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//
// $Id$
//
//
// Original author: Darren Kessner <darren@proteowizard.org>
//
// Copyright 2006 Louis Warschaw Prostate Cancer Center
// Cedars Sinai Medical Center, Los Angeles, California 90048
//
// Licensed under the Apache License, Version 2.0 (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.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
#define PWIZ_SOURCE
#include "Parabola.hpp"
#include "pwiz/utility/misc/Std.hpp"
#ifndef NDEBUG
#define NDEBUG
#endif // NDEBUG
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
namespace ublas = boost::numeric::ublas;
#if BOOST_UBLAS_TYPE_CHECK
goo; // need -DNDEBUG in makefile!
#endif
namespace pwiz {
namespace math {
PWIZ_API_DECL Parabola::Parabola(double a, double b, double c)
: a_(3)
{
a_[0] = a;
a_[1] = b;
a_[2] = c;
}
PWIZ_API_DECL Parabola::Parabola(vector<double> a)
: a_(a)
{
if (a_.size() != 3)
throw logic_error("[Parabola::Parabola()] 3 coefficients required.");
}
namespace {
void solve(ublas::matrix<double>& A, ublas::vector<double>& a)
{
ublas::permutation_matrix<size_t> pm(3);
int singular = lu_factorize(A, pm);
if (singular)
throw runtime_error("[Parabola.cpp::solve()] Matrix is singular.");
lu_substitute(A, pm, a); // may cause assertion without NDEBUG defined for ublas, probably due to roundoff errors
}
void fitExact(const vector< pair<double,double> >& samples, vector<double>& coefficients)
{
if (samples.size() != 3)
throw logic_error("[Parabola.cpp::fitExact()] Exactly 3 samples required.\n");
// fit parabola to the 3 samples (xi,yi):
//
// ( x1^2 x1 1 )( a[0] ) ( y1 )
// ( x2^2 x2 1 )( a[1] ) = ( y2 )
// ( x3^2 x3 1 )( a[2] ) ( y3 )
ublas::matrix<double> A(3,3);
ublas::vector<double> a(3);
for (int i=0; i<3; i++)
{
double x = samples[i].first;
double y = samples[i].second;
A(i,0) = x*x;
A(i,1) = x;
A(i,2) = 1;
a(i) = y;
}
solve(A, a);
copy(a.begin(), a.end(), coefficients.begin());
}
void fitWeightedLeastSquares(const vector< pair<double,double> >& samples,
const vector<double>& weights,
vector<double>& coefficients)
{
if (samples.size() != weights.size())
throw logic_error("[Parabola.cpp::fitWeightedLeastSquares] Wrong weight count.");
// given samples {(xi,yi)} and weights {wi}
// minimize e(a) = sum[wi(p(a,xi)-yi)^2],
// where p(a,xi) = a[0](xi)^2 + a[1](xi) + a[0]c
//
// de/da == 0 =>
// ( sum_wx4 sum_wx3 sum_wx2 )( a[0] ) ( sum_wyx2 )
// ( sum_wx3 sum_wx2 sum_wx1 )( a[1] ) = ( sum_wyx1 )
// ( sum_wx2 sum_wx1 sum_wx0 )( a[2] ) ( sum_wyx0 )
//
// where:
// sum_wxn means sum[wi*(xi)^n]
// sum_wyxn means sum[wi*yi*(xi)^n]
double sum_wx4 = 0;
double sum_wx3 = 0;
double sum_wx2 = 0;
double sum_wx1 = 0;
double sum_wx0 = 0;
double sum_wyx2 = 0;
double sum_wyx1 = 0;
double sum_wyx0 = 0;
for (unsigned int i=0; i<samples.size(); i++)
{
double x = samples[i].first;
double y = samples[i].second;
double w = weights[i];
sum_wx4 += w*pow(x,4);
sum_wx3 += w*pow(x,3);
sum_wx2 += w*x*x;
sum_wx1 += w*x;
sum_wx0 += w;
sum_wyx2 += w*y*x*x;
sum_wyx1 += w*y*x;
sum_wyx0 += w*y;
}
ublas::matrix<double> A(3,3);
ublas::vector<double> a(3);
A(0,0) = sum_wx4;
A(1,0) = A(0,1) = sum_wx3;
A(2,0) = A(1,1) = A(0,2) = sum_wx2;
A(1,2) = A(2,1) = sum_wx1;
A(2,2) = sum_wx0;
a(0) = sum_wyx2;
a(1) = sum_wyx1;
a(2) = sum_wyx0;
solve(A, a);
copy(a.begin(), a.end(), coefficients.begin());
}
} // namespace
PWIZ_API_DECL Parabola::Parabola(const vector< pair<double,double> >& samples)
: a_(3)
{
if (samples.size() < 3)
throw logic_error("[Parabola::Parabola()] At least 3 samples required.");
if (samples.size() == 3)
fitExact(samples, a_);
else
fitWeightedLeastSquares(samples, vector<double>(samples.size(),1), a_);
}
// construct by weighted least squares
PWIZ_API_DECL
Parabola::Parabola(const std::vector< std::pair<double,double> >& samples,
const std::vector<double>& weights)
: a_(3)
{
fitWeightedLeastSquares(samples, weights, a_);
}
PWIZ_API_DECL ostream& operator<<(ostream& os, const Parabola& p)
{
vector<double> a = p.coefficients();
os << "[Parabola (" << a[0] << ", " << a[1] << ", " << a[2] << ")]";
return os;
}
} // namespace math
} // namespace pwiz
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