NAG Library Routine Document

F01ZCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     M – INTEGERInput

3:     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:     KL – INTEGERInput

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

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

5:     KU – INTEGERInput

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

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

6:     A(LDA,N) – REAL (KIND=nag_wp) arrayInput/Output

On entry: if $\mathbf{JOB}=\text{'P'}$, then 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 $\mathbf{JOB}=\text{'U'}$, then 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:     LDA – INTEGERInput

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:     B(LDB,$*$) – REAL (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 $\mathbf{JOB}=\text{'U'}$, then 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 $\mathbf{JOB}=\text{'P'}$, then 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:     LDB – INTEGERInput

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:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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 $\text{'U'}$.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{KL}<0$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{KU}<0$.

$\mathbf{IFAIL}=4$

On entry,

$\mathbf{LDA}<\mathbf{M}$.

$\mathbf{IFAIL}=5$

On entry,

$\mathbf{LDB}<\mathbf{KL}+\mathbf{KU}+1$.

$\mathbf{IFAIL}=6$

On entry,	$\mathbf{M}<1$,
or	$\mathbf{N}<1$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f01zcfe.f90)

9.2  Program Data

Program Data (f01zcfe.d)

9.3  Program Results

Program Results (f01zcfe.r)