sbasis.h revision 07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould/**
07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8Johan Engelen * \file
07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8Johan Engelen * \brief Defines S-power basis function class
07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8Johan Engelen *
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Authors:
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Nathan Hurst <njh@mail.csse.monash.edu.au>
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Michael Sloan <mgsloan@gmail.com>
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen *
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Copyright (C) 2006-2007 authors
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen *
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * This library is free software; you can redistribute it and/or
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * modify it either under the terms of the GNU Lesser General Public
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * License version 2.1 as published by the Free Software Foundation
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * (the "LGPL") or, at your option, under the terms of the Mozilla
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Public License Version 1.1 (the "MPL"). If you do not alter this
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * notice, a recipient may use your version of this file under either
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * the MPL or the LGPL.
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen *
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * You should have received a copy of the LGPL along with this library
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * in the file COPYING-LGPL-2.1; if not, write to the Free Software
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * You should have received a copy of the MPL along with this library
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * in the file COPYING-MPL-1.1
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen *
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * The contents of this file are subject to the Mozilla Public License
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * Version 1.1 (the "License"); you may not use this file except in
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * compliance with the License. You may obtain a copy of the License at
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * http://www.mozilla.org/MPL/
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen *
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * OF ANY KIND, either express or implied. See the LGPL or the MPL for
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen * the specific language governing rights and limitations.
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen */
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen#ifndef SEEN_SBASIS_H
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen#define SEEN_SBASIS_H
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen#include <vector>
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen#include <cassert>
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen#include <iostream>
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
8001ba81cb851b38d86650a2fef5817facffb763johanengelen#include <2geom/linear.h>
8001ba81cb851b38d86650a2fef5817facffb763johanengelen#include <2geom/interval.h>
8001ba81cb851b38d86650a2fef5817facffb763johanengelen#include <2geom/utils.h>
8001ba81cb851b38d86650a2fef5817facffb763johanengelen#include <2geom/exception.h>
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen//#define USE_SBASISN 1
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen#if defined(USE_SBASIS_OF)
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould#include "sbasis-of.h"
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen#elif defined(USE_SBASISN)
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen#include "sbasisN.h"
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelennamespace Geom{
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen/*** An empty SBasis is identically 0. */
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelenclass SBasis : public SBasisN<1>;
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen};
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould#else
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gouldnamespace Geom{
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen/**
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen* \brief S-power basis function class
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen*
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen* An empty SBasis is identically 0. */
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelenclass SBasis{
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen std::vector<Linear> d;
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void push_back(Linear const&l) { d.push_back(l); }
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenpublic:
dc249e33217a0cf547f743fbc08fbce188911972johanengelen // As part of our migration away from SBasis isa vector we provide this minimal set of vector interface methods.
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen size_t size() const {return d.size();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear operator[](unsigned i) const {
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen return d[i];
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen }
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear& operator[](unsigned i) { return d.at(i); }
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear const* begin() const { return (Linear const*)&*d.begin();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear const* end() const { return (Linear const*)&*d.end();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear* begin() { return (Linear*)&*d.begin();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear* end() { return (Linear*)&*d.end();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen bool empty() const {return d.empty();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear &back() {return d.back();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear const &back() const {return d.back();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void pop_back() { d.pop_back();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void resize(unsigned n) { d.resize(n);}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void resize(unsigned n, Linear const& l) { d.resize(n, l);}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void reserve(unsigned n) { d.reserve(n);}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void clear() {d.clear();}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen void insert(Linear* before, const Linear* src_begin, const Linear* src_end) { d.insert(std::vector<Linear>::iterator(before), src_begin, src_end);}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen //void insert(Linear* aa, Linear* bb, Linear* cc} { d.insert(aa, bb, cc);}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen Linear& at(unsigned i) { return d.at(i);}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen //void insert(Linear* before, int& n, Linear const &l) { d.insert(std::vector<Linear>::iterator(before), n, l);}
