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# Class LowerBoundedFunction

source code

```            object --+
|
TransformationFunction --+
|
LowerBoundedFunction
```

A function asymptoting to a finite lower bound as x -> -Inf and linearly diverging as x -> +Inf.

This implements the function 0.5 * x + sqrt(1.0 + 0.25 * x^2), which approaches 1/x for small x and x for large x. Like arctan, this function approaches its asymptote with O(1/x) and may therefore be favourable over exponential functions. Linear divergence may also be much less prone to extremes than exponential divergence.

 Instance Methods

 __init__(self, minValue=0.0) x.__init__(...) initializes x; see x.__class__.__doc__ for signature source code

 __call__(self, x) Compute the transformed value of `x`. source code

 __str__(self) str(x) source code

 parse_variables(self, f) source code

 clip(self, y) Clip `y` to the nearest admissible value. source code

 inverse(self, y) Compute the inverse value of `y`. source code

Inherited from `TransformationFunction`: `check_savefile_magic`, `parse`

Inherited from `object`: `__delattr__`, `__getattribute__`, `__hash__`, `__new__`, `__reduce__`, `__reduce_ex__`, `__repr__`, `__setattr__`

 Class Variables
functionName = `'LowerBoundedFunction'`
 Properties

Inherited from `object`: `__class__`

 Method Details

### __init__(self, minValue=0.0)(Constructor)

source code

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: object.__init__
(inherited documentation)

### __call__(self, x)(Call operator)

source code

Compute the transformed value of `x`.

Overrides: TransformationFunction.__call__
(inherited documentation)

### __str__(self)(Informal representation operator)

source code

str(x)

Overrides: object.__str__
(inherited documentation)

### parse_variables(self, f)

source code
Overrides: TransformationFunction.parse_variables

### clip(self, y)

source code

Clip `y` to the nearest admissible value.

Overrides: TransformationFunction.clip
(inherited documentation)

### inverse(self, y)

source code

Compute the inverse value of `y`.

This method should return the untransformed value `x` corresponding to `y`, such that f(x) = y.

Overrides: TransformationFunction.inverse
(inherited documentation)

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