NAG Library Function Document

nag_superlu_diagnostic_lu (f11mmc)

void	nag_superlu_diagnostic_lu (Integer n, const Integer icolzp[], const double a[], const Integer iprm[], const Integer il[], const double lval[], const Integer iu[], const double uval[], double rpg, NagError fail)

3 Description

nag_superlu_diagnostic_lu (f11mmc) computes the reciprocal pivot growth factor

\max_{j} ({‖A_{j}‖}_{\infty} / {‖U_{j}‖}_{\infty})

from the columns

A_{j}

and

U_{j}

of an

L U

factorization of the matrix

A

P_{r} A P_{c} = L U

where

P_{r}

is a row permutation matrix,

P_{c}

is a column permutation matrix,

L

is unit lower triangular and

U

is upper triangular as computed by nag_superlu_lu_factorize (f11mec).

4 References

None.

5 Arguments

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

Constraint: $n \geq 0$ .
2: $icolzp [\dim]$ – const IntegerInput: Note: the dimension, dim, of the array icolzp must be at least $n + 1$ .

On entry: $icolzp [i - 1]$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the f11 Chapter Introduction.
3: $a [\dim]$ – const doubleInput: Note: the dimension, dim, of the array a must be at least $icolzp [n] - 1$ , the number of nonzeros of the sparse matrix $A$ .

On entry: the array of nonzero values in the sparse matrix $A$ .
4: $iprm [7 \times n]$ – const IntegerInput: On entry: the column permutation which defines $P_{c}$ , the row permutation which defines $P_{r}$ , plus associated data structures as computed by nag_superlu_lu_factorize (f11mec).
5: $il [\dim]$ – const IntegerInput: Note: the dimension, dim, of the array il must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records the sparsity pattern of matrix $L$ as computed by nag_superlu_lu_factorize (f11mec).
6: $lval [\dim]$ – const doubleInput: Note: the dimension, dim, of the array lval must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by nag_superlu_lu_factorize (f11mec).
7: $iu [\dim]$ – const IntegerInput: Note: the dimension, dim, of the array iu must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records the sparsity pattern of matrix $U$ as computed by nag_superlu_lu_factorize (f11mec).
8: $uval [\dim]$ – const doubleInput: Note: the dimension, dim, of the array uval must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records some nonzero values of matrix $U$ as computed by nag_superlu_lu_factorize (f11mec).
9: $rpg$ – double *Output: On exit: the reciprocal pivot growth factor $\max_{j} ({‖A_{j}‖}_{\infty} / {‖U_{j}‖}_{\infty})$ . If the reciprocal pivot growth factor is much less than $1$ , the stability of the $L U$ factorization may be poor.
10: $fail$ – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .
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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction 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 3.6.5 in the Essential Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

If the reciprocal pivot growth factor, rpg, is much less than

1

, then the factorization of the matrix

A

could be poor. This means that using the factorization to obtain solutions to a linear system, forward error bounds and estimates of the condition number could be unreliable. Consider increasing the thresh argument in the call to nag_superlu_lu_factorize (f11mec).

10 Example

To compute the reciprocal pivot growth for the factorization of the matrix

A

, where

A = (\begin{matrix} 2.00 & 1.00 & 0 & 0 & 0 \\ 0 & 0 & 1.00 & - 1.00 & 0 \\ 4.00 & 0 & 1.00 & 0 & 1.00 \\ 0 & 0 & 0 & 1.00 & 2.00 \\ 0 & - 2.00 & 0 & 0 & 3.00 \end{matrix}) .

In this case, it should be equal to

1.0

NAG Library Function Documentnag_superlu_diagnostic_lu (f11mmc)

▸▿ Contents

1 Purpose

2 Specification