98a704c566ce5a750d76d5fc9675ccc804ac65f5johanengelen bool operator==(SBasis const&B) const { return d == B.d;}
98a704c566ce5a750d76d5fc9675ccc804ac65f5johanengelen bool operator!=(SBasis const&B) const { return d != B.d;}
dc249e33217a0cf547f743fbc08fbce188911972johanengelen operator std::vector<Linear>() { return d;}
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis() {}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen explicit SBasis(double a) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen push_back(Linear(a,a));
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
98a704c566ce5a750d76d5fc9675ccc804ac65f5johanengelen explicit SBasis(double a, double b) {
98a704c566ce5a750d76d5fc9675ccc804ac65f5johanengelen push_back(Linear(a,b));
98a704c566ce5a750d76d5fc9675ccc804ac65f5johanengelen }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis(SBasis const & a) :
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen d(a.d)
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen {}
07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8Johan Engelen SBasis(std::vector<Linear> const & ls) :
07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8Johan Engelen d(ls)
07bda0b13ae048815f53f21ad1edbe3cc1b7e4e8Johan Engelen {}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis(Linear const & bo) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen push_back(bo);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti SBasis(Linear* bo) {
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti push_back(*bo);
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti }
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen explicit SBasis(size_t n, Linear const&l) : d(n, l) {}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen //IMPL: FragmentConcept
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen typedef double output_type;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen inline bool isZero() const {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(empty()) return true;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen for(unsigned i = 0; i < size(); i++) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(!(*this)[i].isZero()) return false;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return true;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
bacf092e612ad1911c5a4db58261865e54953b34johanengelen inline bool isConstant() const {
bacf092e612ad1911c5a4db58261865e54953b34johanengelen if (empty()) return true;
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen if(!(*this)[0].isConstant()) return false;
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen for (unsigned i = 1; i < size(); i++) {
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen if(!(*this)[i].isZero()) return false;
bacf092e612ad1911c5a4db58261865e54953b34johanengelen }
bacf092e612ad1911c5a4db58261865e54953b34johanengelen return true;
bacf092e612ad1911c5a4db58261865e54953b34johanengelen }
bacf092e612ad1911c5a4db58261865e54953b34johanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen bool isFinite() const;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen inline double at0() const {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(empty()) return 0; else return (*this)[0][0];
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen inline double at1() const{
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(empty()) return 0; else return (*this)[0][1];
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen int degreesOfFreedom() const { return size()*2;}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double valueAt(double t) const {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double s = t*(1-t);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double p0 = 0, p1 = 0;
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti for(unsigned k = size(); k > 0; k--) {
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti const Linear &lin = (*this)[k-1];
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti p0 = p0*s + lin[0];
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti p1 = p1*s + lin[1];
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return (1-t)*p0 + t*p1;
e6bdf746e2d9e775704a475a29cc1bb167ec271cjohanengelen }
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti //double valueAndDerivative(double t, double &der) const {
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti //}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double operator()(double t) const {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return valueAt(t);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
29684a16b6c92bee28a94fdc2607bcc143950fa8johanengelen
d8fa3c4faade9a5a8e7f79450544b1925e1ade41johanengelen std::vector<double> valueAndDerivatives(double t, unsigned n) const;
29684a16b6c92bee28a94fdc2607bcc143950fa8johanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis toSBasis() const { return SBasis(*this); }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double tailError(unsigned tail) const;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen// compute f(g)
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis operator()(SBasis const & g) const;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//MUTATOR PRISON
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen //remove extra zeros
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen void normalize() {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen while(!empty() && 0 == back()[0] && 0 == back()[1])
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen pop_back();
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen void truncate(unsigned k) { if(k < size()) resize(k); }
d02f89424319afe28fe2cc6696c28108448de3acmcecchettiprivate:
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti void derive(); // in place version
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen};
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//TODO: figure out how to stick this in linear, while not adding an sbasis dep
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis Linear::toSBasis() const { return SBasis(*this); }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//implemented in sbasis-roots.cpp
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed GouldOptInterval bounds_exact(SBasis const &a);
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed GouldOptInterval bounds_fast(SBasis const &a, int order = 0);
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed GouldOptInterval bounds_local(SBasis const &a, const OptInterval &t, int order = 0);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould/** Returns a function which reverses the domain of a.
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould \param a sbasis function
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \relates SBasis
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Goulduseful for reversing a parameteric curve.
