f11mdc computes a column permutation suitable for
factorization (by f11mec) of a real sparse matrix in compressed column (Harwell–Boeing) format and applies it to the matrix. This function must be called prior to f11mec.
The function may be called by the names: f11mdc, nag_sparse_direct_real_gen_setup or nag_superlu_column_permutation.
Given a sparse matrix in compressed column (Harwell–Boeing) format and a choice of column permutation schemes, the function computes those data structures that will be needed by the
factorization function f11mec and associated functions f11mmc, f11mfc and f11mhc. The column permutation choices are:
original order (that is, no permutation);
a permutation, computed by the function, designed to minimize fill-in during the factorization.
The algorithm for this computed permutation is based on the approximate minimum degree column ordering algorithm COLAMD. The computed permutation is not sensitive to the magnitude of the nonzero values of .
Amestoy P R, Davis T A and Duff I S (1996) An approximate minimum degree ordering algorithm SIAM J. Matrix Anal. Appl. 17 886–905
Gilbert J R and Larimore S I (2004) A column approximate minimum degree ordering algorithm ACM Trans. Math. Software30,3 353–376
Gilbert J R, Larimore S I and Ng E G (2004) Algorithm 836: COLAMD, an approximate minimum degree ordering algorithm ACM Trans. Math. Software30, 3 377–380
1: – Nag_ColumnPermutationTypeInput
On entry: indicates the permutation to be applied.
The identity permutation is used (i.e., the columns are not permuted).
The permutation in the iprm array is used, as supplied by you.
The permutation computed by the COLAMD algorithm is used
, or .
2: – IntegerInput
On entry: , the order of the matrix .
3: – const IntegerInput
On entry: the new column index array of sparse matrix . See Section 2.1.3 in the F11 Chapter Introduction.
4: – const IntegerInput
Note: the dimension, dim, of the array irowix
must be at least
On entry: contains the row index in for element . See Section 2.1.3 in the F11 Chapter Introduction.
5: – IntegerInput/Output
On entry: the first entries contain the column permutation if supplied by the user. This will be used if , and ignored otherwise. If used, it must consist of a permutation of all the integers in the range , the leftmost column of the matrix denoted by and the rightmost by . Labelling columns in this way, means that column of is in position in , where expresses the factorization to be performed.
On exit: The column permutation given or computed is returned in the second entries. The rest of the array contains data structures that will be used by other functions in the suite. The function computes the column elimination tree for 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 and this permutation is returned in the first entries. This whole array is needed by the factorization function f11mec and associated functions f11mfc,f11mhcandf11mmc and should be passed to them unchanged.
6: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
COLAMD algorithm failed.
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, . Constraint: .
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 7.5 in the Introduction to the NAG Library CL Interface for further information.
Not applicable. This computation does not use floating-point numbers.
8Parallelism and Performance
f11mdc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
We recommend calling this function with before calling f11mec. The COLAMD algorithm computes a sparsity-preserving permutation solely from the pattern of such that the
factorization remains as sparse as possible, regardless of the subsequent choice of . The algorithm takes advantage of the existence of super-columns (columns with the same sparsity pattern) to reduce running time.
This example computes a sparsity preserving column permutation for the factorization of the matrix , where