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estimate_cond_number.hpp
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/*-------------------------------------------------------
- Module : micpsolver
- File : estimate_cond_number.hpp
- Author : Fabien Georget
Copyright (c) 2014, Fabien Georget <fabieng@princeton.edu>, Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the Princeton University nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
---------------------------------------------------------*/
#ifndef SPECMICP_MICPSOLVER_ESTIMATECONDNUMBER_HPP
#define SPECMICP_MICPSOLVER_ESTIMATECONDNUMBER_HPP
#include <Eigen/Core>
//! \file estimate_cond_number.hpp Estimate the condition number of a matrix
namespace specmicp {
//! \namespace micpsolver Namespace for the MiCP Solver
namespace micpsolver {
//! \brief Estimate the condition number of a dense square triangular matrix
//!
//! References :
//! - \cite Cline1979
//! - \cite Hager1984
//!
//! @param tmatrix a triangular view of a dense matrix
//! @param maxit maximum number of iterations done by the algorithm (2 triangular solve by iteration)
//!
template <class MatrixType, unsigned int mode>
double estimate_condition_number(Eigen::TriangularView<MatrixType, mode> tmatrix, int maxit=10)
{
const int n = tmatrix.cols();
Eigen::VectorXd x = 1/n*Eigen::VectorXd::Ones(n);
Eigen::VectorXd y(n);
int cnt = 0;
y = tmatrix.solve(x);
while (cnt < maxit)
{
for (int i=0; i<n; ++i)
{
if (y(i) >= 0) y(i) = 1;
else y(i) = -1;
}
tmatrix.solveInPlace(y);
y.reverseInPlace(); // transpose
int j;
const double maxi = y.array().abs().maxCoeff(&j);
const double gamma = y.dot(x);
if (maxi <= gamma) break; // This is a local maximum
x= Eigen::VectorXd::Zero(n);
x(j) = 1;
y = tmatrix.solve(x);
++cnt;
}
// norm tmatrix
// ------------
double nnorm;
if (mode == Eigen::Lower)
{
nnorm = std::abs(tmatrix(0, 0));
for (int i=1; i<n; ++i)
{
double normrow = 0;
for (int j=0; j<i+1; ++j)
{
normrow += std::abs(tmatrix(i, j));
}
nnorm = std::max(nnorm, normrow);
}
}
else if (mode == Eigen::Upper)
{
nnorm = std::abs(tmatrix(n-1, n-1));
for (int i=n-2; i>-1; --i)
{
double normrow = 0;
for (int j=i; j<n; ++j)
{
normrow += std::abs(tmatrix(i, j));
}
nnorm = std::max(nnorm, normrow);
}
}
// Return ||A||*||A^-1||
return nnorm*x.lpNorm<1>();
}
} // end namespace micpsolver
} // end namespace specmicp
#endif // SPECMICP_MICPSOLVER_ESTIMATECONDNUMBER_HPP

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