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/*=========================================================================
*
* Copyright NumFOCUS
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#include <iostream>
#include "vnl/algo/vnl_svd.h"
template <typename T>
void
print_vnl_matrix(T & mat)
{
std::cout << mat;
for (unsigned int r = 0; r < mat.rows(); ++r)
{
for (unsigned int c = 0; c < mat.columns(); ++c)
{
std::cout << mat(r, c) << ' ';
}
std::cout << std::endl;
}
}
template <typename V> // V is often double or float
vnl_matrix<V>
solve_with_warning(vnl_matrix<V> const & M, vnl_matrix<V> const & B)
{
// Take svd of vnl_matrix<V> M, setting singular values
// smaller than 1e-8 to 0, and hold the result.
vnl_svd<V> svd(M, 1e-8);
// Check for rank-deficiency
if (svd.singularities() > 1)
{
std::cout << "Warning: Singular matrix, condition = " << svd.well_condition() << std::endl;
}
return svd.solve(B);
}
int
test_svd()
{
double data[] = { 1, 1, 1, 1, 2, 3, 1, 3, 6 };
vnl_matrix<double> M(data, 3, 3);
vnl_matrix<double> B(3, 1, 7.0); // column vector [7 7 7]^T
vnl_matrix<double> result = solve_with_warning(M, B);
std::cout << "Original svd problem solution" << std::endl;
print_vnl_matrix(result);
M(2, 2) = 5;
result = solve_with_warning(M, B);
std::cout << std::endl << "Modified svd problem solution" << std::endl;
print_vnl_matrix(result);
return 0;
}
int
itkNumericsTest(int, char *[])
{
test_svd();
double data[] = { 1, 1, 1, 1, 2, 3, 1, 3, 6 };
vnl_matrix<double> mat(data, 3, 3);
std::cout << std::endl << "A matrix" << std::endl;
for (unsigned int r = 0; r < mat.rows(); ++r)
{
for (unsigned int c = 0; c < mat.rows(); ++c)
{
std::cout << mat(r, c) << ' ';
}
std::cout << std::endl;
}
return 0;
}
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