nag_superlu_diagnostic_lu (f11mmc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_superlu_diagnostic_lu (f11mmc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_superlu_diagnostic_lu (f11mmc) computes the reciprocal pivot growth factor of an LU  factorization of a real sparse matrix in compressed column (Harwell–Boeing) format.

2  Specification

#include <nag.h>
#include <nagf11.h>
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 maxjAj/Uj from the columns Aj and Uj of an LU  factorization of the matrix A, Pr A Pc = LU  where Pr is a row permutation matrix, Pc 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:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
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×n]const IntegerInput
On entry: the column permutation which defines Pc, the row permutation which defines Pr, 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:     rpgdouble *Output
On exit: the reciprocal pivot growth factor maxjAj/Uj. If the reciprocal pivot growth factor is much less than 1, the stability of the LU factorization may be poor.
10:   failNagError *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 number value had an illegal value.
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
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  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).

9  Example

To compute the reciprocal pivot growth for the factorization of the matrix A, where
A= 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 .
In this case, it should be equal to 1.0.

9.1  Program Text

Program Text (f11mmce.c)

9.2  Program Data

Program Data (f11mmce.d)

9.3  Program Results

Program Results (f11mmce.r)


nag_superlu_diagnostic_lu (f11mmc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012