NAG Library Routine Document

F11MDF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     SPEC – CHARACTER(1)Input

On entry: indicates the permutation to be applied.

$\mathbf{SPEC}=\text{'N'}$

The identity permutation is used (i.e., the columns are not permuted).

$\mathbf{SPEC}=\text{'U'}$

The permutation in the IPRM array is used, as supplied by you.

$\mathbf{SPEC}=\text{'M'}$

The permutation computed by the COLAMD algorithm is used

Constraint: $\mathbf{SPEC}=\text{'N'}$, $\text{'U'}$ or $\text{'M'}$.

2:     N – INTEGERInput

On entry: $n$, the order of the matrix $A$.

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

3:     ICOLZP($*$) – INTEGER arrayInput

Note: the dimension of the array ICOLZP must be at least $\mathbf{N}+1$.

On entry: $\mathbf{ICOLZP}\left(i\right)$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the F11 Chapter Introduction.

4:     IROWIX($*$) – INTEGER arrayInput

Note: the dimension of the array IROWIX must be at least $\mathbf{ICOLZP}\left(\mathbf{N}+1\right)-1$, the number of nonzeros of the sparse matrix $A$.

On entry: $\mathbf{IROWIX}\left(i\right)$ contains the row index in $A$ for element $A\left(i\right)$. See Section 2.1.3 in the F11 Chapter Introduction.

5:     IPRM($7\times \mathbf{N}$) – INTEGER arrayInput/Output

On entry: the first $\mathbf{N}$ entries contain the column permutation supplied by you. This will be used if $\mathbf{SPEC}=\text{'U'}$, and ignored otherwise. If used, it must consist of a permutation of all the integers in the range $\left[0,\left(\mathbf{N}-1\right)\right]$, the leftmost column of the matrix $A$ denoted by $0$ and the rightmost by $\mathbf{N}-1$. Labelling columns in this way, $\mathbf{IPRM}\left(i\right)=j$ means that column $i-1$ of $A$ is in position $j$ in $A{P}_c$, where $P_{r}A{P}_c=LU$ expresses the factorization to be performed.

On exit: a new permutation is returned in the first $\mathbf{N}$ entries. The rest of the array contains data structures that will be used by other routines. The routine computes the column elimination tree for $A$ and a post-order permutation on the tree. It then compounds the IPRM permutation given or computed by the COLAMD algorthm with the post-order permutation. This array is needed by the $LU$ factorization routine F11MEF and associated routines F11MFF, F11MHF and F11MMF and should be passed to them unchanged.

6:     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,	$\mathbf{SPEC}\ne \text{'N'}$, $\text{'U'}$ or $\text{'M'}$,
or	$\mathbf{N}<0$.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{SPEC}=\text{'U'}$, but IPRM does not represent a valid permutation of the integers in $\left[0,\left(\mathbf{N}-1\right)\right]$. An input value of IPRM is either out of range or repeated.

$\mathbf{IFAIL}=3$

Unspecified failure of the COLAMD algorithm. This should not happen and should be reported to NAG.

$\mathbf{IFAIL}=4$

On entry, the array ICOLZP failed to satisfy the following constraints:

• $\mathbf{ICOLZP}\left(1\right)=1$;
• $\mathbf{ICOLZP}\left(\mathit{i}-1\right)\le \mathbf{ICOLZP}\left(\mathit{i}\right)$, for $\mathit{i}=2,3,\dots ,\mathbf{N}+1$;
• $\mathbf{ICOLZP}\left(\mathit{i}\right)\le \mathbf{N}\times \mathbf{N}+1$, for $\mathit{i}=1,2,\dots ,\mathbf{N}+1$.

$\mathbf{IFAIL}=5$

On entry, the array IROWIX failed to satisfy the following constraints:

• $1\le \mathbf{IROWIX}\left(\mathit{i}\right)\le \mathbf{N}$, for $\mathit{i}=1,2,\dots ,\mathbf{ICOLZP}\left(\mathbf{N}+1\right)-1$;
• for each column $i=1\dots \mathbf{N}$, the row indices $\mathbf{IROWIX}\left(j\right)$, where $j=\mathbf{ICOLZP}\left(i\right)\dots \mathbf{ICOLZP}\left(i+1\right)-1$, do not repeat.

$\mathbf{IFAIL}=301$

Unable to allocate required internal workspace.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f11mdfe.f90)

9.2  Program Data

Program Data (f11mdfe.d)

9.3  Program Results

Program Results (f11mdfe.r)