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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012 Peter Caspers
Copyright (C) 2013 Klaus Spanderen
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
<http://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 "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/math/matrixutilities/expm.hpp>
#include <ql/math/ode/adaptiverungekutta.hpp>
#include <complex>
using namespace QuantLib;
using namespace boost::unit_test_framework;
using std::exp;
using std::sin;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(OdeTests)
struct ode1 {
Real operator()(Real x, Real y) const { return y; }
};
struct ode2 {
std::complex<Real> operator()(Real x,
const std::complex<Real>& y) {
return std::complex<Real>(0.0,1.0)*y;
}
};
struct ode3 {
std::vector<Real> operator()(Real x, const std::vector<Real>& y) {
std::vector<Real> r(2);
r[0] = y[1]; r[1] = -y[0];
return r;
}
};
struct ode4 {
std::vector<std::complex<Real> > operator()(
const std::complex<Real>& x,
const std::vector<std::complex<Real> >& y) {
std::vector<std::complex<Real> > r(2);
r[0] = y[1]; r[1] = -y[0];
return r;
}
};
BOOST_AUTO_TEST_CASE(testAdaptiveRungeKutta) {
BOOST_TEST_MESSAGE("Testing adaptive Runge Kutta...");
AdaptiveRungeKutta<Real> rk_real(1E-12,1E-4,0.0);
AdaptiveRungeKutta<std::complex<Real> > rk_complex(1E-12,1E-4,0.0);
Real tol1 = 5E-10, tol2 = 2E-12, tol3 = 2E-12, tol4 = 2E-12;
// f'=f, f(0)=1
AdaptiveRungeKutta<Real>::OdeFct1d ode1_ = ode1();
Real y10=1;
// f'=f, f(0)=i
AdaptiveRungeKutta<std::complex<Real> >::OdeFct1d ode2_ = ode2();
std::complex<Real> y20(0.0,1.0);
// f''=-f, f(0)=0, f'(0)=1
AdaptiveRungeKutta<Real>::OdeFct ode3_ = ode3();
std::vector<Real> y30(2); y30[0] = 0.0; y30[1] = 1.0;
// f''=-f, f(0)=1, f'(0)=i
AdaptiveRungeKutta<std::complex<Real> >::OdeFct ode4_ = ode4();
std::vector<std::complex<Real> > y40(2);
y40[0] = 1.0;
y40[1] = std::complex<Real>(0.0,1.0);
Real x=0.0;
Real y1 = y10;
std::complex<Real> y2 = y20;
std::vector<Real> y3 = y30;
std::vector<std::complex<Real> > y4 = y40;
while (x<5.0) {
Real exact1 = exp(x);
std::complex<Real> exact2 =
std::exp(std::complex<Real>(0.0,x)) * std::complex<Real>(0.0,1.0);
Real exact3 = sin(x);
std::complex<Real> exact4 = std::exp(std::complex<Real>(0.0,x));
if ( std::fabs( exact1 - y1 ) > tol1 )
BOOST_FAIL("Error in ode #1: exact solution at x=" << x
<< " is " << exact1
<< ", numerical solution is " << y1
<< " difference " << std::fabs(exact1-y1)
<< " outside tolerance " << tol1);
if ( abs( exact2 - y2 ) > tol2 )
BOOST_FAIL("Error in ode #2: exact solution at x=" << x
<< " is " << exact2
<< ", numerical solution is " << y2
<< " difference " << abs(exact2-y2)
<< " outside tolerance " << tol2);
if ( std::fabs( exact3 - y3[0] ) > tol3 )
BOOST_FAIL("Error in ode #3: exact solution at x=" << x
<< " is " << exact3
<< ", numerical solution is " << y3[0]
<< " difference " << std::fabs(exact3-y3[0])
<< " outside tolerance " << tol3);
if ( abs( exact4 - y4[0] ) > tol4 )
BOOST_FAIL("Error in ode #4: exact solution at x=" << x
<< " is " << exact4
<< ", numerical solution is " << y4[0]
<< " difference " << abs(exact4-y4[0])
<< " outside tolerance " << tol4);
x+=0.01;
y1=rk_real(ode1_,y10,0.0,x);
y2=rk_complex(ode2_,y20,0.0,x);
y3=rk_real(ode3_,y30,0.0,x);
y4=rk_complex(ode4_,y40,0.0,x);
}
}
Real frobenuiusNorm(const Matrix& m) {
return std::sqrt(DotProduct((m*transpose(m)).diagonal(),
Array(m.rows(), 1.0)));
}
BOOST_AUTO_TEST_CASE(testMatrixExponential) {
BOOST_TEST_MESSAGE("Testing matrix exponential based on ode...");
// Reference results are taken from
// http://www.millersville.edu/~bikenaga/linear-algebra/matrix-exponential/matrix-exponential.html
Matrix m(3, 3);
m[0][0] = 5; m[0][1] =-6; m[0][2] =-6;
m[1][0] =-1; m[1][1] = 4; m[1][2] = 2;
m[2][0] = 3; m[2][1] =-6; m[2][2] =-4;
const Real tol = 1e-12;
for (Real t=0.01; t < 11; t+=t) {
const Matrix calculated = Expm(m, t, tol);
Matrix expected(3, 3);
expected[0][0] = -3*std::exp(t)+4*std::exp(2*t);
expected[0][1] = 6*std::exp(t)-6*std::exp(2*t);
expected[0][2] = 6*std::exp(t)-6*std::exp(2*t);
expected[1][0] = std::exp(t)- std::exp(2*t);
expected[1][1] = -2*std::exp(t)+3*std::exp(2*t);
expected[1][2] = -2*std::exp(t)+2*std::exp(2*t);
expected[2][0] = -3*std::exp(t)+3*std::exp(2*t);
expected[2][1] = 6*std::exp(t)-6*std::exp(2*t);
expected[2][2] = 6*std::exp(t)-5*std::exp(2*t);
Matrix diff = calculated - expected;
Real relDiffNorm = frobenuiusNorm(diff)/frobenuiusNorm(expected);
if ( std::fabs(relDiffNorm) > 100*tol) {
BOOST_FAIL("Failed to reproduce expected matrix exponential."
<< "\n rel. difference norm: " << relDiffNorm
<< "\n tolerance : " << 100*tol);
}
const Matrix negativeTime = Expm((-1)*m, -t, tol);
diff = negativeTime - expected;
relDiffNorm = frobenuiusNorm(diff)/frobenuiusNorm(expected);
if ( std::fabs(relDiffNorm) > 100*tol) {
BOOST_FAIL("Failed to reproduce expected matrix exponential."
<< "\n rel. difference norm: " << relDiffNorm
<< "\n tolerance : " << 100*tol);
}
}
}
BOOST_AUTO_TEST_CASE(testMatrixExponentialOfZero) {
BOOST_TEST_MESSAGE("Testing matrix exponential of a zero matrix "
"based on ode...");
Matrix m(3, 3, 0.0);
constexpr double tol = 100*QL_EPSILON;
constexpr double t=1.0;
const Matrix calculated = Expm(m, t);
for (Size i=0; i < calculated.rows(); ++i) {
for (Size j=0; j < calculated.columns(); ++j) {
const Real kroneckerDelta = (i==j)? 1.0 : 0.0;
if (std::fabs(calculated[i][j] -kroneckerDelta) > tol) {
BOOST_FAIL("Failed to reproduce expected matrix exponential."
<< "\n tolerance : " << tol);
}
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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