NAG Library Function Document

nag_superlu_condition_number_lu (f11mgc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{norm}$ – 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:    $\mathbf{n}$ – IntegerInput

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

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

3:    $\mathbf{il}\left[\mathit{dim}\right]$ – 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:    $\mathbf{lval}\left[\mathit{dim}\right]$ – 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:    $\mathbf{iu}\left[\mathit{dim}\right]$ – 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:    $\mathbf{uval}\left[\mathit{dim}\right]$ – 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:    $\mathbf{anorm}$ – 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:    $\mathbf{rcond}$ – 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:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL

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

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11mgce.c)

10.2

Program Data

Program Data (f11mgce.d)

10.3

Program Results

Program Results (f11mgce.r)