polynomial.inl

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/** @file
 *  @author Bram de Greve (bramz@users.sourceforge.net)
 *  @author Tom De Muer (tomdemuer@users.sourceforge.net)
 *
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 *  The contents of this file are subject to the Common Public Attribution License 
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 *  the License. You may obtain a copy of the License at 
 *  http://lass.sourceforge.net/cpal-license. The License is based on the 
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 *  use of software over a computer network and provide for limited attribution for 
 *  the Original Developer. In addition, Exhibit A has been modified to be consistent 
 *  with Exhibit B.
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 *  The Original Code is LASS - Library of Assembled Shared Sources.
 *  
 *  The Initial Developer of the Original Code is Bram de Greve and Tom De Muer.
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 */

#ifndef LASS_GUARDIAN_OF_INCLUSION_NUM_POLYNOMIAL_INL
#define LASS_GUARDIAN_OF_INCLUSION_NUM_POLYNOMIAL_INL

#include "num_common.h"
#include "polynomial.h"

namespace lass
{
namespace num
{

// --- public --------------------------------------------------------------------------------------

template <typename T>
Polynomial<T>::Polynomial()
{
}


template <typename T>
Polynomial<T>::Polynomial(TParam iScalar):
    a_(1, iScalar)
{
}



template <typename T>
Polynomial<T>::Polynomial(const TCoefficients& iCoefficients):
    a_(iCoefficients)
{
}


template <typename T>
template <typename InputIterator> 
Polynomial<T>::Polynomial(InputIterator iBegin, InputIterator iEnd):
    a_(iBegin, iEnd)
{
}



template <typename T> inline
const typename Polynomial<T>::TCoefficients& 
Polynomial<T>::coefficients() const
{
    return a_;
}



template <typename T> inline
const typename Polynomial<T>::TValue
Polynomial<T>::operator[](size_t iIndex) const
{
    LASS_ASSERT(iIndex < a_.size());
    return a_[iIndex];
}



template <typename T> inline
const typename Polynomial<T>::TValue 
Polynomial<T>::at(size_t iIndex) const
{
    return iIndex < a_.size() ? a_[iIndex] : TNumTraits::zero;
}



template <typename T>
const typename Polynomial<T>::TValue 
Polynomial<T>::operator()(TParam iX) const
{
    TValue result = TNumTraits::zero;
    TValue x = TNumTraits::one;
    const size_t n = a_.size();
    for (size_t i = 0; i < n; ++i)
    {
        result += a_[i] * x;
        x *= iX;
    }
    return result;
}



template <typename T>
const Polynomial<T>& Polynomial<T>::operator+() const
{
    return *this;
}



template <typename T>
const Polynomial<T> Polynomial<T>::operator-() const
{
    const size_t n = a_.size();
    TCoefficients result(n);
    for (size_t i = 0; i < n; ++i)
    {
        result[i] = -a_[i];
    }
    return Polynomial<T>(result);
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator+=(const Polynomial<T>& iOther)
{
    const size_t n = iOther.a_.size();
    if (a_.size() < n)
    {
        a_.resize(n, TNumTraits::zero);
    }
    for (size_t i = 0; i < n; ++i)
    {
        a_[i] += iOther.a_[i];
    }
    return *this;
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator-=(const Polynomial<T>& iOther)
{
    const size_t n = iOther.a_.size();
    if (a_.size() < n)
    {
        a_.resize(n, TNumTraits::zero);
    }
    for (size_t i = 0; i < n; ++i)
    {
        a_[i] -= iOther.a_[i];
    }
    return *this;
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator*=(const Polynomial<T>& iOther)
{
    const size_t m = a_.size();
    const size_t n = iOther.a_.size();
    TCoefficients result(m + n - 1, TNumTraits::zero);
    for (size_t i = 0; i < m; ++i)
    {
        const TValue a = a_[i];
        for (size_t k = 0; k < n; ++k)
        {
            result[i + k] += a * iOther.a_[k];
        }
    }
    a_.swap(result);
    return *this;
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator+=(TParam iScalar)
{
    if (a_.empty())
    {
        a_.resize(1, iScalar);
    }
    else
    {
        a_[0] += iScalar;
    }
    return *this;
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator-=(TParam iScalar)
{
    if (a_.empty())
    {
        a_.resize(1, -iScalar);
    }
    else
    {
        a_[0] -= iScalar;
    }
    return *this;
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator*=(TParam iScalar)
{
    const size_t n = a_.size();
    for (size_t i = 0; i < n; ++i)
    {
        a_[i] *= iScalar;
    }
    return *this;
}



template <typename T>
Polynomial<T>& Polynomial<T>::operator/=(TParam iScalar)
{
    const size_t n = a_.size();
    for (size_t i = 0; i < n; ++i)
    {
        a_[i] /= iScalar;
    }
    return *this;
}



