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/*
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* Copyright (c) 2011. Philipp Wagner <bytefish[at]gmx[dot]de>.
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* Released to public domain under terms of the BSD Simplified license.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* * Neither the name of the organization nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* See <http://www.opensource.org/licenses/bsd-license>
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*/
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#include "precomp.hpp"
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#include <iostream>
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#include <map>
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#include <set>
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namespace cv
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{
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using std::map;
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using std::set;
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using std::cout;
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using std::endl;
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// Removes duplicate elements in a given vector.
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template<typename _Tp>
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inline vector<_Tp> remove_dups(const vector<_Tp>& src) {
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typedef typename set<_Tp>::const_iterator constSetIterator;
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typedef typename vector<_Tp>::const_iterator constVecIterator;
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set<_Tp> set_elems;
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for (constVecIterator it = src.begin(); it != src.end(); ++it)
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set_elems.insert(*it);
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vector<_Tp> elems;
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for (constSetIterator it = set_elems.begin(); it != set_elems.end(); ++it)
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elems.push_back(*it);
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return elems;
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}
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static Mat argsort(InputArray _src, bool ascending=true)
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{
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Mat src = _src.getMat();
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if (src.rows != 1 && src.cols != 1)
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CV_Error(CV_StsBadArg, "cv::argsort only sorts 1D matrices.");
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int flags = CV_SORT_EVERY_ROW+(ascending ? CV_SORT_ASCENDING : CV_SORT_DESCENDING);
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Mat sorted_indices;
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sortIdx(src.reshape(1,1),sorted_indices,flags);
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return sorted_indices;
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}
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static Mat asRowMatrix(InputArrayOfArrays src, int rtype, double alpha=1, double beta=0)
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{
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// number of samples
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int n = (int) src.total();
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// return empty matrix if no data given
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if(n == 0)
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return Mat();
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// dimensionality of samples
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int d = (int)src.getMat(0).total();
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// create data matrix
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Mat data(n, d, rtype);
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// copy data
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for(int i = 0; i < n; i++) {
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Mat xi = data.row(i);
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src.getMat(i).reshape(1, 1).convertTo(xi, rtype, alpha, beta);
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}
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return data;
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}
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static void sortMatrixColumnsByIndices(InputArray _src, InputArray _indices, OutputArray _dst) {
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if(_indices.getMat().type() != CV_32SC1)
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CV_Error(CV_StsUnsupportedFormat, "cv::sortColumnsByIndices only works on integer indices!");
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Mat src = _src.getMat();
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vector<int> indices = _indices.getMat();
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_dst.create(src.rows, src.cols, src.type());
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Mat dst = _dst.getMat();
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for(size_t idx = 0; idx < indices.size(); idx++) {
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Mat originalCol = src.col(indices[idx]);
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Mat sortedCol = dst.col((int)idx);
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originalCol.copyTo(sortedCol);
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}
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}
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static Mat sortMatrixColumnsByIndices(InputArray src, InputArray indices) {
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Mat dst;
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sortMatrixColumnsByIndices(src, indices, dst);
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return dst;
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}
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template<typename _Tp> static bool
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isSymmetric_(InputArray src) {
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Mat _src = src.getMat();
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if(_src.cols != _src.rows)
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return false;
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for (int i = 0; i < _src.rows; i++) {
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for (int j = 0; j < _src.cols; j++) {
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_Tp a = _src.at<_Tp> (i, j);
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_Tp b = _src.at<_Tp> (j, i);
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if (a != b) {
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return false;
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}
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}
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}
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return true;
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}
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template<typename _Tp> static bool
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isSymmetric_(InputArray src, double eps) {
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Mat _src = src.getMat();
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if(_src.cols != _src.rows)
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return false;
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for (int i = 0; i < _src.rows; i++) {
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for (int j = 0; j < _src.cols; j++) {
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_Tp a = _src.at<_Tp> (i, j);
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_Tp b = _src.at<_Tp> (j, i);
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if (std::abs(a - b) > eps) {
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return false;
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}
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}
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}
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return true;
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}
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static bool isSymmetric(InputArray src, double eps=1e-16)
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{
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Mat m = src.getMat();
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switch (m.type()) {
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case CV_8SC1: return isSymmetric_<char>(m); break;
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case CV_8UC1:
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return isSymmetric_<unsigned char>(m); break;
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case CV_16SC1:
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return isSymmetric_<short>(m); break;
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case CV_16UC1:
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return isSymmetric_<unsigned short>(m); break;
