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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Klaus Spanderen
Copyright (C) 2015 Peter Caspers
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/math/optimization/constraint.hpp>
#include <ql/math/optimization/lmdif.hpp>
#include <ql/math/optimization/levenbergmarquardt.hpp>
#include <ql/functional.hpp>
#include <memory>
namespace QuantLib {
LevenbergMarquardt::LevenbergMarquardt(Real epsfcn,
Real xtol,
Real gtol,
bool useCostFunctionsJacobian)
: epsfcn_(epsfcn), xtol_(xtol), gtol_(gtol),
useCostFunctionsJacobian_(useCostFunctionsJacobian) {}
EndCriteria::Type LevenbergMarquardt::minimize(Problem& P,
const EndCriteria& endCriteria) {
P.reset();
const Array& initX = P.currentValue();
currentProblem_ = &P;
initCostValues_ = P.costFunction().values(initX);
int m = initCostValues_.size();
int n = initX.size();
if (useCostFunctionsJacobian_) {
initJacobian_ = Matrix(m,n);
P.costFunction().jacobian(initJacobian_, initX);
}
Array xx = initX;
std::unique_ptr<Real[]> fvec(new Real[m]);
std::unique_ptr<Real[]> diag(new Real[n]);
int mode = 1;
// magic number recommended by the documentation
Real factor = 100;
// lmdif() evaluates cost function n+1 times for each iteration (technically, 2n+1
// times if useCostFunctionsJacobian is true, but lmdif() doesn't account for that)
int maxfev = endCriteria.maxIterations() * (n + 1);
int nprint = 0;
int info = 0;
int nfev = 0;
std::unique_ptr<Real[]> fjac(new Real[m*n]);
int ldfjac = m;
std::unique_ptr<int[]> ipvt(new int[n]);
std::unique_ptr<Real[]> qtf(new Real[n]);
std::unique_ptr<Real[]> wa1(new Real[n]);
std::unique_ptr<Real[]> wa2(new Real[n]);
std::unique_ptr<Real[]> wa3(new Real[n]);
std::unique_ptr<Real[]> wa4(new Real[m]);
// requirements; check here to get more detailed error messages.
QL_REQUIRE(n > 0, "no variables given");
QL_REQUIRE(m >= n,
"less functions (" << m <<
") than available variables (" << n << ")");
QL_REQUIRE(endCriteria.functionEpsilon() >= 0.0,
"negative f tolerance");
QL_REQUIRE(xtol_ >= 0.0, "negative x tolerance");
QL_REQUIRE(gtol_ >= 0.0, "negative g tolerance");
QL_REQUIRE(maxfev > 0, "null number of evaluations");
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
MINPACK::LmdifCostFunction lmdifCostFunction =
[this](const auto m, const auto n, const auto x, const auto fvec, const auto iflag) {
this->fcn(m, n, x, fvec);
};
MINPACK::LmdifCostFunction lmdifJacFunction =
useCostFunctionsJacobian_
? [this](const auto m, const auto n, const auto x, const auto fjac, const auto iflag) {
this->jacFcn(m, n, x, fjac);
}
: MINPACK::LmdifCostFunction();
MINPACK::lmdif(m, n, xx.begin(), fvec.get(),
endCriteria.functionEpsilon(),
xtol_,
gtol_,
maxfev,
epsfcn_,
diag.get(), mode, factor,
nprint, &info, &nfev, fjac.get(),
ldfjac, ipvt.get(), qtf.get(),
wa1.get(), wa2.get(), wa3.get(), wa4.get(),
lmdifCostFunction,
lmdifJacFunction);
// for the time being
info_ = info;
// check requirements & endCriteria evaluation
QL_REQUIRE(info != 0, "MINPACK: improper input parameters");
QL_REQUIRE(info != 7, "MINPACK: xtol is too small. no further "
"improvement in the approximate "
"solution x is possible.");
QL_REQUIRE(info != 8, "MINPACK: gtol is too small. fvec is "
"orthogonal to the columns of the "
"jacobian to machine precision.");
EndCriteria::Type ecType = EndCriteria::None;
switch (info) {
case 1:
case 2:
case 3:
case 4:
// 2 and 3 should be StationaryPoint, 4 a new gradient-related value,
// but we keep StationaryFunctionValue for backwards compatibility.
ecType = EndCriteria::StationaryFunctionValue;
break;
case 5:
ecType = EndCriteria::MaxIterations;
break;
case 6:
ecType = EndCriteria::FunctionEpsilonTooSmall;
break;
default:
QL_FAIL("unknown MINPACK result: " << info);
}
// set problem
P.setCurrentValue(std::move(xx));
P.setFunctionValue(P.costFunction().value(P.currentValue()));
return ecType;
}
void LevenbergMarquardt::fcn(int, int n, Real* x, Real* fvec) {
Array xt(n);
std::copy(x, x+n, xt.begin());
// constraint handling needs some improvement in the future:
// starting point should not be close to a constraint violation
if (currentProblem_->constraint().test(xt)) {
const Array& tmp = currentProblem_->values(xt);
std::copy(tmp.begin(), tmp.end(), fvec);
} else {
std::copy(initCostValues_.begin(), initCostValues_.end(), fvec);
}
}
void LevenbergMarquardt::jacFcn(int m, int n, Real* x, Real* fjac) {
Array xt(n);
std::copy(x, x+n, xt.begin());
// constraint handling needs some improvement in the future:
// starting point should not be close to a constraint violation
if (currentProblem_->constraint().test(xt)) {
Matrix tmp(m,n);
currentProblem_->costFunction().jacobian(tmp, xt);
Matrix tmpT = transpose(tmp);
std::copy(tmpT.begin(), tmpT.end(), fjac);
} else {
Matrix tmpT = transpose(initJacobian_);
std::copy(tmpT.begin(), tmpT.end(), fjac);
}
}
}
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