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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.0 (2010/01/01)
#include "NoniterativeEigensolver.h"
WM5_CONSOLE_APPLICATION(NoniterativeEigensolver);
// Enable only one of these. You should run all of these in release mode.
#define MEASURE_NONITERATIVE
//#define TIMING_NONITERATIVE
//#define TIMING_ITERATIVE
//----------------------------------------------------------------------------
NoniterativeEigensolver::NoniterativeEigensolver ()
:
ConsoleApplication("SampleMathematics/NoniterativeEigensolver")
{
}
//----------------------------------------------------------------------------
int NoniterativeEigensolver::Main (int, char**)
{
#ifdef MEASURE_NONITERATIVE
float maxIterativeError = 0.0f;
float maxNoniterativeError = 0.0f;
int iterativeErrorIndex = -1;
int noniterativeErrorIndex = -1;
float minIterativeDeterminant = 1.0f;
float minNoniterativeDeterminant = 1.0f;
int iterativeDeterminantIndex = -1;
int noniterativeDeterminantIndex = -1;
const int imax = (1 << 28);
#endif
#if defined(TIMING_ITERATIVE) || defined(TIMING_NONITERATIVE)
const int imax = (1 << 24);
clock_t startTime = clock();
#endif
for (int i = 0, type = 0; i < imax; ++i)
{
Vector3f axis = Vector3f(Mathf::SymmetricRandom(),
Mathf::SymmetricRandom(), Mathf::SymmetricRandom());
axis.Normalize();
float angle = Mathf::IntervalRandom(0.0f, Mathf::PI);
Matrix3f rotate(axis, angle);
float d0, d1, d2;
if (type == 0)
{
// d0 = d1 = d2
d1 = Mathf::IntervalRandom(-1.0f, 1.0f);
d0 = d1;
d2 = d1;
}
else if (type == 1)
{
// d0 = d1 < d2
d1 = Mathf::IntervalRandom(-1.0f, 1.0f);
d0 = d1;
d2 = Mathf::IntervalRandom(0.5f*(d1 + 1.0f), 1.0f);
}
else if (type == 2)
{
// d0 < d1 = d2
d1 = Mathf::IntervalRandom(-1.0f, 1.0f);
d0 = Mathf::IntervalRandom(-1.0f, 0.5f*(d1 - 1.0f));
d2 = d1;
}
else
{
// d0 < d1 < d2
d1 = Mathf::IntervalRandom(-1.0f, 1.0f);
d0 = Mathf::IntervalRandom(-1.0f, 0.5f*(d1 - 1.0f));
d2 = Mathf::IntervalRandom(0.5f*(d1 + 1.0f), 1.0f);
}
Matrix3f A = rotate.TransposeTimes(Matrix3f(d0, d1, d2)*rotate);
#ifdef MEASURE_NONITERATIVE
float iterativeError, noniterativeError;
float iterativeDeterminant, noniterativeDeterminant;
SolveAndMeasure(A, iterativeError, noniterativeError,
iterativeDeterminant, noniterativeDeterminant);
if (iterativeError > maxIterativeError)
{
maxIterativeError = iterativeError;
iterativeErrorIndex = i;
}
if (noniterativeError > maxNoniterativeError)
{
maxNoniterativeError = noniterativeError;
noniterativeErrorIndex = i;
}
if (iterativeDeterminant < minIterativeDeterminant)
{
minIterativeDeterminant = iterativeDeterminant;
iterativeDeterminantIndex = i;
}
if (noniterativeDeterminant < minNoniterativeDeterminant)
{
minNoniterativeDeterminant = noniterativeDeterminant;
noniterativeDeterminantIndex = i;
}
#endif
#ifdef TIMING_ITERATIVE
EigenDecompositionf iterativeSolver(A);
iterativeSolver.Solve(true);
#endif
#ifdef TIMING_NONITERATIVE
NoniterativeEigen3x3f noniterativeSolve(A);
#endif
if (++type == 4)
{
type = 0;
}
}
#ifdef MEASURE_NONITERATIVE
std::ofstream measureOutFile("measures.txt");
measureOutFile << "iterations = "
<< imax << std::endl;
measureOutFile << "max iterative error = "
<< maxIterativeError << std::endl;
measureOutFile << "max noniterative error = "
<< maxNoniterativeError << std::endl;
measureOutFile << "min iterative determinant = "
<< minIterativeDeterminant << std::endl;
measureOutFile << "min noniterative determinant = "
<< minNoniterativeDeterminant << std::endl;
measureOutFile.close();
#endif
#if defined(TIMING_ITERATIVE) || defined(TIMING_NONITERATIVE)
clock_t finalTime = clock();
long diffTime = finalTime - startTime;
#endif
#ifdef TIMING_ITERATIVE
std::ofstream iterativeOutFile("iterative.txt");
iterativeOutFile << "ticks = " << diffTime << std::endl;
iterativeOutFile.close();
#endif
#ifdef TIMING_NONITERATIVE
std::ofstream noniterativeOutFile("noniterative.txt");
noniterativeOutFile << "ticks = " << diffTime << std::endl;
noniterativeOutFile.close();
#endif
return 0;
}
//----------------------------------------------------------------------------
void NoniterativeEigensolver::SolveAndMeasure (const Matrix3f& A,
float& iterativeError, float& noniterativeError,
float& iterativeDeterminant, float& noniterativeDeterminant)
{
int i;
Vector3f result;
float length;
iterativeError = 0.0f;
noniterativeError = 0.0f;
// Iterative eigensolver.
EigenDecompositionf iterativeSolver(A);
iterativeSolver.Solve(true);
for (i = 0; i < 3; ++i)
{
mIterativeEigenvalues[i] = iterativeSolver.GetEigenvalue(i);
mIterativeEigenvectors[i] = iterativeSolver.GetEigenvector3(i);
result = A*mIterativeEigenvectors[i] -
mIterativeEigenvalues[i]*mIterativeEigenvectors[i];
length = result.Length();
if (length > iterativeError)
{
iterativeError = length;
}
}
iterativeDeterminant = Mathf::FAbs(
mIterativeEigenvectors[0].Dot(mIterativeEigenvectors[1].Cross(
mIterativeEigenvectors[2])));
// Bounded-time eigensolver.
NoniterativeEigen3x3f noniterativeSolver(A);
for (i = 0; i < 3; ++i)
{
mNoniterativeEigenvalues[i] = noniterativeSolver.GetEigenvalue(i);
mNoniterativeEigenvectors[i] = noniterativeSolver.GetEigenvector(i);
result = A*mNoniterativeEigenvectors[i] -
mNoniterativeEigenvalues[i]*mNoniterativeEigenvectors[i];
length = result.Length();
if (length > noniterativeError)
{
noniterativeError = length;
}
}
noniterativeDeterminant = Mathf::FAbs(
mNoniterativeEigenvectors[0].Dot(mNoniterativeEigenvectors[1].Cross(
mNoniterativeEigenvectors[2])));
}
//----------------------------------------------------------------------------
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