# QuantLib_AbcdMathFunction man page

AbcdMathFunction — Abcd functional form

## Synopsis

`#include <ql/math/abcdmathfunction.hpp>`

Inherits unary_function< Time, Real >.

Inherited by AbcdFunction.

### Public Member Functions

AbcdMathFunction (Real a=0.002, Real b=0.001, Real c=0.16, Real d=0.0005)
AbcdMathFunction (const std::vector< Real > &abcd)
Real operator() (Time t) const
function value at time t: [ f(t) ]
Time maximumLocation () const
time at which the function reaches maximum (if any)
Real maximumValue () const
maximum value of the function
Real longTermValue () const
function value at time +inf: [ f(inf) ]
Real derivative (Time t) const
Real primitive (Time t) const
Real definiteIntegral (Time t1, Time t2) const
Real a () const
Real b () const
Real c () const
Real d () const
const std::vector< Real > & coefficients ()
const std::vector< Real > & derivativeCoefficients ()
std::vector< Real > definiteIntegralCoefficients (Time t, Time t2) const
std::vector< Real > definiteDerivativeCoefficients (Time t, Time t2) const

### Static Public Member Functions

static void validate (Real a, Real b, Real c, Real d)

Real a_
Real b_
Real c_
Real d_

## Detailed Description

Abcd functional form

[ f(t) = [ a + b*t ] e^{-c*t} + d ] following Rebonato's notation.

## Member Function Documentation

### Real derivative (Time t) const

first derivative of the function at time t [ f'(t) = [ (b-c*a) + (-c*b)*t) ] e^{-c*t} ]

### Real primitive (Time t) const

indefinite integral of the function at time t [ int f(t)dt = [ (-a/c-b/c^2) + (-b/c)*t ] e^{-c*t} + d*t ]

### Real definiteIntegral (Time t1, Time t2) const

definite integral of the function between t1 and t2 [ int_{t1}^{t2} f(t)dt ]

Inspectors

### std::vector<Real> definiteIntegralCoefficients (Time t, Time t2) const

coefficients of a AbcdMathFunction defined as definite integral on a rolling window of length tau, with tau = t2-t

### std::vector<Real> definiteDerivativeCoefficients (Time t, Time t2) const

coefficients of a AbcdMathFunction defined as definite derivative on a rolling window of length tau, with tau = t2-t

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

The man pages a_(3), AbcdMathFunction(3), b_(3), c_(3), coefficients(3), d_(3), definiteDerivativeCoefficients(3), definiteIntegral(3), definiteIntegralCoefficients(3), derivative(3), derivativeCoefficients(3), longTermValue(3), maximumLocation(3), maximumValue(3), operator()(3) and validate(3) are aliases of QuantLib_AbcdMathFunction(3).

Wed Feb 7 2018 Version 1.10.1 QuantLib