NAG Library Routine Document

f11mgf (direct_real_gen_cond)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{norm}$ – Character(1)Input

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

$\mathbf{norm}=\text{'1'}$ or $\text{'O'}$

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

$\mathbf{norm}=\text{'I'}$

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

Constraint: $\mathbf{norm}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$.

2:     $\mathbf{n}$ – IntegerInput

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

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

3:     $\mathbf{il}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array il must be at least as large as the dimension of the array of the same name in f11mef.

On entry: records the sparsity pattern of matrix $L$ as computed by f11mef.

4:     $\mathbf{lval}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array lval must be at least as large as the dimension of the array of the same name in f11mef.

On entry: records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by f11mef.

5:     $\mathbf{iu}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array iu must be at least as large as the dimension of the array of the same name in f11mef.

On entry: records the sparsity pattern of matrix $U$ as computed by f11mef.

6:     $\mathbf{uval}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array uval must be at least as large as the dimension of the array of the same name in f11mef.

On entry: records some nonzero values of matrix $U$ as computed by f11mef.

7:     $\mathbf{anorm}$ – Real (Kind=nag_wp)Input

On entry: if $\mathbf{norm}=\text{'1'}$ or $\text{'O'}$, the $1$-norm of the matrix $A$.

If $\mathbf{norm}=\text{'I'}$, the $\infty$-norm of the matrix $A$.

anorm may be computed by calling f11mlf with the same value for the argument norm.

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

8:     $\mathbf{rcond}$ – Real (Kind=nag_wp)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:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

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

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{norm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{norm}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11mgfe.f90)

10.2

Program Data

Program Data (f11mgfe.d)

10.3

Program Results

Program Results (f11mgfe.r)