sbasis.h revision 981b809bc6ed10a21e89444d9447e5475801874f
/*
* sbasis.h - S-power basis function class
*
* Authors:
* Nathan Hurst <njh@mail.csse.monash.edu.au>
* Michael Sloan <mgsloan@gmail.com>
*
* Copyright (C) 2006-2007 authors
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
#ifndef SEEN_SBASIS_H
#define SEEN_SBASIS_H
#include <vector>
#include <cassert>
#include <iostream>
#include "linear.h"
#include "interval.h"
namespace Geom {
/*** An empty SBasis is identically 0. */
class SBasis : public std::vector<Linear>{
public:
SBasis() {}
explicit SBasis(double a) {
push_back(Linear(a,a));
}
SBasis(SBasis const & a) :
std::vector<Linear>(a)
{}
SBasis(Linear const & bo) {
push_back(bo);
}
//IMPL: FragmentConcept
typedef double output_type;
inline bool isZero() const {
if(empty()) return true;
for(unsigned i = 0; i < size(); i++) {
if(!(*this)[i].isZero()) return false;
}
return true;
}
bool isFinite() const;
inline double at0() const {
if(empty()) return 0; else return (*this)[0][0];
}
inline double at1() const{
if(empty()) return 0; else return (*this)[0][1];
}
double valueAt(double t) const {
double s = t*(1-t);
double p0 = 0, p1 = 0;
double sk = 1;
//TODO: rewrite as horner
for(unsigned k = 0; k < size(); k++) {
p0 += sk*(*this)[k][0];
p1 += sk*(*this)[k][1];
sk *= s;
}
return (1-t)*p0 + t*p1;
}
double operator()(double t) const {
return valueAt(t);
}
SBasis toSBasis() const { return SBasis(*this); }
double tailError(unsigned tail) const;
// compute f(g)
SBasis operator()(SBasis const & g) const;
Linear operator[](unsigned i) const {
assert(i < size());
return std::vector<Linear>::operator[](i);
}
//MUTATOR PRISON
Linear& operator[](unsigned i) { return this->at(i); }
//remove extra zeros
void normalize() {
while(!empty() && 0 == back()[0] && 0 == back()[1])
pop_back();
}
void truncate(unsigned k) { if(k < size()) resize(k); }
};
//TODO: figure out how to stick this in linear, while not adding an sbasis dep
inline SBasis Linear::toSBasis() const { return SBasis(*this); }
//implemented in sbasis-roots.cpp
Interval bounds_exact(SBasis const &a);
Interval bounds_fast(SBasis const &a, int order = 0);
Interval bounds_local(SBasis const &a, const Interval &t, int order = 0);
inline SBasis reverse(SBasis const &a) {
SBasis result;
result.reserve(a.size());
for(unsigned k = 0; k < a.size(); k++)
result.push_back(reverse(a[k]));
return result;
}
//IMPL: ScalableConcept
inline SBasis operator-(const SBasis& p) {
if(p.isZero()) return SBasis();
SBasis result;
result.reserve(p.size());
for(unsigned i = 0; i < p.size(); i++) {
result.push_back(-p[i]);
}
return result;
}
SBasis operator*(SBasis const &a, double k);
inline SBasis operator*(double k, SBasis const &a) { return a*k; }
inline SBasis operator/(SBasis const &a, double k) { return a*(1./k); }
SBasis& operator*=(SBasis& a, double b);
inline SBasis& operator/=(SBasis& a, double b) { return (a*=(1./b)); }
//IMPL: AddableConcept
SBasis operator+(const SBasis& a, const SBasis& b);
SBasis operator-(const SBasis& a, const SBasis& b);
SBasis& operator+=(SBasis& a, const SBasis& b);
SBasis& operator-=(SBasis& a, const SBasis& b);
//TODO: remove?