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould*/
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis reverse(SBasis const &a) {
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen SBasis result(a.size(), Linear());
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen for(unsigned k = 0; k < a.size(); k++)
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen result[k] = reverse(a[k]);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return result;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//IMPL: ScalableConcept
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator-(const SBasis& p) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(p.isZero()) return SBasis();
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen SBasis result(p.size(), Linear());
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen for(unsigned i = 0; i < p.size(); i++) {
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen result[i] = -p[i];
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return result;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis operator*(SBasis const &a, double k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator*(double k, SBasis const &a) { return a*k; }
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator/(SBasis const &a, double k) { return a*(1./k); }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis& operator*=(SBasis& a, double b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis& operator/=(SBasis& a, double b) { return (a*=(1./b)); }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//IMPL: AddableConcept
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis operator+(const SBasis& a, const SBasis& b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis operator-(const SBasis& a, const SBasis& b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis& operator+=(SBasis& a, const SBasis& b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis& operator-=(SBasis& a, const SBasis& b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//TODO: remove?
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen/*inline SBasis operator+(const SBasis & a, Linear const & b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(b.isZero()) return a;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero()) return b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis result(a);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen result[0] += b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return result;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator-(const SBasis & a, Linear const & b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(b.isZero()) return a;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis result(a);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen result[0] -= b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return result;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis& operator+=(SBasis& a, const Linear& b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero())
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a.push_back(b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen else
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a[0] += b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return a;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis& operator-=(SBasis& a, const Linear& b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero())
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a.push_back(-b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen else
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a[0] -= b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return a;
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen }*/
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//IMPL: OffsetableConcept
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator+(const SBasis & a, double b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero()) return Linear(b, b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis result(a);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen result[0] += b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return result;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator-(const SBasis & a, double b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero()) return Linear(-b, -b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis result(a);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen result[0] -= b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return result;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis& operator+=(SBasis& a, double b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero())
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen a = SBasis(Linear(b,b));
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen else
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a[0] += b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return a;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis& operator-=(SBasis& a, double b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen if(a.isZero())
c3a8ad9235ff81909bd472707550aef5b91daf7bjohanengelen a = SBasis(Linear(-b,-b));
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen else
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a[0] -= b;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return a;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis shift(SBasis const &a, int sh);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis shift(Linear const &a, int sh);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis truncate(SBasis const &a, unsigned terms) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen SBasis c;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen c.insert(c.begin(), a.begin(), a.begin() + std::min(terms, (unsigned)a.size()));
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return c;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis multiply(SBasis const &a, SBasis const &b);
d02f89424319afe28fe2cc6696c28108448de3acmcecchetti// This performs a multiply and accumulate operation in about the same time as multiply. return a*b + c
d02f89424319afe28fe2cc6696c28108448de3acmcecchettiSBasis multiply_add(SBasis const &a, SBasis const &b, SBasis c);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis integral(SBasis const &c);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis derivative(SBasis const &a);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis sqrt(SBasis const &a, int k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen// return a kth order approx to 1/a)
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis reciprocal(Linear const &a, int k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis divide(SBasis const &a, SBasis const &b, int k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis operator*(SBasis const & a, SBasis const & b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return multiply(a, b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis& operator*=(SBasis& a, SBasis const & b) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen a = multiply(a, b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return a;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould/** Returns the degree of the first non zero coefficient.
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould \param a sbasis function
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould \param tol largest abs val considered 0
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \return first non zero coefficient
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \relates SBasis
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould*/
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline unsigned
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenvaluation(SBasis const &a, double tol=0){
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen unsigned val=0;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen while( val<a.size() &&
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen fabs(a[val][0])<tol &&
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen fabs(a[val][1])<tol )
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen val++;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return val;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen// a(b(t))
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis compose(SBasis const &a, SBasis const &b);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis compose(SBasis const &a, SBasis const &b, unsigned k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis inverse(SBasis a, int k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//compose_inverse(f,g)=compose(f,inverse(g)), but is numerically more stable in some good cases...
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen//TODO: requires g(0)=0 & g(1)=1 atm. generalization should be obvious.
