Function.h

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#ifndef SimTK_SIMMATH_FUNCTION_H_
#define SimTK_SIMMATH_FUNCTION_H_

/* -------------------------------------------------------------------------- *
 *                      SimTK Core: SimTK Simmath(tm)                         *
 * -------------------------------------------------------------------------- *
 * This is part of the SimTK Core biosimulation toolkit originating from      *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org.               *
 *                                                                            *
 * Portions copyright (c) 2008 Stanford University and the Authors.           *
 * Authors: Peter Eastman                                                     *
 * Contributors:                                                              *
 *                                                                            *
 * Permission is hereby granted, free of charge, to any person obtaining a    *
 * copy of this software and associated documentation files (the "Software"), *
 * to deal in the Software without restriction, including without limitation  *
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,   *
 * and/or sell copies of the Software, and to permit persons to whom the      *
 * Software is furnished to do so, subject to the following conditions:       *
 *                                                                            *
 * The above copyright notice and this permission notice shall be included in *
 * all copies or substantial portions of the Software.                        *
 *                                                                            *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,   *
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL    *
 * THE AUTHORS, CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,    *
 * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR      *
 * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE  *
 * USE OR OTHER DEALINGS IN THE SOFTWARE.                                     *
 * -------------------------------------------------------------------------- */

#include "SimTKcommon.h"

namespace SimTK {

template <int N>
class Function {
public:
    class Constant;
    class Linear;
    class Polynomial;
    virtual ~Function() {
    }
    virtual Vec<N> calcValue(const Vector& x) const = 0;
    virtual Vec<N> calcDerivative(const std::vector<int>& derivComponents, const Vector& x) const = 0;
    virtual int getArgumentSize() const = 0;
    virtual int getMaxDerivativeOrder() const = 0;
};

template <int N>
class Function<N>::Constant : public Function<N> {
public:
    Constant(Vec<N> value, int argumentSize) : value(value), argumentSize(argumentSize) {
    }
    Vec<N> calcValue(const Vector& x) const {
        assert(x.size() == argumentSize);
        return value;
    }
    Vec<N> calcDerivative(const std::vector<int>& derivComponents, const Vector& x) const {
        return Vec<N>(0.0);
    }
    virtual int getArgumentSize() const {
        return argumentSize;
    }
    int getMaxDerivativeOrder() const {
        return std::numeric_limits<int>::max();
    }
private:
    const int argumentSize;
    const Vec<N> value;
};

template <int N>
class Function<N>::Linear : public Function<N> {
public:
    Linear(const Vector_<Vec<N> >& coefficients) : coefficients(coefficients) {
    }
    Vec<N> calcValue(const Vector& x) const {
        assert(x.size() == coefficients.size()-1);
        Vec<N> value(0);
        for (int i = 0; i < x.size(); ++i)
            value += x[i]*coefficients[i];
        value += coefficients[x.size()];
        return value;
    }
    Vec<N> calcDerivative(const std::vector<int>& derivComponents, const Vector& x) const {
        assert(x.size() == coefficients.size()-1);
        assert(derivComponents.size() > 0);
        if (derivComponents.size() == 1)
            return coefficients(derivComponents[0]);
        return Vec<N>(0.0);
    }
    virtual int getArgumentSize() const {
        return coefficients.size()-1;
    }
    int getMaxDerivativeOrder() const {
        return std::numeric_limits<int>::max();
    }
private:
    const Vector_<Vec<N> > coefficients;
};


template <int N>
class Function<N>::Polynomial : public Function<N> {
public:
    Polynomial(const Vector_<Vec<N> >& coefficients) : coefficients(coefficients) {
    }
    Vec<N> calcValue(const Vector& x) const {
        assert(x.size() == 1);
        Real arg = x[0];
        Vec<N> value(0);
        for (int i = 0; i < coefficients.size(); ++i)
            value = value*arg + coefficients[i];
        return value;
    }
    Vec<N> calcDerivative(const std::vector<int>& derivComponents, const Vector& x) const {
        assert(x.size() == 1);
        assert(derivComponents.size() > 0);
        Real arg = x[0];
        Vec<N> value(0);
        const int derivOrder = (int)derivComponents.size();
        const int polyOrder = coefficients.size()-1;
        for (int i = 0; i <= polyOrder-derivOrder; ++i) {
            Vec<N> coeff = coefficients[i];
            for (int j = 0; j < derivOrder; ++j)
                coeff *= polyOrder-i-j;
            value = value*arg + coeff;
        }
        return value;
    }
    virtual int getArgumentSize() const {
        return 1;
    }
    int getMaxDerivativeOrder() const {
        return std::numeric_limits<int>::max();
    }
private:
    const Vector_<Vec<N> > coefficients;
};

} // namespace SimTK

#endif // SimTK_SIMMATH_FUNCTION_H_