ku},\mathbf{n}\right)$.

On entry: if $\mathbf{job}=\text{'U'}$, b must contain the band matrix in packed form, in the leading $\left(k_l+k_u+1\right)$ by $\min \left(m+k_u,n\right)$ part of the array. The matrix is packed column by column, with the leading diagonal of the matrix in row $\left(k_u+1\right)$ of b, the first superdiagonal starting at position $2$ in row $k_u$, the first subdiagonal starting at position $1$ in row $\left(k_u+2\right)$, and so on. Elements of b that are not needed to store the band matrix, for instance the leading $k_u$ by $k_u$ triangle, are not referenced and need not be assigned.

On exit: if $\mathbf{job}=\text{'P'}$, b contains the band matrix stored in packed form. Elements of b that are not needed to store the band matrix are not referenced.

9: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f01zcf is called.

Constraint: $\mathbf{ldb}\ge \left(\mathbf{kl}+\mathbf{ku}+1\right)$.

10: $\mathbf{ifail}$ – Integer Input/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 4 in the Introduction to the NAG Library FL Interface 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, $\mathbf{job}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{job}=\text{'P'}$ or $\text{'U'}$.

$\mathbf{ifail}=2$

On entry, $\mathbf{kl}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{kl}\ge 0$.

$\mathbf{ifail}=3$

On entry, $\mathbf{ku}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ku}\ge 0$.

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=5$

On entry, $\mathbf{ldb}=〈\mathit{\text{value}}〉$, $\mathbf{kl}=〈\mathit{\text{value}}〉$ and $\mathbf{ku}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldb}\ge \mathbf{kl}+\mathbf{ku}+1$.

$\mathbf{ifail}=6$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}>0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}>0$.

$\mathbf{ifail}=-99$

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