NAG Library Routine Document

c05baf (lambertw_real)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: if $\mathbf{offset}=\mathrm{.TRUE.}$, x is the offset $\Delta x$ from $-\exp \left(-1\right)$ of the intended argument to $W$; that is, $W\left(\beta \right)$ is computed, where $\beta =-\exp \left(-1\right)+\Delta x$.

If $\mathbf{offset}=\mathrm{.FALSE.}$, x is the argument $x$ of the function; that is, $W\left(\beta \right)$ is computed, where $\beta =x$.

Constraints:

• if $\mathbf{branch}=0$, $-\exp \left(-1\right)\le \beta$;
• if $\mathbf{branch}=-1$, $-\exp \left(-1\right)\le \beta <0.0$.

2:     $\mathbf{branch}$ – IntegerInput

On entry: the real branch required.

$\mathbf{branch}=0$

The branch $W_0$ is selected.

$\mathbf{branch}=-1$

The branch $W_{-1}$ is selected.

Constraint: $\mathbf{branch}=0$ or $-1$.

3:     $\mathbf{offset}$ – LogicalInput

On entry: controls whether or not x is being specified as an offset from $-\exp \left(-1\right)$.

4:     $\mathbf{ifail}$ – 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, because for this routine the values of the output arguments may be useful even if $\mathbf{ifail}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ 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, $\mathbf{branch}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{branch}=0$ or $-1$.

On entry, $\mathbf{branch}=-1$, $\mathbf{offset}=\mathrm{.FALSE.}$ and $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{branch}=-1$ and $\mathbf{offset}=\mathrm{.FALSE.}$ then $\mathbf{x}<0.0$.

On entry, $\mathbf{branch}=-1$, $\mathbf{offset}=\mathrm{.TRUE.}$ and $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{branch}=-1$ and $\mathbf{offset}=\mathrm{.TRUE.}$ then $\mathbf{x}<\exp \left(-1.0\right)$.

On entry, $\mathbf{offset}=\mathrm{.FALSE.}$ and $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{offset}=\mathrm{.FALSE.}$ then $\mathbf{x}\ge -\exp \left(-1.0\right)$.

On entry, $\mathbf{offset}=\mathrm{.TRUE.}$ and $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{offset}=\mathrm{.TRUE.}$ then $\mathbf{x}\ge 0.0$.

$\mathbf{ifail}=2$

For the given offset x, $W$ is negligibly different from $-1$: $\mathbf{x}=〈\mathit{\text{value}}〉$.

x is close to $-\exp \left(-1\right)$. Enter x as an offset to $-\exp \left(-1\right)$ for greater accuracy: $\mathbf{x}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

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 (c05bafe.f90)

10.2

Program Data

Program Data (c05bafe.d)

10.3

Program Results

Program Results (c05bafe.r)