inline SBasis operator+(const SBasis & a, Linear const & b) {
if(b.isZero()) return a;
if(a.isZero()) return b;
SBasis result(a);
result[0] += b;
return result;
}
inline SBasis operator-(const SBasis & a, Linear const & b) {
if(b.isZero()) return a;
SBasis result(a);
result[0] -= b;
return result;
}
inline SBasis& operator+=(SBasis& a, const Linear& b) {
if(a.isZero())
a.push_back(b);
else
a[0] += b;
return a;
}
inline SBasis& operator-=(SBasis& a, const Linear& b) {
if(a.isZero())
a.push_back(-b);
else
a[0] -= b;
return a;
}
//IMPL: OffsetableConcept
inline SBasis operator+(const SBasis & a, double b) {
if(a.isZero()) return Linear(b, b);
SBasis result(a);
result[0] += b;
return result;
}
inline SBasis operator-(const SBasis & a, double b) {
if(a.isZero()) return Linear(-b, -b);
SBasis result(a);
result[0] -= b;
return result;
}
inline SBasis& operator+=(SBasis& a, double b) {
if(a.isZero())
a.push_back(Linear(b,b));
else
a[0] += b;
return a;
}
inline SBasis& operator-=(SBasis& a, double b) {
if(a.isZero())
a.push_back(Linear(-b,-b));
else
a[0] -= b;
return a;
}
SBasis shift(SBasis const &a, int sh);
SBasis shift(Linear const &a, int sh);
inline SBasis truncate(SBasis const &a, unsigned terms) {
SBasis c;
c.insert(c.begin(), a.begin(), a.begin() + std::min(terms, (unsigned)a.size()));
return c;
}
SBasis multiply(SBasis const &a, SBasis const &b);
SBasis integral(SBasis const &c);
SBasis derivative(SBasis const &a);
SBasis sqrt(SBasis const &a, int k);
// return a kth order approx to 1/a)
SBasis reciprocal(Linear const &a, int k);
SBasis divide(SBasis const &a, SBasis const &b, int k);
inline SBasis operator*(SBasis const & a, SBasis const & b) {
return multiply(a, b);
}
inline SBasis& operator*=(SBasis& a, SBasis const & b) {
a = multiply(a, b);
return a;
}
//valuation: degree of the first non zero coefficient.
inline unsigned
valuation(SBasis const &a, double tol=0){
unsigned val=0;
while( val<a.size() &&
fabs(a[val][0])<tol &&
fabs(a[val][1])<tol )
val++;
return val;
}
// a(b(t))
SBasis compose(SBasis const &a, SBasis const &b);
SBasis compose(SBasis const &a, SBasis const &b, unsigned k);
SBasis inverse(SBasis a, int k);
//compose_inverse(f,g)=compose(f,inverse(g)), but is numerically more stable in some good cases...
//TODO: requires g(0)=0 & g(1)=1 atm. generalization should be obvious.
SBasis compose_inverse(SBasis const &f, SBasis const &g, unsigned order=2, double tol=1e-3);
inline SBasis portion(const SBasis &t, double from, double to) { return compose(t, Linear(from, to)); }
// compute f(g)
inline SBasis
SBasis::operator()(SBasis const & g) const {
return compose(*this, g);
}
inline std::ostream &operator<< (std::ostream &out_file, const Linear &bo) {
out_file << "{" << bo[0] << ", " << bo[1] << "}";
return out_file;
}
inline std::ostream &operator<< (std::ostream &out_file, const SBasis & p) {
for(unsigned i = 0; i < p.size(); i++) {
out_file << p[i] << "s^" << i << " + ";
}
return out_file;
}
SBasis sin(Linear bo, int k);
SBasis cos(Linear bo, int k);
std::vector<double> roots(SBasis const & s);
std::vector<std::vector<double> > multi_roots(SBasis const &f,
std::vector<double> const &levels,
double htol=1e-7,
double vtol=1e-7,
double a=0,
double b=1);
}
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
#endif