mirror of
https://github.com/NGSolve/netgen.git
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357 lines
7.7 KiB
C++
357 lines
7.7 KiB
C++
#ifndef FILE_AUTODIFF
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#define FILE_AUTODIFF
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/**************************************************************************/
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/* File: autodiff.hpp */
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/* Author: Joachim Schoeberl */
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/* Date: 24. Oct. 02 */
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/**************************************************************************/
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// Automatic differentiation datatype
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namespace netgen
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{
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/**
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Datatype for automatic differentiation.
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Contains function value and D derivatives. Algebraic
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operations are overloaded by using product-rule etc. etc.
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**/
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template <int D, typename SCAL = double>
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class AutoDiff
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{
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SCAL val;
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SCAL dval[D];
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public:
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typedef AutoDiff<D,SCAL> TELEM;
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typedef SCAL TSCAL;
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/// elements are undefined
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AutoDiff () throw() { };
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// { val = 0; for (int i = 0; i < D; i++) dval[i] = 0; } // !
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/// copy constructor
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AutoDiff (const AutoDiff & ad2) throw()
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{
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val = ad2.val;
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for (int i = 0; i < D; i++)
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dval[i] = ad2.dval[i];
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}
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/// initial object with constant value
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AutoDiff (SCAL aval) throw()
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{
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val = aval;
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for (int i = 0; i < D; i++)
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dval[i] = 0;
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}
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/// init object with (val, e_diffindex)
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AutoDiff (SCAL aval, int diffindex) throw()
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{
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val = aval;
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for (int i = 0; i < D; i++)
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dval[i] = 0;
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dval[diffindex] = 1;
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}
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/// assign constant value
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AutoDiff & operator= (SCAL aval) throw()
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{
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val = aval;
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for (int i = 0; i < D; i++)
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dval[i] = 0;
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return *this;
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}
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/// returns value
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SCAL Value() const throw() { return val; }
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/// returns partial derivative
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SCAL DValue (int i) const throw() { return dval[i]; }
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/// access value
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SCAL & Value() throw() { return val; }
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/// accesses partial derivative
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SCAL & DValue (int i) throw() { return dval[i]; }
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///
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AutoDiff<D,SCAL> & operator+= (const AutoDiff<D,SCAL> & y) throw()
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{
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val += y.val;
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for (int i = 0; i < D; i++)
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dval[i] += y.dval[i];
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return *this;
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}
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///
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AutoDiff<D,SCAL> & operator-= (const AutoDiff<D,SCAL> & y) throw()
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{
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val -= y.val;
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for (int i = 0; i < D; i++)
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dval[i] -= y.dval[i];
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return *this;
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}
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///
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AutoDiff<D,SCAL> & operator*= (const AutoDiff<D,SCAL> & y) throw()
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{
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for (int i = 0; i < D; i++)
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{
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// dval[i] *= y.val;
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// dval[i] += val * y.dval[i];
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dval[i] = dval[i] * y.val + val * y.dval[i];
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}
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val *= y.val;
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return *this;
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}
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///
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AutoDiff<D,SCAL> & operator*= (const SCAL & y) throw()
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{
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val *= y;
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for (int i = 0; i < D; i++)
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dval[i] *= y;
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return *this;
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}
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///
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AutoDiff<D,SCAL> & operator/= (const SCAL & y) throw()
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{
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SCAL iy = 1.0 / y;
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val *= iy;
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for (int i = 0; i < D; i++)
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dval[i] *= iy;
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return *this;
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}
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///
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bool operator== (SCAL val2) throw()
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{
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return val == val2;
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}
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///
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bool operator!= (SCAL val2) throw()
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{
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return val != val2;
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}
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///
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bool operator< (SCAL val2) throw()
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{
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return val < val2;
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}
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///
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bool operator> (SCAL val2) throw()
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{
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return val > val2;
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}
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};
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//@{ AutoDiff helper functions.
