NAG Library Routine Document

f01zdf (complex_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:     $\mathbf{m}$ – IntegerInput

3:     $\mathbf{n}$ – IntegerInput

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

Constraints:

• $\mathbf{m}>0$;
• $\mathbf{n}>0$.

4:     $\mathbf{kl}$ – IntegerInput

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

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

5:     $\mathbf{ku}$ – IntegerInput

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

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

6:     $\mathbf{a}\left(\mathbf{lda},\mathbf{n}\right)$ – Complex (Kind=nag_wp) arrayInput/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:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f01zdf is called.

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

8:     $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Complex (Kind=nag_wp) arrayInput/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:     $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f01zdf is called.

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

10:   $\mathbf{ifail}$ – 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, $\mathbf{job}=〈\mathit{\text{value}}〉$.
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 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 (f01zdfe.f90)

10.2

Program Data

Program Data (f01zdfe.d)

10.3

Program Results

Program Results (f01zdfe.r)