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case CV_32SC1:
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return isSymmetric_<int>(m); break;
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case CV_32FC1:
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return isSymmetric_<float>(m, eps); break;
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case CV_64FC1:
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return isSymmetric_<double>(m, eps); break;
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default:
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break;
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}
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return false;
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}
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//------------------------------------------------------------------------------
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// subspace::project
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//------------------------------------------------------------------------------
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Mat subspaceProject(InputArray _W, InputArray _mean, InputArray _src)
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{
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// get data matrices
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Mat W = _W.getMat();
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Mat mean = _mean.getMat();
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Mat src = _src.getMat();
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// create temporary matrices
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Mat X, Y;
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// copy data & make sure we are using the correct type
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src.convertTo(X, W.type());
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// get number of samples and dimension
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int n = X.rows;
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int d = X.cols;
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// center the data if correct aligned sample mean is given
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if(mean.total() == (size_t)d)
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subtract(X, repeat(mean.reshape(1,1), n, 1), X);
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// finally calculate projection as Y = (X-mean)*W
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gemm(X, W, 1.0, Mat(), 0.0, Y);
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return Y;
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}
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//------------------------------------------------------------------------------
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// subspace::reconstruct
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//------------------------------------------------------------------------------
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Mat subspaceReconstruct(InputArray _W, InputArray _mean, InputArray _src)
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{
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// get data matrices
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Mat W = _W.getMat();
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Mat mean = _mean.getMat();
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Mat src = _src.getMat();
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// get number of samples
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int n = src.rows;
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// initalize temporary matrices
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Mat X, Y;
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// copy data & make sure we are using the correct type
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src.convertTo(Y, W.type());
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// calculate the reconstruction
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gemm(Y, W, 1.0, Mat(), 0.0, X, GEMM_2_T);
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if(mean.total() == (size_t) X.cols)
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add(X, repeat(mean.reshape(1,1), n, 1), X);
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return X;
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}
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class EigenvalueDecomposition {
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private:
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// Holds the data dimension.
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int n;
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// Stores real/imag part of a complex division.
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double cdivr, cdivi;
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// Pointer to internal memory.
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double *d, *e, *ort;
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double **V, **H;
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// Holds the computed eigenvalues.
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Mat _eigenvalues;
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// Holds the computed eigenvectors.
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Mat _eigenvectors;
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// Allocates memory.
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template<typename _Tp>
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_Tp *alloc_1d(int m) {
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return new _Tp[m];
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}
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// Allocates memory.
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template<typename _Tp>
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_Tp *alloc_1d(int m, _Tp val) {
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_Tp *arr = alloc_1d<_Tp> (m);
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for (int i = 0; i < m; i++)
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arr[i] = val;
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return arr;
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}
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// Allocates memory.
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template<typename _Tp>
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_Tp **alloc_2d(int m, int _n) {
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_Tp **arr = new _Tp*[m];
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for (int i = 0; i < m; i++)
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arr[i] = new _Tp[_n];
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return arr;
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}
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// Allocates memory.
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template<typename _Tp>
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_Tp **alloc_2d(int m, int _n, _Tp val) {
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_Tp **arr = alloc_2d<_Tp> (m, _n);
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for (int i = 0; i < m; i++) {
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for (int j = 0; j < _n; j++) {
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arr[i][j] = val;
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}
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}
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return arr;
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}
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void cdiv(double xr, double xi, double yr, double yi) {
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double r, dv;
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if (std::abs(yr) > std::abs(yi)) {
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r = yi / yr;
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dv = yr + r * yi;
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cdivr = (xr + r * xi) / dv;
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cdivi = (xi - r * xr) / dv;
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} else {
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r = yr / yi;
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dv = yi + r * yr;
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cdivr = (r * xr + xi) / dv;
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cdivi = (r * xi - xr) / dv;
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}
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}
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// Nonsymmetric reduction from Hessenberg to real Schur form.
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void hqr2() {
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// This is derived from the Algol procedure hqr2,
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// by Martin and Wilkinson, Handbook for Auto. Comp.,
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// Vol.ii-Linear Algebra, and the corresponding
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// Fortran subroutine in EISPACK.
