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estimate_cond_number.hpp
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/* =============================================================================
Copyright (c) 2014 - 2016
F. 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:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. 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.
3. Neither the name of the copyright holder 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 HOLDER 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 "specmicp_common/types.hpp"
//! \file micpsolver/estimate_cond_number.hpp
//! \brief Estimate the condition number of a matrix
namespace specmicp {
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
{
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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