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/////////////////////////////////////////////////////////////
// //
// Copyright (c) 2003-2014 by The University of Queensland //
// Centre for Geoscience Computing //
// http://earth.uq.edu.au/centre-geoscience-computing //
// //
// Primary Business: Brisbane, Queensland, Australia //
// Licensed under the Open Software License version 3.0 //
// http://www.apache.org/licenses/LICENSE-2.0 //
// //
/////////////////////////////////////////////////////////////
#ifndef ESYS_LSMEIGENVALUECALCULATOR_H
#define ESYS_LSMEIGENVALUECALCULATOR_H
#include "Foundation/Matrix3.h"
#include <iostream>
#include <complex>
#include <vector>
#include <algorithm>
namespace esys
{
namespace lsm
{
class EigenvalueCalculator
{
public:
typedef std::complex<double> Complex;
typedef std::vector<Complex> ComplexVector;
static const double ONE_THIRD;
static const double SQRT_THREE;
inline double cbrt(double a)
{
// cube root is antisymmetric
return (a < 0) ? -std::pow(-a, ONE_THIRD) : std::pow(a, ONE_THIRD);
}
bool hasComplexEigenvalues(const Matrix3 &a) const
{
double b = -(a(0, 0) + a(1, 1) + a(2, 2));
double a00a11 = a(0, 0) * a(1, 1);
double a11a22 = a(1, 1) * a(2, 2);
double a00a22 = a(0, 0) * a(2, 2);
double a10a01 = a(1, 0) * a(0, 1);
double a12a21 = a(1, 2) * a(2, 1);
double a20a02 = a(2, 0) * a(0, 2);
double c = a00a11 + a11a22 + a00a22 - a10a01 - a12a21 - a20a02;
double a10a01a22 = a10a01 * a(2, 2);
double a12a21a00 = a12a21 * a(0, 0);
double a20a02a11 = a20a02 * a(1, 1);
double a00a11a22 = a00a11 * a(2, 2);
double a01a12a20 = a(0, 1) * a( 1, 2) * a( 2, 0);
double a02a10a21 = a(0, 2) * a( 1, 0) * a( 2, 1);
double d = a10a01a22 + a12a21a00 + a20a02a11
- a00a11a22 - a01a12a20 - a02a10a21;
double bb = b * b;
double Q = (3.0 * c - bb) / 9.0;
double R = (9.0 * b * c - 27.0 * d - 2.0 * bb * b) / 54.0;
return (Q * Q * Q > -(R * R));
}
class ComplexRealImagComparer
{
public:
bool operator()(const Complex &c1, const Complex &c2) const
{
return
(
(c1.real() < c2.real())
||
(
(c1.real() == c2.real())
&&
(c1.imag() < c2.imag())
)
);
}
};
class ComplexAbsRealImagComparer
{
public:
bool operator()(const Complex &c1, const Complex &c2) const
{
return
(
(fabs(c1.real()) < fabs(c2.real()))
||
(
(fabs(c1.real()) == fabs(c2.real()))
&&
(fabs(c1.imag()) < fabs(c2.imag()))
)
);
}
};
class ComplexNormComparer
{
public:
bool operator()(const Complex &c1, const Complex &c2) const
{
return (std::norm(c1) < std::norm(c2));
}
};
ComplexVector getEigenvalues(const Matrix3 &a)
{
ComplexVector e(3, Complex(0.0, 0.0));
double b = -(a(0, 0) + a(1, 1) + a(2, 2));
double a00a11 = a(0, 0) * a(1, 1);
double a11a22 = a(1, 1) * a(2, 2);
double a00a22 = a(0, 0) * a(2, 2);
double a10a01 = a(1, 0) * a(0, 1);
double a12a21 = a(1, 2) * a(2, 1);
double a20a02 = a(2, 0) * a(0, 2);
double c = a00a11 + a11a22 + a00a22 - a10a01 - a12a21 - a20a02;
double a10a01a22 = a10a01 * a(2, 2);
double a12a21a00 = a12a21 * a(0, 0);
double a20a02a11 = a20a02 * a(1, 1);
double a00a11a22 = a00a11 * a(2, 2);
double a01a12a20 = a(0, 1) * a(1, 2) * a(2, 0);
double a02a10a21 = a(0, 2) * a(1, 0) * a(2, 1);
double d = a10a01a22 + a12a21a00 + a20a02a11
- a00a11a22 - a01a12a20 - a02a10a21;
double bb = b * b;
double Q = (3.0 * c - bb) / 9.0;
double R = (9.0 * b * c - 27.0 * d - 2.0 * bb * b) / 54.0;
double D = Q * Q * Q + R * R;
double nOTb = -ONE_THIRD * b;
if (D > 0) {
// one real and two Complex conjugate
double sqrtD = sqrt(D);
double S = cbrt(R + sqrtD);
double T = cbrt(R - sqrtD);
double SpT = S + T;
e[0] = nOTb + SpT;
double x = nOTb - 0.5 * SpT;
double y = 0.5 * SQRT_THREE * (S - T);
e[1] = Complex(x, y);
e[2] = Complex(x, -y);
}
else if (D < 0) {
// all real and unequal
double sqrtD = sqrt(-D);
Complex S = std::pow(Complex(R, sqrtD), ONE_THIRD); // T == S.conj()
e[0] = nOTb + 2.0 * S.real();
double x = nOTb - S.real();
double y = SQRT_THREE * S.imag();
e[1] = x - y;
e[2] = x + y;
}
else {
// all real and at least two equal
double S = cbrt(R); // T == S
e[0] = nOTb + 2.0 * S;
e[1] = nOTb - S;
e[2] = e[1];
}
std::sort(e.begin(), e.end(), ComplexRealImagComparer());
return e;
}
void printEigenvalues(const Matrix3 &a)
{
std::cout << "a: " << a(0, 0) << " " << a(0, 1) << " " << a(0, 2) << std::endl
<< " " << a(1, 0) << " " << a(1, 1) << " " << a(1, 2) << std::endl
<< " " << a(2, 0) << " " << a(2, 1) << " " << a(2, 2) << std::endl;
if (hasComplexEigenvalues(a))
std::cout << "Complex eigenvalues" << std::endl;
else
std::cout << "Real eigenvalues" << std::endl;
ComplexVector e = getEigenvalues(a);
std::cout << "e0: " << e[0] << std::endl;
std::cout << "e1: " << e[1] << std::endl;
std::cout << "e2: " << e[2] << std::endl;
std::cout << std::endl;
}
};
}
}
inline std::ostream &operator<<(std::ostream &oStream, const esys::lsm::EigenvalueCalculator::ComplexVector &vec)
{
esys::lsm::EigenvalueCalculator::ComplexVector::const_iterator it = vec.begin();
if (it != vec.end()) {
oStream << (*it);
it++;
}
for (; it != vec.end(); it++)
{
oStream << " " << (*it);
}
return oStream;
}
#endif
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