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// Initialize
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int nn = this->n;
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int n1 = nn - 1;
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int low = 0;
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int high = nn - 1;
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double eps = pow(2.0, -52.0);
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double exshift = 0.0;
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double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
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// Store roots isolated by balanc and compute matrix norm
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double norm = 0.0;
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for (int i = 0; i < nn; i++) {
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if (i < low || i > high) {
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d[i] = H[i][i];
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e[i] = 0.0;
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}
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for (int j = max(i - 1, 0); j < nn; j++) {
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norm = norm + std::abs(H[i][j]);
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}
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}
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// Outer loop over eigenvalue index
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int iter = 0;
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while (n1 >= low) {
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// Look for single small sub-diagonal element
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int l = n1;
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while (l > low) {
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s = std::abs(H[l - 1][l - 1]) + std::abs(H[l][l]);
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if (s == 0.0) {
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s = norm;
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}
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if (std::abs(H[l][l - 1]) < eps * s) {
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break;
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}
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l--;
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}
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// Check for convergence
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// One root found
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if (l == n1) {
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H[n1][n1] = H[n1][n1] + exshift;
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d[n1] = H[n1][n1];
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e[n1] = 0.0;
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n1--;
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iter = 0;
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// Two roots found
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} else if (l == n1 - 1) {
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w = H[n1][n1 - 1] * H[n1 - 1][n1];
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p = (H[n1 - 1][n1 - 1] - H[n1][n1]) / 2.0;
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q = p * p + w;
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z = sqrt(std::abs(q));
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H[n1][n1] = H[n1][n1] + exshift;
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H[n1 - 1][n1 - 1] = H[n1 - 1][n1 - 1] + exshift;
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x = H[n1][n1];
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// Real pair
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if (q >= 0) {
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if (p >= 0) {
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z = p + z;
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} else {
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z = p - z;
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}
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d[n1 - 1] = x + z;
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d[n1] = d[n1 - 1];
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if (z != 0.0) {
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d[n1] = x - w / z;
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}
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e[n1 - 1] = 0.0;
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e[n1] = 0.0;
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x = H[n1][n1 - 1];
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s = std::abs(x) + std::abs(z);
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p = x / s;
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q = z / s;
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r = sqrt(p * p + q * q);
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p = p / r;
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q = q / r;
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// Row modification
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for (int j = n1 - 1; j < nn; j++) {
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z = H[n1 - 1][j];
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H[n1 - 1][j] = q * z + p * H[n1][j];
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H[n1][j] = q * H[n1][j] - p * z;
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}
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// Column modification
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for (int i = 0; i <= n1; i++) {
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z = H[i][n1 - 1];
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H[i][n1 - 1] = q * z + p * H[i][n1];
|
|
|
|
H[i][n1] = q * H[i][n1] - p * z;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Accumulate transformations
|
|
|
|
|
|
|
|
for (int i = low; i <= high; i++) {
|
|
|
|
z = V[i][n1 - 1];
|
|
|
|
V[i][n1 - 1] = q * z + p * V[i][n1];
|
|
|
|
V[i][n1] = q * V[i][n1] - p * z;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Complex pair
|
|
|
|
|
|
|
|
} else {
|
|
|
|
d[n1 - 1] = x + p;
|
|
|
|
d[n1] = x + p;
|
|
|
|
e[n1 - 1] = z;
|
|
|
|
e[n1] = -z;
|
|
|
|
}
|
|
|
|
n1 = n1 - 2;
|
|
|
|
iter = 0;
|
|
|
|
|
|
|
|
// No convergence yet
|
|
|
|
|
|
|
|
} else {
|
|
|
|
|
|
|
|
// Form shift
|
|
|
|
|
|
|
|
x = H[n1][n1];
|
|
|
|
y = 0.0;
|
|
|
|
w = 0.0;
|
|
|
|
if (l < n1) {
|
|
|
|
y = H[n1 - 1][n1 - 1];
|
|
|
|
w = H[n1][n1 - 1] * H[n1 - 1][n1];
|
|
|
|
}
|
|
|
|
|
|
|
|
// Wilkinson's original ad hoc shift
|
|
|
|
|
|
|
|
if (iter == 10) {
|
|
|
|
exshift += x;
|
|
|
|
for (int i = low; i <= n1; i++) {
|
|
|
|
H[i][i] -= x;
|
|
|
|
}
|
|
|
|
s = std::abs(H[n1][n1 - 1]) + std::abs(H[n1 - 1][n1 - 2]);
|
|
|
|
x = y = 0.75 * s;
|
|
|
|
w = -0.4375 * s * s;
|
|
|
|
}
|
|
|
|
|
|
|
|
// MATLAB's new ad hoc shift
|
|
|
|
|
|
|
|
if (iter == 30) {
|
|
|
|
s = (y - x) / 2.0;
|
|
|
|
s = s * s + w;
|
|
|
|
if (s > 0) {
|
|
|
|
s = sqrt(s);
|
|
|
|
if (y < x) {
|
|
|
|
s = -s;
|
|
|
|
}
|
|
|
|
s = x - w / ((y - x) / 2.0 + s);
|
|
|
|
for (int i = low; i <= n1; i++) {
|
|
|
|
H[i][i] -= s;
|
|
|
|
}
|
|
|
|
exshift += s;
|
|
|
|
x = y = w = 0.964;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
iter = iter + 1; // (Could check iteration count here.)
