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/*****************************************************************************
* \file
* class for automatic differentiation on scalar values and 1st
* derivatives .
*
* \author
* Erwin Aertbelien, Div. PMA, Dep. of Mech. Eng., K.U.Leuven
*
* \version
* ORO_Geometry V0.2
*
* \par Note
* VC6++ contains a bug, concerning the use of inlined friend functions
* in combination with namespaces. So, try to avoid inlined friend
* functions !
*
* \par History
* - $log$
*
* \par Release
* $Id: rall1d.h 19905 2009-04-23 13:29:54Z ben2610 $
* $Name: $
****************************************************************************/
#ifndef Rall1D_H
#define Rall1D_H
#include <assert.h>
#include "utility.h"
namespace KDL {
/**
* Rall1d contains a value, and its gradient, and defines an algebraic structure on this pair.
* This template class has 3 template parameters :
* - T contains the type of the value.
* - V contains the type of the gradient (can be a vector-like type).
* - S defines a scalar type that can operate on Rall1d. This is the type that
* is used to give back values of Norm() etc.
*
* S is usefull when you recurse a Rall1d object into itself to create a 2nd, 3th, 4th,..
* derivatives. (e.g. Rall1d< Rall1d<double>, Rall1d<double>, double> ).
*
* S is always passed by value.
*
* \par Class Type
* Concrete implementation
*/
template <typename T,typename V=T,typename S=T>
class Rall1d
{
public:
typedef T valuetype;
typedef V gradienttype;
typedef S scalartype;
public :
T t; //!< value
V grad; //!< gradient
public :
INLINE Rall1d() {}
T value() const {
return t;
}
V deriv() const {
return grad;
}
explicit INLINE Rall1d(typename TI<T>::Arg c)
{t=T(c);SetToZero(grad);}
INLINE Rall1d(typename TI<T>::Arg tn, typename TI<V>::Arg afg):t(tn),grad(afg) {}
INLINE Rall1d(const Rall1d<T,V,S>& r):t(r.t),grad(r.grad) {}
//if one defines this constructor, it's better optimized then the
//automatically generated one ( this one set's up a loop to copy
// word by word.
INLINE T& Value() {
return t;
}
INLINE V& Gradient() {
return grad;
}
INLINE static Rall1d<T,V,S> Zero() {
Rall1d<T,V,S> tmp;
SetToZero(tmp);
return tmp;
}
INLINE static Rall1d<T,V,S> Identity() {
Rall1d<T,V,S> tmp;
SetToIdentity(tmp);
return tmp;
}
INLINE Rall1d<T,V,S>& operator =(S c)
{t=c;SetToZero(grad);return *this;}
INLINE Rall1d<T,V,S>& operator =(const Rall1d<T,V,S>& r)
{t=r.t;grad=r.grad;return *this;}
INLINE Rall1d<T,V,S>& operator /=(const Rall1d<T,V,S>& rhs)
{
grad = LinComb(rhs.t,grad,-t,rhs.grad) / (rhs.t*rhs.t);
t /= rhs.t;
return *this;
}
INLINE Rall1d<T,V,S>& operator *=(const Rall1d<T,V,S>& rhs)
{
LinCombR(rhs.t,grad,t,rhs.grad,grad);
t *= rhs.t;
return *this;
}
INLINE Rall1d<T,V,S>& operator +=(const Rall1d<T,V,S>& rhs)
{
grad +=rhs.grad;
t +=rhs.t;
return *this;
}
INLINE Rall1d<T,V,S>& operator -=(const Rall1d<T,V,S>& rhs)
{
grad -= rhs.grad;
t -= rhs.t;
return *this;
}
INLINE Rall1d<T,V,S>& operator /=(S rhs)
{
grad /= rhs;
t /= rhs;
return *this;
}
INLINE Rall1d<T,V,S>& operator *=(S rhs)
{
grad *= rhs;
t *= rhs;
return *this;
}
INLINE Rall1d<T,V,S>& operator +=(S rhs)
{
t += rhs;
return *this;
}
INLINE Rall1d<T,V,S>& operator -=(S rhs)
{
t -= rhs;
return *this;
}
// = operators
/* gives warnings on cygwin
template <class T2,class V2,class S2>
friend INLINE Rall1d<T2,V2,S2> operator /(const Rall1d<T2,V2,S2>& lhs,const Rall1d<T2,V2,S2>& rhs);
friend INLINE Rall1d<T,V,S> operator *(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs);
friend INLINE Rall1d<T,V,S> operator +(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs);
friend INLINE Rall1d<T,V,S> operator -(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs);
friend INLINE Rall1d<T,V,S> operator -(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> operator *(S s,const Rall1d<T,V,S>& v);
