fims_math.hpp File Reference

A collection of mathematical functions used in FIMS. More...

#include <cmath>
#include <random>
#include <sstream>
#include "../interface/interface.hpp"
#include "fims_vector.hpp"

Go to the source code of this file.

Functions
template<class Type >
const Type	fims_math::logistic (const Type &inflection_point, const Type &slope, const Type &x)
	The general logistic function.
template<class Type >
const Type	fims_math::logit (const Type &a, const Type &b, const Type &x)
	A logit function for bounding of parameters.
template<class Type >
const Type	fims_math::inv_logit (const Type &a, const Type &b, const Type &logit_x)
	An inverse logit function for bounding of parameters.
template<class Type >
const Type	fims_math::double_logistic (const Type &inflection_point_asc, const Type &slope_asc, const Type &inflection_point_desc, const Type &slope_desc, const Type &x)
	The general double logistic function.
template<class Type >
const Type	fims_math::ad_fabs (const Type &x, Type C=1e-5)
template<typename Type >
const Type	fims_math::ad_min (const Type &a, const Type &b, Type C=1e-5)
template<typename Type >
const Type	fims_math::ad_max (const Type &a, const Type &b, Type C=1e-5)
template<class T >
T	fims_math::sum (const std::vector< T > &v)
template<class T >
T	fims_math::sum (const fims::Vector< T > &v)

Detailed Description

A collection of mathematical functions used in FIMS.

Copyright

This file is part of the NOAA, National Marine Fisheries Service Fisheries Integrated Modeling System project. See LICENSE in the source folder for reuse information.

Function Documentation

ad_fabs()

template<class Type >

const Type fims_math::ad_fabs	(	const Type &	x,
		Type	C = 1e-5
	)

Used when x could evaluate to zero, which will result in a NaN for derivative values.

Evaluates:

\( (x^2+C)^.5 \)

Parameters

x	value to keep positive
C	default = 1e-5

Returns

ad_max()

template<typename Type >

const Type fims_math::ad_max ( const Type &  a, const Type &  b, Type  C = 1e-5  )

inline

Returns the maximum between a and b in a continuous manner using:

(a + b + fims_math::ad_fabs(a - b)) *.5; Reference: fims_math::ad_fabs() This is an approximation with minimal error.

Parameters

a
b
C	default = 1e-5

Returns

ad_min()

template<typename Type >

const Type fims_math::ad_min ( const Type &  a, const Type &  b, Type  C = 1e-5  )

inline

Returns the minimum between a and b in a continuous manner using:

(a + b - fims_math::ad_fabs(a - b))*.5; Reference: fims_math::ad_fabs()

This is an approximation with minimal error.

Parameters

a
b
C	default = 1e-5

Returns

double_logistic()

template<class Type >

const Type fims_math::double_logistic ( const Type &  inflection_point_asc, const Type &  slope_asc, const Type &  inflection_point_desc, const Type &  slope_desc, const Type &  x  )

inline

The general double logistic function.

\( \frac{1.0}{ 1.0 + exp(-1.0 * slope_{asc} (x - inflection_point_{asc}))} \left(1-\frac{1.0}{ 1.0 + exp(-1.0 * slope_{desc} (x - inflection_point_{desc}))} \right)\)

Parameters

inflection_point_asc	the inflection point of the ascending limb of the double logistic function
slope_asc	the slope of the ascending limb of the double logistic function
inflection_point_desc	the inflection point of the descending limb of the double logistic function, where inflection_point_desc > inflection_point_asc
slope_desc	the slope of the descending limb of the double logistic function
x	the index the logistic function should be evaluated at

Returns

inv_logit()

template<class Type >

const Type fims_math::inv_logit ( const Type &  a, const Type &  b, const Type &  logit_x  )

inline

An inverse logit function for bounding of parameters.

\( a+\frac{b-a}{1+\mathrm{exp}(-\mathrm{logit}(x))}\)

Parameters

a	lower bound
b	upper bound
logit_x	the parameter in real space

Returns

the parameter in bounded space

logistic()

template<class Type >

const Type fims_math::logistic ( const Type &  inflection_point, const Type &  slope, const Type &  x  )

inline

The general logistic function.

The logistic function can range from zero to one or one to zero, depending on the slope parameter, but it is not normalized to force values to reach those ranges.

\( \frac{1.0}{ 1.0 + exp(-1.0 * slope (x - inflection_point))} \)

Parameters

inflection_point	the inflection point of the logistic function
slope	the slope of the logistic function. A positive slope results in an ascending logistic curve (0 to 1), while a negative slope results in a descending logistic curve (1 to 0).
x	the index the logistic function should be evaluated at

Returns

logit()

template<class Type >

const Type fims_math::logit ( const Type &  a, const Type &  b, const Type &  x  )

inline

A logit function for bounding of parameters.

\( -\mathrm{log}(b-x) + \mathrm{log}(x-a) \)

Parameters

a	lower bound
b	upper bound
x	the parameter in bounded space

Returns

the parameter in real space

sum() [1/2]

template<class T >

T fims_math::sum

(

const fims::Vector< T > &

v

)

Sum elements of a vector

Parameters

v	A vector of constants.

Returns

A single numeric value.

sum() [2/2]

template<class T >

T fims_math::sum

(

const std::vector< T > &

v

)

Sum elements of a vector

Parameters

v	A vector of constants.

Returns

A single numeric value.