|
|
|
|
|
|
|
|
// Look for two consecutive small sub-diagonal elements
|
|
|
|
int m = n1 - 2;
|
|
|
|
while (m >= l) {
|
|
|
|
z = H[m][m];
|
|
|
|
r = x - z;
|
|
|
|
s = y - z;
|
|
|
|
p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
|
|
|
|
q = H[m + 1][m + 1] - z - r - s;
|
|
|
|
r = H[m + 2][m + 1];
|
|
|
|
s = std::abs(p) + std::abs(q) + std::abs(r);
|
|
|
|
p = p / s;
|
|
|
|
q = q / s;
|
|
|
|
r = r / s;
|
|
|
|
if (m == l) {
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
if (std::abs(H[m][m - 1]) * (std::abs(q) + std::abs(r)) < eps * (std::abs(p)
|
|
|
|
* (std::abs(H[m - 1][m - 1]) + std::abs(z) + std::abs(
|
|
|
|
H[m + 1][m + 1])))) {
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
m--;
|
|
|
|
}
|
|
|
|
|
|
|
|
for (int i = m + 2; i <= n1; i++) {
|
|
|
|
H[i][i - 2] = 0.0;
|
|
|
|
if (i > m + 2) {
|
|
|
|
H[i][i - 3] = 0.0;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Double QR step involving rows l:n and columns m:n
|
|
|
|
|
|
|
|
for (int k = m; k <= n1 - 1; k++) {
|
|
|
|
bool notlast = (k != n1 - 1);
|
|
|
|
if (k != m) {
|
|
|
|
p = H[k][k - 1];
|
|
|
|
q = H[k + 1][k - 1];
|
|
|
|
r = (notlast ? H[k + 2][k - 1] : 0.0);
|
|
|
|
x = std::abs(p) + std::abs(q) + std::abs(r);
|
|
|
|
if (x != 0.0) {
|
|
|
|
p = p / x;
|
|
|
|
q = q / x;
|
|
|
|
r = r / x;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (x == 0.0) {
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
s = sqrt(p * p + q * q + r * r);
|
|
|
|
if (p < 0) {
|
|
|
|
s = -s;
|
|
|
|
}
|
|
|
|
if (s != 0) {
|
|
|
|
if (k != m) {
|
|
|
|
H[k][k - 1] = -s * x;
|
|
|
|
} else if (l != m) {
|
|
|
|
H[k][k - 1] = -H[k][k - 1];
|
|
|
|
}
|
|
|
|
p = p + s;
|
|
|
|
x = p / s;
|
|
|
|
y = q / s;
|
|
|
|
z = r / s;
|
|
|
|
q = q / p;
|
|
|
|
r = r / p;
|
|
|
|
|
|
|
|
// Row modification
|
|
|
|
|
|
|
|
for (int j = k; j < nn; j++) {
|
|
|
|
p = H[k][j] + q * H[k + 1][j];
|
|
|
|
if (notlast) {
|
|
|
|
p = p + r * H[k + 2][j];
|
|
|
|
H[k + 2][j] = H[k + 2][j] - p * z;
|
|
|
|
}
|
|
|
|
H[k][j] = H[k][j] - p * x;
|
|
|
|
H[k + 1][j] = H[k + 1][j] - p * y;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Column modification
|
|
|
|
|
|
|
|
for (int i = 0; i <= min(n1, k + 3); i++) {
|
|
|
|
p = x * H[i][k] + y * H[i][k + 1];
|
|
|
|
if (notlast) {
|
|
|
|
p = p + z * H[i][k + 2];
|
|
|
|
H[i][k + 2] = H[i][k + 2] - p * r;
|
|
|
|
}
|
|
|
|
H[i][k] = H[i][k] - p;
|
|
|
|
H[i][k + 1] = H[i][k + 1] - p * q;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Accumulate transformations
|
|
|
|
|
|
|
|
for (int i = low; i <= high; i++) {
|
|
|
|
p = x * V[i][k] + y * V[i][k + 1];
|
|
|
|
if (notlast) {
|
|
|
|
p = p + z * V[i][k + 2];
|
|
|
|
V[i][k + 2] = V[i][k + 2] - p * r;
|
|
|
|
}
|
|
|
|
V[i][k] = V[i][k] - p;
|
|
|
|
V[i][k + 1] = V[i][k + 1] - p * q;
|
|
|
|
}
|
|
|
|
} // (s != 0)
|
|
|
|
} // k loop
|
|
|
|
} // check convergence
|
|
|
|
} // while (n1 >= low)
|
|
|
|
|
|
|
|
// Backsubstitute to find vectors of upper triangular form