friend INLINE Rall1d<T,V,S> operator *(const Rall1d<T,V,S>& v,S s);
friend INLINE Rall1d<T,V,S> operator +(S s,const Rall1d<T,V,S>& v);
friend INLINE Rall1d<T,V,S> operator +(const Rall1d<T,V,S>& v,S s);
friend INLINE Rall1d<T,V,S> operator -(S s,const Rall1d<T,V,S>& v);
friend INLINE Rall1d<T,V,S> operator -(const Rall1d<T,V,S>& v,S s);
friend INLINE Rall1d<T,V,S> operator /(S s,const Rall1d<T,V,S>& v);
friend INLINE Rall1d<T,V,S> operator /(const Rall1d<T,V,S>& v,S s);
// = Mathematical functions that operate on Rall1d objects
friend INLINE Rall1d<T,V,S> exp(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> log(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> sin(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> cos(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> tan(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> sinh(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> cosh(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> sqr(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> pow(const Rall1d<T,V,S>& arg,double m) ;
friend INLINE Rall1d<T,V,S> sqrt(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> atan(const Rall1d<T,V,S>& x);
friend INLINE Rall1d<T,V,S> hypot(const Rall1d<T,V,S>& y,const Rall1d<T,V,S>& x);
friend INLINE Rall1d<T,V,S> asin(const Rall1d<T,V,S>& x);
friend INLINE Rall1d<T,V,S> acos(const Rall1d<T,V,S>& x);
friend INLINE Rall1d<T,V,S> abs(const Rall1d<T,V,S>& x);
friend INLINE S Norm(const Rall1d<T,V,S>& value) ;
friend INLINE Rall1d<T,V,S> tanh(const Rall1d<T,V,S>& arg);
friend INLINE Rall1d<T,V,S> atan2(const Rall1d<T,V,S>& y,const Rall1d<T,V,S>& x);
// = Utility functions to improve performance
friend INLINE Rall1d<T,V,S> LinComb(S alfa,const Rall1d<T,V,S>& a,
const T& beta,const Rall1d<T,V,S>& b );
friend INLINE void LinCombR(S alfa,const Rall1d<T,V,S>& a,
const T& beta,const Rall1d<T,V,S>& b,Rall1d<T,V,S>& result );
// = Setting value of a Rall1d object to 0 or 1
friend INLINE void SetToZero(Rall1d<T,V,S>& value);
friend INLINE void SetToOne(Rall1d<T,V,S>& value);
// = Equality in an eps-interval
friend INLINE bool Equal(const Rall1d<T,V,S>& y,const Rall1d<T,V,S>& x,double eps);
*/
};
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator /(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs)
{
return Rall1d<T,V,S>(lhs.t/rhs.t,(lhs.grad*rhs.t-lhs.t*rhs.grad)/(rhs.t*rhs.t));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator *(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs)
{
return Rall1d<T,V,S>(lhs.t*rhs.t,rhs.t*lhs.grad+lhs.t*rhs.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator +(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs)
{
return Rall1d<T,V,S>(lhs.t+rhs.t,lhs.grad+rhs.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator -(const Rall1d<T,V,S>& lhs,const Rall1d<T,V,S>& rhs)
{
return Rall1d<T,V,S>(lhs.t-rhs.t,lhs.grad-rhs.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator -(const Rall1d<T,V,S>& arg)
{
return Rall1d<T,V,S>(-arg.t,-arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator *(S s,const Rall1d<T,V,S>& v)
{
return Rall1d<T,V,S>(s*v.t,s*v.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator *(const Rall1d<T,V,S>& v,S s)
{
return Rall1d<T,V,S>(v.t*s,v.grad*s);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator +(S s,const Rall1d<T,V,S>& v)
{
return Rall1d<T,V,S>(s+v.t,v.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator +(const Rall1d<T,V,S>& v,S s)
{
return Rall1d<T,V,S>(v.t+s,v.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator -(S s,const Rall1d<T,V,S>& v)
{
return Rall1d<T,V,S>(s-v.t,-v.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator -(const Rall1d<T,V,S>& v,S s)
{
return Rall1d<T,V,S>(v.t-s,v.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator /(S s,const Rall1d<T,V,S>& v)
{
