VpsMap.h

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#ifndef CLASSIC_VpsMap_HH
#define CLASSIC_VpsMap_HH
 
// ------------------------------------------------------------------------
// $RCSfile: VpsMap.h,v $
// ------------------------------------------------------------------------
// $Revision: 1.1.1.1.2.1 $
// ------------------------------------------------------------------------
// Copyright: see Copyright.readme
// ------------------------------------------------------------------------
//
// Class: VpsMap
//
// ------------------------------------------------------------------------
// Class category: Algebra
// ------------------------------------------------------------------------
//
// $Date: 2004/11/18 22:18:06 $
// $Author: jsberg $
//
// ------------------------------------------------------------------------
 
#include "Algebra/LUMatrix.h"
#include "Algebra/Matrix.h"
#include "Algebra/Tps.h"
#include "Algebra/TpsData.h"
#include "Algebra/TpsMonomial.h"
#include "Algebra/TpsSubstitution.h"
#include "Algebra/Vector.h"
#include "Algebra/Vps.h"
#include "Algebra/VpsMap.h"
#include "Utilities/SizeError.h"
#include <iosfwd>
 
 
// Template class VpsMap<T>, declaration.
// ------------------------------------------------------------------------
//  This class includes substitution operations.
//  The input and output dimensions need not be the same.
 
template <class T>
class VpsMap: public Vps<T> {
 
public:

    //  Construct [b]nDim[/b] series in [b]nVar[/b] variables each.
    VpsMap(int nDim, int nVar);

    VpsMap(const Vps<T> &rhs);

    //  Assign the [b]nDim[/b] components from [b]rhs[/b].
    VpsMap(int nDim, const Tps<T> rhs[]);

    //  The constant terms are zero.
    //  The linear terms are taken from [b]M[/b].
    VpsMap(const Matrix<T> &M);

    //  The constant terms are taken from [b]V[/b].
    //  The linear terms are zero.
    VpsMap(const Vector<T> &V);
 
    VpsMap();
    VpsMap(const VpsMap<T> &rhs);
    ~VpsMap();
    VpsMap<T> &operator=(const VpsMap<T> &y);

    VpsMap<T> substitute(const VpsMap<T> &vv) const;

    VpsMap<T> substitute(const Matrix<T> &M) const;

    VpsMap<T> substitute(const VpsMap<T> &y, int trunc) const;

    VpsMap<T> substituteInto(const Matrix<T> &x) const;

    //  Return the point [b]y[/b] mapped by the map.
    Vector<T> constantTerm(const Vector<T> &y) const;

    //  Extract constant part.
    Vector<T> constantTerm() const;

    //  Return the linear terms of the map around the point [b]y[/b],
    //  i.e. the linear part of the partial differentials at [b]y[/b].
    Matrix<T> linearTerms(const Vector<T> &y) const;

    //  Return the linear part.
    Matrix<T> linearTerms() const;

    VpsMap<T> derivative(int var) const;

    VpsMap<T> integral(int var) const;
};
 
 
// Global Operators on VpsMap<T>
// ------------------------------------------------------------------------

template <class T> VpsMap<T> operator*(const VpsMap<T> &x, const Tps<T> &y);

template <class T> VpsMap<T> operator*(const Tps<T> &x, const VpsMap<T> &y);

template <class T> VpsMap<T> operator*(const VpsMap<T> &x, const T &y);

template <class T> VpsMap<T> operator*(const T &x, const VpsMap<T> &y);

//  Throw DivideError if constant part of [b]y[/b] is zero.
template <class T> VpsMap<T> operator/(const VpsMap<T> &x, const Tps<T> &y);

//  Throw DivideError if [b]y[/b] is zero.
template <class T> VpsMap<T> operator/(const VpsMap<T> &x, const T &y);

template <class T> VpsMap<T> operator+(const VpsMap<T> &x, const VpsMap<T> &y);

template <class T> VpsMap<T> operator-(const VpsMap<T> &x, const VpsMap<T> &y);

template <class T> VpsMap<T> operator+(const VpsMap<T> &x, const Vector<T> &y);

template <class T> VpsMap<T> operator-(const VpsMap<T> &x, const Vector<T> &y);

template <class T> VpsMap<T> operator+(const Vector<T> &x, const VpsMap<T> &y);

template <class T> VpsMap<T> operator-(const Vector<T> &x, const VpsMap<T> &y);

template <class T> std::istream &operator>>(std::istream &, VpsMap<T> &x);

template <class T> std::ostream &operator<<(std::ostream &, const VpsMap<T> &x);

template <class T> inline
VpsMap<T> operator*(const Matrix<T> &x, const VpsMap<T> &y)
{ return y.substituteInto(x); }
 