|
|
|
|
|
|
|
|
if (norm == 0.0) {
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
|
|
for (n1 = nn - 1; n1 >= 0; n1--) {
|
|
|
|
p = d[n1];
|
|
|
|
q = e[n1];
|
|
|
|
|
|
|
|
// Real vector
|
|
|
|
|
|
|
|
if (q == 0) {
|
|
|
|
int l = n1;
|
|
|
|
H[n1][n1] = 1.0;
|
|
|
|
for (int i = n1 - 1; i >= 0; i--) {
|
|
|
|
w = H[i][i] - p;
|
|
|
|
r = 0.0;
|
|
|
|
for (int j = l; j <= n1; j++) {
|
|
|
|
r = r + H[i][j] * H[j][n1];
|
|
|
|
}
|
|
|
|
if (e[i] < 0.0) {
|
|
|
|
z = w;
|
|
|
|
s = r;
|
|
|
|
} else {
|
|
|
|
l = i;
|
|
|
|
if (e[i] == 0.0) {
|
|
|
|
if (w != 0.0) {
|
|
|
|
H[i][n1] = -r / w;
|
|
|
|
} else {
|
|
|
|
H[i][n1] = -r / (eps * norm);
|
|
|
|
}
|
|
|
|
|
|
|
|
// Solve real equations
|
|
|
|
|
|
|
|
} else {
|
|
|
|
x = H[i][i + 1];
|
|
|
|
y = H[i + 1][i];
|
|
|
|
q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
|
|
|
|
t = (x * s - z * r) / q;
|
|
|
|
H[i][n1] = t;
|
|
|
|
if (std::abs(x) > std::abs(z)) {
|
|
|
|
H[i + 1][n1] = (-r - w * t) / x;
|
|
|
|
} else {
|
|
|
|
H[i + 1][n1] = (-s - y * t) / z;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Overflow control
|
|
|
|
|
|
|
|
t = std::abs(H[i][n1]);
|
|
|
|
if ((eps * t) * t > 1) {
|
|
|
|
for (int j = i; j <= n1; j++) {
|
|
|
|
H[j][n1] = H[j][n1] / t;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Complex vector
|
|
|
|
|
|
|
|
} else if (q < 0) {
|
|
|
|
int l = n1 - 1;
|
|
|
|
|
|
|
|
// Last vector component imaginary so matrix is triangular
|
|
|
|
|
|
|
|
if (std::abs(H[n1][n1 - 1]) > std::abs(H[n1 - 1][n1])) {
|
|
|
|
H[n1 - 1][n1 - 1] = q / H[n1][n1 - 1];
|
|
|
|
H[n1 - 1][n1] = -(H[n1][n1] - p) / H[n1][n1 - 1];
|
|
|
|
} else {
|
|
|
|
cdiv(0.0, -H[n1 - 1][n1], H[n1 - 1][n1 - 1] - p, q);
|
|
|
|
H[n1 - 1][n1 - 1] = cdivr;
|
|
|
|
H[n1 - 1][n1] = cdivi;
|
|
|
|
}
|
|
|
|
H[n1][n1 - 1] = 0.0;
|
|
|
|
H[n1][n1] = 1.0;
|
|
|
|
for (int i = n1 - 2; i >= 0; i--) {
|
|
|
|
double ra, sa, vr, vi;
|
|
|
|
ra = 0.0;
|
|
|
|
sa = 0.0;
|
|
|
|
for (int j = l; j <= n1; j++) {
|
|
|
|
ra = ra + H[i][j] * H[j][n1 - 1];
|
|
|
|
sa = sa + H[i][j] * H[j][n1];
|
|
|
|
}
|
|
|
|
w = H[i][i] - p;
|
|
|
|
|
|
|
|
if (e[i] < 0.0) {
|
|
|
|
z = w;
|
|
|
|
r = ra;
|
|
|
|
s = sa;
|
|
|
|
} else {
|
|
|
|
l = i;
|
|
|
|
if (e[i] == 0) {
|
|
|
|
cdiv(-ra, -sa, w, q);
|
|
|
|
H[i][n1 - 1] = cdivr;
|
|
|
|
H[i][n1] = cdivi;
|
|
|
|
} else {
|
|
|
|
|
|
|
|
// Solve complex equations
|
|
|
|
|
|
|
|
x = H[i][i + 1];
|
|
|
|
y = H[i + 1][i];
|
|
|
|
vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
|
|
|
|
vi = (d[i] - p) * 2.0 * q;
|
|
|
|
if (vr == 0.0 && vi == 0.0) {
|
|
|
|
vr = eps * norm * (std::abs(w) + std::abs(q) + std::abs(x)
|
|
|
|
+ std::abs(y) + std::abs(z));
|
|
|
|
}
|
|
|
|
cdiv(x * r - z * ra + q * sa,
|
|
|
|
x * s - z * sa - q * ra, vr, vi);
|
|
|
|
H[i][n1 - 1] = cdivr;
|
|
|
|
H[i][n1] = cdivi;
|
|
|
|
if (std::abs(x) > (std::abs(z) + std::abs(q))) {
|
|
|
|
H[i + 1][n1 - 1] = (-ra - w * H[i][n1 - 1] + q
