NAG Library Function Document

nag_superlu_column_permutation (f11mdc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{spec}$ – Nag_ColumnPermutationTypeInput

On entry: indicates the permutation to be applied.

$\mathbf{spec}=\mathrm{Nag\_Sparse\_Identity}$

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

$\mathbf{spec}=\mathrm{Nag\_Sparse\_User}$

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

$\mathbf{spec}=\mathrm{Nag\_Sparse\_Colamd}$

The permutation computed by the COLAMD algorithm is used

Constraint: $\mathbf{spec}=\mathrm{Nag\_Sparse\_Identity}$, $\mathrm{Nag\_Sparse\_User}$ or $\mathrm{Nag\_Sparse\_Colamd}$.

2:    $\mathbf{n}$ – IntegerInput

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

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

3:    $\mathbf{icolzp}\left[\max \left(1,\left(\mathbf{n}+1\right)\right)\right]$ – const IntegerInput

On entry: $\mathbf{icolzp}\left[i-1\right]$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the f11 Chapter Introduction.

4:    $\mathbf{irowix}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array irowix must be at least $\max \left(1,\left(\mathbf{icolzp}\left[\max \left(1,\left(\mathbf{n}+1\right)\right)-1\right]-1\right)\right)$.

On entry: $\mathbf{irowix}\left[i-1\right]$ contains the row index in $A$ for element $A\left(i\right)$. See Section 2.1.3 in the f11 Chapter Introduction.

5:    $\mathbf{iprm}\left[\max \left(1,\left(7\times \mathbf{n}\right)\right)\right]$ – IntegerInput/Output

On entry: the first $\mathbf{n}$ entries contain the column permutation supplied by you. This will be used if $\mathbf{spec}=\mathrm{Nag\_Sparse\_User}$, 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 functions. The function 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 function nag_superlu_lu_factorize (f11mec) and associated functions nag_superlu_solve_lu (f11mfc), nag_superlu_refine_lu (f11mhc) and nag_superlu_diagnostic_lu (f11mmc) and should be passed to them unchanged.

6:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALG_FAIL

COLAMD algorithm failed.

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_PERM_COL

Incorrect column permutations in array iprm.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_SPARSE_COL

Incorrect specification of argument icolzp.

NE_SPARSE_ROW

Incorrect specification of argument irowix.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11mdce.c)

10.2

Program Data

Program Data (f11mdce.d)

10.3

Program Results

Program Results (f11mdce.r)