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.
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.
NE_INVALID_PERM_COL: Incorrect column permutations in array iprm.

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