|
|
|
|
* H[i][n1]) / x;
|
|
|
|
H[i + 1][n1] = (-sa - w * H[i][n1] - q * H[i][n1
|
|
|
|
- 1]) / x;
|
|
|
|
} else {
|
|
|
|
cdiv(-r - y * H[i][n1 - 1], -s - y * H[i][n1], z,
|
|
|
|
q);
|
|
|
|
H[i + 1][n1 - 1] = cdivr;
|
|
|
|
H[i + 1][n1] = cdivi;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Overflow control
|
|
|
|
|
|
|
|
t = max(std::abs(H[i][n1 - 1]), std::abs(H[i][n1]));
|
|
|
|
if ((eps * t) * t > 1) {
|
|
|
|
for (int j = i; j <= n1; j++) {
|
|
|
|
H[j][n1 - 1] = H[j][n1 - 1] / t;
|
|
|
|
H[j][n1] = H[j][n1] / t;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Vectors of isolated roots
|
|
|
|
|
|
|
|
for (int i = 0; i < nn; i++) {
|
|
|
|
if (i < low || i > high) {
|
|
|
|
for (int j = i; j < nn; j++) {
|
|
|
|
V[i][j] = H[i][j];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Back transformation to get eigenvectors of original matrix
|
|
|
|
|
|
|
|
for (int j = nn - 1; j >= low; j--) {
|
|
|
|
for (int i = low; i <= high; i++) {
|
|
|
|
z = 0.0;
|
|
|
|
for (int k = low; k <= min(j, high); k++) {
|
|
|
|
z = z + V[i][k] * H[k][j];
|
|
|
|
}
|
|
|
|
V[i][j] = z;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Nonsymmetric reduction to Hessenberg form.
|
|
|
|
void orthes() {
|
|
|
|
// This is derived from the Algol procedures orthes and ortran,
|
|
|
|
// by Martin and Wilkinson, Handbook for Auto. Comp.,
|
|
|
|
// Vol.ii-Linear Algebra, and the corresponding
|
|
|
|
// Fortran subroutines in EISPACK.
|
|
|
|
int low = 0;
|
|
|
|
int high = n - 1;
|
|
|
|
|
|
|
|
for (int m = low + 1; m <= high - 1; m++) {
|
|
|
|
|
|
|
|
// Scale column.
|
|
|
|
|
|
|
|
double scale = 0.0;
|
|
|
|
for (int i = m; i <= high; i++) {
|
|
|
|
scale = scale + std::abs(H[i][m - 1]);
|
|
|
|
}
|
|
|
|
if (scale != 0.0) {
|
|
|
|
|
|
|
|
// Compute Householder transformation.
|
|
|
|
|
|
|
|
double h = 0.0;
|
|
|
|
for (int i = high; i >= m; i--) {
|
|
|
|
ort[i] = H[i][m - 1] / scale;
|
|
|
|
h += ort[i] * ort[i];
|
|
|
|
}
|
|
|
|
double g = sqrt(h);
|
|
|
|
if (ort[m] > 0) {
|
|
|
|
g = -g;
|
|
|
|
}
|
|
|
|
h = h - ort[m] * g;
|
|
|
|
ort[m] = ort[m] - g;
|
|
|
|
|
|
|
|
// Apply Householder similarity transformation
|
|
|
|
// H = (I-u*u'/h)*H*(I-u*u')/h)
|
|
|
|
|
|
|
|
for (int j = m; j < n; j++) {
|
|
|
|
double f = 0.0;
|
|
|
|
for (int i = high; i >= m; i--) {
|
|
|
|
f += ort[i] * H[i][j];
|
|
|
|
}
|
|
|
|
f = f / h;
|
|
|
|
for (int i = m; i <= high; i++) {
|
|
|
|
H[i][j] -= f * ort[i];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
for (int i = 0; i <= high; i++) {
|
|
|
|
double f = 0.0;
|
|
|
|
for (int j = high; j >= m; j--) {
|
|
|
|
f += ort[j] * H[i][j];
|
|
|
|
}
|
|
|
|
f = f / h;
|
|
|
|
for (int j = m; j <= high; j++) {
|
|
|
|
H[i][j] -= f * ort[j];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
ort[m] = scale * ort[m];
|
|
|
|
H[m][m - 1] = scale * g;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Accumulate transformations (Algol's ortran).
