NAG Library Function Document

nag_superlu_condition_number_lu (f11mgc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     norm – Nag_NormTypeInput

On entry: indicates whether ${\kappa }_1\left(A\right)$ or ${\kappa }_{\infty }\left(A\right)$ is to be estimated.

$\mathbf{norm}=\mathrm{Nag\_RealOneNorm}$

${\kappa }_1\left(A\right)$ is estimated.

$\mathbf{norm}=\mathrm{Nag\_RealInfNorm}$

${\kappa }_{\infty }\left(A\right)$ is estimated.

Constraint: $\mathbf{norm}=\mathrm{Nag\_RealOneNorm}$ or $\mathrm{Nag\_RealInfNorm}$.

2:     n – IntegerInput

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

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

3:     il[$\mathit{dim}$] – 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).

4:     lval[$\mathit{dim}$] – 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).

5:     iu[$\mathit{dim}$] – 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).

6:     uval[$\mathit{dim}$] – 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).

7:     anorm – doubleInput

On entry: if $\mathbf{norm}=\mathrm{Nag\_RealOneNorm}$, the $1$-norm of the matrix $A$.

If $\mathbf{norm}=\mathrm{Nag\_RealInfNorm}$, the $\infty$-norm of the matrix $A$.

anorm may be computed by calling nag_superlu_matrix_norm (f11mlc) with the same value for the argument norm.

Constraint: $\mathbf{anorm}\ge 0.0$.

8:     rcond – double *Output

On exit: an estimate of the reciprocal of the condition number of $A$. rcond is set to zero if exact singularity is detected or the estimate underflows. If rcond is less than machine precision, $A$ is singular to working precision.

9:     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 number $〈\mathit{\text{value}}〉$ had an illegal value.

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.

NE_REAL

On entry, $\mathbf{anorm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{anorm}\ge 0.0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f11mgce.c)

9.2  Program Data

Program Data (f11mgce.d)

9.3  Program Results

Program Results (f11mgce.r)