template <typename T>
Polynomial<T> Polynomial<T>::derivative() const
{
    const size_t n = a_.size();
    if (n < 2)
    {
        return Polynomial<T>();
    }
    TCoefficients result(n - 1);
    for (size_t i = 1; i < n; ++i)
    {
        result[i - 1] = static_cast<T>(i) * a_[i];
    }
    return Polynomial<T>(result);
}



template <typename T>
Polynomial<T> Polynomial<T>::integral() const
{
    const size_t n = a_.size();
    if (n == 0)
    {
        return Polynomial<T>();
    }
    TCoefficients result(n + 1);
    result[0] = TNumTraits::zero;
    for (size_t i = 0; i < n; ++i)
    {
        result[i + 1] = a_[i] / static_cast<T>(i);
    }
    return Polynomial<T>(result);
}



template <typename T>
Polynomial<T> Polynomial<T>::pow(unsigned iPower) const
{
    Polynomial<T> result(1);
    for (unsigned i = 0; i < iPower; ++i)
    {
        result *= *this;
    }
    return result;
}



/** return size of coefficients.
 */
template <typename T>
const typename Polynomial<T>::size_type Polynomial<T>::size() const
{
    return a_.size();
}



/** return iterator to first (lowest) coefficient
 */
template <typename T>
const typename Polynomial<T>::const_iterator Polynomial<T>::begin() const
{
    return a_.begin();
}



/** return iterator to last (highest) coefficient
 */
template <typename T>
const typename Polynomial<T>::const_iterator Polynomial<T>::end() const
{
    return a_.end();
}



/** return constant polynomial 1
 */
template <typename T>
Polynomial<T> Polynomial<T>::one()
{
    static Polynomial<T> result(1);
    return result;
}



/** return linear polynomial x
 */
template <typename T>
Polynomial<T> Polynomial<T>::x()
{
    static TValue coefficients[2] = { 0, 1 };
    static Polynomial<T> result(coefficients, coefficients + 2);
    return result;
}



// --- free ----------------------------------------------------------------------------------------

template <typename T> 
bool operator==(const Polynomial<T>& iA, const Polynomial<T>& iB)
{
    typedef typename Polynomial<T>::TCoefficients TCoefficients;
    const TCoefficients& a = iA.coefficients();
    const TCoefficients& b = iA.coefficients();
    const size_t m = a.size();
    const size_t n = b.size();
    if (m != n)
    {
        return false;
    }
    for (size_t i = 0; i < n; ++i)
    {
        if (a[i] != b[i])
        {
            return false;
        }
    }
    return true;
}



template <typename T> inline 
bool operator!=(const Polynomial<T>& iA, const Polynomial<T>& iB)
{
    return !(iA == iB);
}



template <typename T> inline
Polynomial<T> operator+(const Polynomial<T>& iA, const Polynomial<T>& iB)
{
    Polynomial<T> result(iA);
    result += iB;
    return result;
}



template <typename T> inline
Polynomial<T> operator-(const Polynomial<T>& iA, const Polynomial<T>& iB)
{
    Polynomial<T> result(iA);
    result -= iB;
    return result;
}



template <typename T> inline
Polynomial<T> operator*(const Polynomial<T>& iA, const Polynomial<T>& iB)
{
    Polynomial<T> result(iA);
    result *= iB;
    return result;
}



template <typename T> inline
Polynomial<T> operator+(const T& iA, const Polynomial<T>& iB)
{
    Polynomial<T> result(iB);
    result += iA;
    return result;
}



template <typename T> inline
Polynomial<T> operator-(const T& iA, const Polynomial<T>& iB)
{
    Polynomial<T> result(-iB);
    result += iA;
    return result;
}



template <typename T> inline
Polynomial<T> operator*(const T& iA, const Polynomial<T>& iB)
{
    Polynomial<T> result(iB);
    result *= iA;
    return result;
}



template <typename T> inline
Polynomial<T> operator+(const Polynomial<T>& iA, const T& iB)
{
    Polynomial<T> result(iA);
    result += iB;
    return result;
}



template <typename T> inline
Polynomial<T> operator-(const Polynomial<T>& iA, const T& iB)
{
    Polynomial<T> result(iA);
    result -= iB;
    return result;
}



template <typename T> inline
Polynomial<T> operator*(const Polynomial<T>& iA, const T& iB)
{
    Polynomial<T> result(iA);
    result *= iB;
    return result;
}



template <typename T> inline
Polynomial<T> operator/(const Polynomial<T>& iA, const T& iB)
{
    Polynomial<T> result(iA);
    result /= iB;
    return result;
}



template <typename T, typename Char, typename Traits>
std::basic_ostream<Char, Traits>&
operator<<(std::basic_ostream<Char, Traits>& iS, const Polynomial<T>& iA)
{
    typedef typename Polynomial<T>::TCoefficients TCoefficients;
    const TCoefficients& a = iA.coefficients();
    const size_t n = a.size();
    if (n == 0)
    {
        iS << T();
        return iS;
    }
    iS << a[0];
    for (size_t i = 1; i < n; ++i)
    {
        iS << " + " << a[i] << "x^" << static_cast<unsigned long>(i);
    }
    return iS;
}



}

}

#endif

// EOF