|
|
|
|
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
|
|
for (int j = 0; j < n; j++) {
|
|
|
|
V[i][j] = (i == j ? 1.0 : 0.0);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
for (int m = high - 1; m >= low + 1; m--) {
|
|
|
|
if (H[m][m - 1] != 0.0) {
|
|
|
|
for (int i = m + 1; i <= high; i++) {
|
|
|
|
ort[i] = H[i][m - 1];
|
|
|
|
}
|
|
|
|
for (int j = m; j <= high; j++) {
|
|
|
|
double g = 0.0;
|
|
|
|
for (int i = m; i <= high; i++) {
|
|
|
|
g += ort[i] * V[i][j];
|
|
|
|
}
|
|
|
|
// Double division avoids possible underflow
|
|
|
|
g = (g / ort[m]) / H[m][m - 1];
|
|
|
|
for (int i = m; i <= high; i++) {
|
|
|
|
V[i][j] += g * ort[i];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Releases all internal working memory.
|
|
|
|
void release() {
|
|
|
|
// releases the working data
|
|
|
|
delete[] d;
|
|
|
|
delete[] e;
|
|
|
|
delete[] ort;
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
|
|
delete[] H[i];
|
|
|
|
delete[] V[i];
|
|
|
|
}
|
|
|
|
delete[] H;
|
|
|
|
delete[] V;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Computes the Eigenvalue Decomposition for a matrix given in H.
|
|
|
|
void compute() {
|
|
|
|
// Allocate memory for the working data.
|
|
|
|
V = alloc_2d<double> (n, n, 0.0);
|
|
|
|
d = alloc_1d<double> (n);
|
|
|
|
e = alloc_1d<double> (n);
|
|
|
|
ort = alloc_1d<double> (n);
|
|
|
|
// Reduce to Hessenberg form.
|
|
|
|
orthes();
|
|
|
|
// Reduce Hessenberg to real Schur form.
|
|
|
|
hqr2();
|
|
|
|
// Copy eigenvalues to OpenCV Matrix.
|
|
|
|
_eigenvalues.create(1, n, CV_64FC1);
|
|
|
|
for (int i = 0; i < n; i++) {
|
|
|
|
_eigenvalues.at<double> (0, i) = d[i];
|
|
|
|
}
|
|
|
|
// Copy eigenvectors to OpenCV Matrix.
|
|
|
|
_eigenvectors.create(n, n, CV_64FC1);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
|
|
for (int j = 0; j < n; j++)
|
|
|
|
_eigenvectors.at<double> (i, j) = V[i][j];
|
|
|
|
// Deallocate the memory by releasing all internal working data.
|
|
|
|
release();
|
|
|
|
}
|
|
|
|
|
|
|
|
public:
|
|
|
|
EigenvalueDecomposition()
|
|
|
|
: n(0) { }
|
|
|
|
|
|
|
|
// Initializes & computes the Eigenvalue Decomposition for a general matrix
|
|
|
|
// given in src. This function is a port of the EigenvalueSolver in JAMA,
|
|
|
|
// which has been released to public domain by The MathWorks and the
|
|
|
|
// National Institute of Standards and Technology (NIST).
|
|
|
|
EigenvalueDecomposition(InputArray src) {
|
|
|
|
compute(src);
|
|
|
|
}
|
|
|
|
|
|
|
|
// This function computes the Eigenvalue Decomposition for a general matrix
|
|
|
|
// given in src. This function is a port of the EigenvalueSolver in JAMA,
|
|
|
|
// which has been released to public domain by The MathWorks and the
|
|
|
|
// National Institute of Standards and Technology (NIST).
|
|
|
|
void compute(InputArray src)
|
|
|
|
{
|
|
|
|
if(isSymmetric(src)) {
|
|
|
|
// Fall back to OpenCV for a symmetric matrix!
|
|
|
|
cv::eigen(src, _eigenvalues, _eigenvectors);
|
|
|
|
} else {
|
|
|
|
Mat tmp;
|
|
|
|
// Convert the given input matrix to double. Is there any way to
|
|
|
|
// prevent allocating the temporary memory? Only used for copying
|
|
|
|
// into working memory and deallocated after.