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis compose_inverse(SBasis const &f, SBasis const &g, unsigned order=2, double tol=1e-3);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould/** Returns the sbasis on domain [0,1] that was t on [from, to]
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param t sbasis function
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould \param from,to interval
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \return sbasis
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \relates SBasis
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould*/
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis portion(const SBasis &t, double from, double to) { return compose(t, Linear(from, to)); }
40742313779ee5e43be93a9191f1c86412cf183bKrzysztof Kosińskiinline SBasis portion(const SBasis &t, Interval ivl) { return compose(t, Linear(ivl.min(), ivl.max())); }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen// compute f(g)
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline SBasis
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis::operator()(SBasis const & g) const {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return compose(*this, g);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline std::ostream &operator<< (std::ostream &out_file, const Linear &bo) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen out_file << "{" << bo[0] << ", " << bo[1] << "}";
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return out_file;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengeleninline std::ostream &operator<< (std::ostream &out_file, const SBasis & p) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen for(unsigned i = 0; i < p.size(); i++) {
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen out_file << p[i] << "s^" << i << " + ";
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen }
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen return out_file;
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
01d27eab5fca2dcb8e883011f8be77ae6b78a11cTed Gould// These are deprecated, use sbasis-math.h versions if possible
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis sin(Linear bo, int k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenSBasis cos(Linear bo, int k);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenstd::vector<double> roots(SBasis const & s);
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelenstd::vector<double> roots(SBasis const & s, Interval const inside);
981b809bc6ed10a21e89444d9447e5475801874fjohanengelenstd::vector<std::vector<double> > multi_roots(SBasis const &f,
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen std::vector<double> const &levels,
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double htol=1e-7,
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double vtol=1e-7,
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double a=0,
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen double b=1);
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen//--------- Levelset like functions -----------------------------------------------------
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen/** Solve f(t) = v +/- tolerance. The collection of intervals where
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen * v - vtol <= f(t) <= v+vtol
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen * is returned (with a precision tol on the boundaries).
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param f sbasis function
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param level the value of v.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param vtol: error tolerance on v.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param a, b limit search on domain [a,b]
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param tol: tolerance on the result bounds.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \returns a vector of intervals.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen*/
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelenstd::vector<Interval> level_set (SBasis const &f,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double level,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double vtol = 1e-5,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double a=0.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double b=1.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double tol = 1e-5);
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen/** Solve f(t)\in I=[u,v], which defines a collection of intervals (J_k). More precisely,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen * a collection (J'_k) is returned with J'_k = J_k up to a given tolerance.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param f sbasis function
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param level: the given interval of deisred values for f.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param a, b limit search on domain [a,b]
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param tol: tolerance on the bounds of the result.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \returns a vector of intervals.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen*/
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelenstd::vector<Interval> level_set (SBasis const &f,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen Interval const &level,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double a=0.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double b=1.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double tol = 1e-5);
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen/** 'Solve' f(t) = v +/- tolerance for several values of v at once.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param f sbasis function
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param levels vector of values, that should be sorted.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param vtol: error tolerance on v.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param a, b limit search on domain [a,b]
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param tol: the bounds of the returned intervals are exact up to that tolerance.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \returns a vector of vectors of intervals.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen*/
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelenstd::vector<std::vector<Interval> > level_sets (SBasis const &f,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen std::vector<double> const &levels,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double a=0.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double b=1.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double vtol = 1e-5,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double tol = 1e-5);
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen/** 'Solve' f(t)\in I=[u,v] for several intervals I at once.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param f sbasis function
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param levels vector of 'y' intervals, that should be disjoints and sorted.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param a, b limit search on domain [a,b]
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \param tol: the bounds of the returned intervals are exact up to that tolerance.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen \returns a vector of vectors of intervals.
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen*/
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelenstd::vector<std::vector<Interval> > level_sets (SBasis const &f,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen std::vector<Interval> const &levels,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double a=0.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double b=1.,
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen double tol = 1e-5);
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen}
6c3e745a94ef6b25a4ef9f018d350a7535aa45afTed Gould#endif
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen/*
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen Local Variables:
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen mode:c++
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen c-file-style:"stroustrup"
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen indent-tabs-mode:nil
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen fill-column:99
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen End:
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen*/
a4030d5ca449e7e384bc699cd249ee704faaeab0Chris Morgan// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
981b809bc6ed10a21e89444d9447e5475801874fjohanengelen#endif