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/// prints AutoDiff
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template<int D, typename SCAL>
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inline ostream & operator<< (ostream & ost, const AutoDiff<D,SCAL> & x)
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{
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ost << x.Value() << ", D = ";
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for (int i = 0; i < D; i++)
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ost << x.DValue(i) << " ";
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return ost;
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}
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/// AutoDiff plus AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator+ (const AutoDiff<D,SCAL> & x, const AutoDiff<D,SCAL> & y) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value () = x.Value()+y.Value();
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// AutoDiff<D,SCAL> res(x.Value()+y.Value());
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for (int i = 0; i < D; i++)
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res.DValue(i) = x.DValue(i) + y.DValue(i);
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return res;
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}
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/// AutoDiff minus AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator- (const AutoDiff<D,SCAL> & x, const AutoDiff<D,SCAL> & y) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x.Value()-y.Value();
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// AutoDiff<D,SCAL> res (x.Value()-y.Value());
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for (int i = 0; i < D; i++)
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res.DValue(i) = x.DValue(i) - y.DValue(i);
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return res;
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}
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/// double plus AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator+ (double x, const AutoDiff<D,SCAL> & y) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x+y.Value();
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for (int i = 0; i < D; i++)
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res.DValue(i) = y.DValue(i);
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return res;
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}
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/// AutoDiff plus double
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator+ (const AutoDiff<D,SCAL> & y, double x) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x+y.Value();
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for (int i = 0; i < D; i++)
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res.DValue(i) = y.DValue(i);
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return res;
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}
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/// minus AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator- (const AutoDiff<D,SCAL> & x) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = -x.Value();
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for (int i = 0; i < D; i++)
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res.DValue(i) = -x.DValue(i);
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return res;
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}
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/// AutoDiff minus double
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator- (const AutoDiff<D,SCAL> & x, double y) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x.Value()-y;
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for (int i = 0; i < D; i++)
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res.DValue(i) = x.DValue(i);
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return res;
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}
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///
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator- (double x, const AutoDiff<D,SCAL> & y) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x-y.Value();
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for (int i = 0; i < D; i++)
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res.DValue(i) = -y.DValue(i);
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return res;
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}
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/// double times AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator* (double x, const AutoDiff<D,SCAL> & y) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x*y.Value();
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for (int i = 0; i < D; i++)
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res.DValue(i) = x*y.DValue(i);
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return res;
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}
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/// AutoDiff times double
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator* (const AutoDiff<D,SCAL> & y, double x) throw()
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{
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AutoDiff<D,SCAL> res;
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res.Value() = x*y.Value();
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for (int i = 0; i < D; i++)
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res.DValue(i) = x*y.DValue(i);
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return res;
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}
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/// AutoDiff times AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator* (const AutoDiff<D,SCAL> & x, const AutoDiff<D,SCAL> & y) throw()
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{
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AutoDiff<D,SCAL> res;
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SCAL hx = x.Value();
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SCAL hy = y.Value();
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res.Value() = hx*hy;
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for (int i = 0; i < D; i++)
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res.DValue(i) = hx*y.DValue(i) + hy*x.DValue(i);
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return res;
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}
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/// Inverse of AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> Inv (const AutoDiff<D,SCAL> & x)
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{
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AutoDiff<D,SCAL> res(1.0 / x.Value());
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for (int i = 0; i < D; i++)
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res.DValue(i) = -x.DValue(i) / (x.Value() * x.Value());
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return res;
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}
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/// AutoDiff div AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator/ (const AutoDiff<D,SCAL> & x, const AutoDiff<D,SCAL> & y)
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{
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return x * Inv (y);
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}
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/// AutoDiff div double
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator/ (const AutoDiff<D,SCAL> & x, double y)
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{
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return (1/y) * x;
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}
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/// double div AutoDiff
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template<int D, typename SCAL>
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inline AutoDiff<D,SCAL> operator/ (double x, const AutoDiff<D,SCAL> & y)
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{
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return x * Inv(y);
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}
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} // namespace netgen
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namespace ngcore
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{
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/// AutoDiff times AutoDiff
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template<int D, typename SCAL>
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inline netgen::AutoDiff<D,SCAL> sqr (const netgen::AutoDiff<D,SCAL> & x) throw()
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{
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netgen::AutoDiff<D,SCAL> res;
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SCAL hx = x.Value();
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res.Value() = hx*hx;
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hx *= 2;
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for (int i = 0; i < D; i++)
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res.DValue(i) = hx*x.DValue(i);
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return res;
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}
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} // namespace ngcore
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namespace std
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{
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template<int D, typename SCAL>
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inline netgen::AutoDiff<D,SCAL> fabs (const netgen::AutoDiff<D,SCAL> & x)
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{
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double abs = fabs (x.Value());
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netgen::AutoDiff<D,SCAL> res( abs );
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if (abs != 0.0)
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for (int i = 0; i < D; i++)
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res.DValue(i) = x.DValue(i) / abs;
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else
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for (int i = 0; i < D; i++)
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res.DValue(i) = 0.0;
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return res;
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}
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} // namespace std
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#endif
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