return Rall1d<T,V,S>(s/v.t,(-s*v.grad)/(v.t*v.t));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> operator /(const Rall1d<T,V,S>& v,S s)
{
return Rall1d<T,V,S>(v.t/s,v.grad/s);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> exp(const Rall1d<T,V,S>& arg)
{
T v;
v= (exp(arg.t));
return Rall1d<T,V,S>(v,v*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> log(const Rall1d<T,V,S>& arg)
{
T v;
v=(log(arg.t));
return Rall1d<T,V,S>(v,arg.grad/arg.t);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> sin(const Rall1d<T,V,S>& arg)
{
T v;
v=(sin(arg.t));
return Rall1d<T,V,S>(v,cos(arg.t)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> cos(const Rall1d<T,V,S>& arg)
{
T v;
v=(cos(arg.t));
return Rall1d<T,V,S>(v,-sin(arg.t)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> tan(const Rall1d<T,V,S>& arg)
{
T v;
v=(tan(arg.t));
return Rall1d<T,V,S>(v,arg.grad/sqr(cos(arg.t)));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> sinh(const Rall1d<T,V,S>& arg)
{
T v;
v=(sinh(arg.t));
return Rall1d<T,V,S>(v,cosh(arg.t)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> cosh(const Rall1d<T,V,S>& arg)
{
T v;
v=(cosh(arg.t));
return Rall1d<T,V,S>(v,sinh(arg.t)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> sqr(const Rall1d<T,V,S>& arg)
{
T v;
v=(arg.t*arg.t);
return Rall1d<T,V,S>(v,(2.0*arg.t)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> pow(const Rall1d<T,V,S>& arg,double m)
{
T v;
v=(pow(arg.t,m));
return Rall1d<T,V,S>(v,(m*v/arg.t)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> sqrt(const Rall1d<T,V,S>& arg)
{
T v;
v=sqrt(arg.t);
return Rall1d<T,V,S>(v, (0.5/v)*arg.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> atan(const Rall1d<T,V,S>& x)
{
T v;
v=(atan(x.t));
return Rall1d<T,V,S>(v,x.grad/(1.0+sqr(x.t)));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> hypot(const Rall1d<T,V,S>& y,const Rall1d<T,V,S>& x)
{
T v;
v=(hypot(y.t,x.t));
return Rall1d<T,V,S>(v,(x.t/v)*x.grad+(y.t/v)*y.grad);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> asin(const Rall1d<T,V,S>& x)
{
T v;
v=(asin(x.t));
return Rall1d<T,V,S>(v,x.grad/sqrt(1.0-sqr(x.t)));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> acos(const Rall1d<T,V,S>& x)
{
T v;
v=(acos(x.t));
return Rall1d<T,V,S>(v,-x.grad/sqrt(1.0-sqr(x.t)));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> abs(const Rall1d<T,V,S>& x)
{
T v;
v=(Sign(x));
return Rall1d<T,V,S>(v*x,v*x.grad);
}
template <class T,class V,class S>
INLINE S Norm(const Rall1d<T,V,S>& value)
{
return Norm(value.t);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> tanh(const Rall1d<T,V,S>& arg)
{
T v(tanh(arg.t));
return Rall1d<T,V,S>(v,arg.grad/sqr(cosh(arg.t)));
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> atan2(const Rall1d<T,V,S>& y,const Rall1d<T,V,S>& x)
{
T v(x.t*x.t+y.t*y.t);
return Rall1d<T,V,S>(atan2(y.t,x.t),(x.t*y.grad-y.t*x.grad)/v);
}
template <class T,class V,class S>
INLINE Rall1d<T,V,S> LinComb(S alfa,const Rall1d<T,V,S>& a,
const T& beta,const Rall1d<T,V,S>& b ) {
return Rall1d<T,V,S>(
LinComb(alfa,a.t,beta,b.t),
LinComb(alfa,a.grad,beta,b.grad)
);
}
template <class T,class V,class S>
INLINE void LinCombR(S alfa,const Rall1d<T,V,S>& a,
const T& beta,const Rall1d<T,V,S>& b,Rall1d<T,V,S>& result ) {
LinCombR(alfa, a.t, beta, b.t, result.t);
LinCombR(alfa, a.grad, beta, b.grad, result.grad);
}
template <class T,class V,class S>
INLINE void SetToZero(Rall1d<T,V,S>& value)
{
SetToZero(value.grad);
SetToZero(value.t);
}
template <class T,class V,class S>
INLINE void SetToIdentity(Rall1d<T,V,S>& value)
{
SetToIdentity(value.t);
SetToZero(value.grad);
}
template <class T,class V,class S>
INLINE bool Equal(const Rall1d<T,V,S>& y,const Rall1d<T,V,S>& x,double eps=epsilon)
{
return (Equal(x.t,y.t,eps)&&Equal(x.grad,y.grad,eps));
}
}
#endif
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