 
// Template class VpsMap<T>, implementation.
// ------------------------------------------------------------------------
 
template <class T> inline
VpsMap<T>::VpsMap():
    Vps<T>()
{}
 
 
template <class T> inline
VpsMap<T>::VpsMap(int nDim, int nVar):
    Vps<T>(nDim, nVar)
{}
 
 
template <class T> inline
VpsMap<T>::VpsMap(const VpsMap<T> &rhs):
    Vps<T>(rhs)
{}
 
 
template <class T> inline
VpsMap<T>::VpsMap(const Vps<T> &rhs):
    Vps<T>(rhs)
{}
 
 
template <class T> inline
VpsMap<T>::VpsMap(int nDim, const Tps<T> rhs[]):
    Vps<T>(nDim, rhs)
{}
 
 
template <class T> inline
VpsMap<T>::VpsMap(const Matrix<T> &x):
    Vps<T>(x)
{}
 
 
template <class T> inline
VpsMap<T>::VpsMap(const Vector<T> &x):
    Vps<T>(x)
{}
 
 
template <class T> inline
VpsMap<T>::~VpsMap()
{}
 
 
template <class T> inline
VpsMap<T> &VpsMap<T>::operator=(const VpsMap<T> &y) {
    Vps<T>::operator=(y);
    return *this;
}
 
 
template <class T> inline
VpsMap<T> VpsMap<T>::substitute(const VpsMap<T> &y) const {
    return substitute(y, this->getTruncOrder());
}
 
 
template <class T> inline
VpsMap<T> VpsMap<T>::substitute(const Matrix<T> &y) const {
    return substitute(VpsMap<T>(y));
}
 
 
template <class T>
Vector<T> VpsMap<T>::constantTerm(const Vector<T> &y) const {
    if(this->getVariables() != y.size()) {
        throw SizeError("VpsMap::constantTerm()", "Inconsistent dimensions.");
    }
 
    // This statement makes sure that the substitution table exists.
    const Array1D<TpsSubstitution> &table =
        TpsData::getTpsData(this->getTopOrder(),
                            this->getVariables())->getSubTable();
 
    // Copy the constant term.
    Vector<T> z = constantTerm();
    Array1D<T> product(table.size());
    product[0] = T(1);
 
    for(int next = 1; next < table.size();) {
        const TpsSubstitution &s = table[next];
        product[s.order] = product[s.order-1] * y[s.variable];
 
        for(int v = 0; v < this->getDimension(); v++) {
            if(this->data[v][s.index] != T(0)) {
                z[v] += this->data[v][s.index] * product[s.order];
            }
        }
 
        next = (s.order < this->getTopOrder()) ? next + 1 : s.skip;
    }
 
    return z;
}
 
 
template <class T>
Vector<T> VpsMap<T>::constantTerm() const {
    Vector<T> z(this->getDimension());
    for(int i = 0; i < this->getDimension(); i++) z[i] = this->data[i][0];
    return z;
}
 
 
template <class T>
Matrix<T> VpsMap<T>::linearTerms(const Vector<T> &y) const {
    Matrix<T> z(this->getDimension(), this->getVariables());
 
    for(int i = 0; i < z.nrows(); i++) {
        for(int j = 0; j < z.ncols(); j++) {
            z[i][j] = this->data[i].derivative(j).evaluate(y);
        }
    }
 
    return z;
}
 
 
template <class T>
Matrix<T> VpsMap<T>::linearTerms() const {
    Matrix<T> M(this->getDimension(), this->getVariables());
 
    for(int i = 0; i < this->getDimension(); i++) {
        for(int j = 0; j < this->getVariables(); j++) {
            M(i, j) = this->data[i][j+1];
        }
    }
 
    return M;
}
 
 
template <class T>
VpsMap<T> VpsMap<T>::derivative(int var) const {
    VpsMap<T> z(this->getDimension(), this->getVariables());
 
    for(int i = 0; i < this->getDimension(); i++) {
        z[i] = this->data[i].derivative(var);
    }
 
    return z;
}
 
 
template <class T>
VpsMap<T> VpsMap<T>::integral(int var) const {
    VpsMap<T> z(this->getDimension(), this->getVariables());
 
    for(int i = 0; i < this->getDimension(); i++) {
        z[i] = this->data[i].integral(var);
    }
 
    return z;
}
 
 
template <class T>
VpsMap<T> VpsMap<T>::substitute(const VpsMap<T> &y, int trunc) const {
    // Consistency checks.
    this->check();
    y.check();
 
    if(this->variables != y.getDimension()) {
        throw SizeError("VpsMap::substitute()", "Inconsistent dimensions.");
    }
 
