NAG FL Interface
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: $\mathbf{branch}$ – Integer Input

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: $\mathbf{offset}$ – Logical Input

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

4: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $-1$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. When the value $-\mathbf{1}$ 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, $\mathbf{branch}=⟨\mathit{\text{value}}⟩$.
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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results