    // This statement makes sure that the substitution table exists.
    const Array1D<TpsSubstitution> &table =
        TpsData::getTpsData(trunc, this->getVariables())->getSubTable();
 
 
    // Highest order present in this Vps.
    int topOrder = this->getTopOrder();
    VpsMap<T> z = constantTerm();
 
    if(topOrder) {
        Array1D< Tps<T> > product(topOrder + 1);
        product[0] = Tps<T>(T(1));
 
        for(int next = 1; next < table.size();) {
            const TpsSubstitution &s = table[next];
            product[s.order] = product[s.order-1].multiply(y[s.variable], trunc);
 
            for(int v = 0; v < this->getDimension(); v++) {
                int maxOrder = this->data[v].getMaxOrder();
                int cutOrder = std::min(this->data[v].getTruncOrder(), trunc);
 
                if(s.order <= maxOrder  &&  this->data[v][s.index] != T(0)) {
                    z.data[v] += this->data[v][s.index] *
                                 product[s.order].truncate(cutOrder);
                }
            }
 
            next = (s.order < topOrder) ? next + 1 : s.skip;
        }
    }
 
    return z;
}
 
 
template <class T>
VpsMap<T> VpsMap<T>::substituteInto(const Matrix<T> &x) const {
    if(x.ncols() != this->getDimension()) {
        throw SizeError("VpsMap::substituteInto()", "Inconsistent dimensions.");
    }
 
    VpsMap<T> z(x.nrows(), this->getVariables());
 
    for(int i = 0; i < this->getDimension(); i++) {
        for(int j = 0; j < this->data.size(); j++) {
            z[i] += this->data[j] * x(i, j);
        }
    }
 
    return z;
}
 
 
// Implementation of global functions for class Vps<T>.
// ------------------------------------------------------------------------
 
template <class T> inline
VpsMap<T> operator*(const VpsMap<T> &x, const Tps<T> &y)
{ VpsMap<T> z(x); return z *= y; }
 
template <class T> inline
VpsMap<T> operator*(const Tps<T> &x, const VpsMap<T> &y)
{ VpsMap<T> z(x); return z *= y; }
 
template <class T> inline
VpsMap<T> operator*(const VpsMap<T> &x, const T &y)
{ VpsMap<T> z(x); return z *= y; }
 
template <class T> inline
VpsMap<T> operator*(const T &x, const VpsMap<T> &y)
{ VpsMap<T> z(x); return z *= y; }
 
template <class T> inline
VpsMap<T> operator/(const VpsMap<T> &x, const Tps<T> &y)
{ VpsMap<T> z(x); return z /= y; }
 
template <class T> inline
VpsMap<T> operator/(const VpsMap<T> &x, const T &y)
{ VpsMap<T> z(x); return z /= y; }
 
 
template <class T> inline
VpsMap<T> operator+(const VpsMap<T> &x, const VpsMap<T> &y)
{ VpsMap<T> z(x); return z += y; }
 
template <class T> inline
VpsMap<T> operator-(const VpsMap<T> &x, const VpsMap<T> &y)
{ VpsMap<T> z(x); return z -= y; }
 
template <class T> inline
VpsMap<T> operator+(const VpsMap<T> &x, const Vector<T> &y)
{ VpsMap<T> z(x); return z += y; }
 
template <class T> inline
VpsMap<T> operator-(const VpsMap<T> &x, const Vector<T> &y)
{ VpsMap<T> z(x); return z -= y; }
 
template <class T> inline
VpsMap<T> operator+(const Vector<T> &x, const VpsMap<T> &y)
{ VpsMap<T> z(y); return z += x; }
 
template <class T> inline
VpsMap<T> operator-(const Vector<T> &x, const VpsMap<T> &y)
{ VpsMap<T> z(- y); return z += x; }
 
template <class T> inline
std::istream &operator>>(std::istream &is, VpsMap<T> &x)
{ return x.get(is); }
 
template <class T> inline
std::ostream &operator<<(std::ostream &os, const VpsMap<T> &x)
{ return x.put(os); }
 
#endif // CLASSIC_VpsMap_HH