|
|
|
|
src.getMat().convertTo(tmp, CV_64FC1);
|
|
|
|
// Get dimension of the matrix.
|
|
|
|
this->n = tmp.cols;
|
|
|
|
// Allocate the matrix data to work on.
|
|
|
|
this->H = alloc_2d<double> (n, n);
|
|
|
|
// Now safely copy the data.
|
|
|
|
for (int i = 0; i < tmp.rows; i++) {
|
|
|
|
for (int j = 0; j < tmp.cols; j++) {
|
|
|
|
this->H[i][j] = tmp.at<double>(i, j);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
// Deallocates the temporary matrix before computing.
|
|
|
|
tmp.release();
|
|
|
|
// Performs the eigenvalue decomposition of H.
|
|
|
|
compute();
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
~EigenvalueDecomposition() {}
|
|
|
|
|
|
|
|
// Returns the eigenvalues of the Eigenvalue Decomposition.
|
|
|
|
Mat eigenvalues() { return _eigenvalues; }
|
|
|
|
// Returns the eigenvectors of the Eigenvalue Decomposition.
|
|
|
|
Mat eigenvectors() { return _eigenvectors; }
|
|
|
|
};
|
|
|
|
|
|
|
|
|
|
|
|
//------------------------------------------------------------------------------
|
|
|
|
// Linear Discriminant Analysis implementation
|
|
|
|
//------------------------------------------------------------------------------
|
|
|
|
void LDA::save(const string& filename) const {
|
|
|
|
FileStorage fs(filename, FileStorage::WRITE);
|
|
|
|
if (!fs.isOpened())
|
|
|
|
CV_Error(CV_StsError, "File can't be opened for writing!");
|
|
|
|
this->save(fs);
|
|
|
|
fs.release();
|
|
|
|
}
|
|
|
|
|
|
|
|
// Deserializes this object from a given filename.
|
|
|
|
void LDA::load(const string& filename) {
|
|
|
|
FileStorage fs(filename, FileStorage::READ);
|
|
|
|
if (!fs.isOpened())
|
|
|
|
CV_Error(CV_StsError, "File can't be opened for writing!");
|
|
|
|
this->load(fs);
|
|
|
|
fs.release();
|
|
|
|
}
|
|
|
|
|
|
|
|
// Serializes this object to a given FileStorage.
|
|
|
|
void LDA::save(FileStorage& fs) const {
|
|
|
|
// write matrices
|
|
|
|
fs << "num_components" << _num_components;
|
|
|
|
fs << "eigenvalues" << _eigenvalues;
|
|
|
|
fs << "eigenvectors" << _eigenvectors;
|
|
|
|
}
|
|
|
|
|
|
|
|
// Deserializes this object from a given FileStorage.
|
|
|
|
void LDA::load(const FileStorage& fs) {
|
|
|
|
//read matrices
|
|
|
|
fs["num_components"] >> _num_components;
|
|
|
|
fs["eigenvalues"] >> _eigenvalues;
|
|
|
|
fs["eigenvectors"] >> _eigenvectors;
|
|
|
|
}
|
|
|
|
|
|
|
|
void LDA::lda(InputArray _src, InputArray _lbls) {
|
|
|
|
// get data
|
|
|
|
Mat src = _src.getMat();
|
|
|
|
vector<int> labels = _lbls.getMat();
|
|
|
|
// turn into row sampled matrix
|
|
|
|
Mat data;
|
|
|
|
// ensure working matrix is double precision
|
|
|
|
src.convertTo(data, CV_64FC1);
|
|
|
|
// maps the labels, so they're ascending: [0,1,...,C]
|
|
|
|
vector<int> mapped_labels(labels.size());
|
|
|
|
vector<int> num2label = remove_dups(labels);
|
|
|
|
map<int, int> label2num;
|
|
|
|
for (size_t i = 0; i < num2label.size(); i++)
|
|
|
|
label2num[num2label[i]] = (int)i;
|
|
|
|
for (size_t i = 0; i < labels.size(); i++)
|
|
|
|
mapped_labels[i] = label2num[labels[i]];
|
|
|
|
// get sample size, dimension
|
|
|
|
int N = data.rows;
|
|
|
|
int D = data.cols;
|
|
|
|
// number of unique labels
|
|
|
|
int C = (int)num2label.size();
|
|
|
|
// throw error if less labels, than samples
|
|
|
|
if (labels.size() != (size_t)N)
|
|
|
|
CV_Error(CV_StsBadArg, "Error: The number of samples must equal the number of labels.");
|
|
|
|
// warn if within-classes scatter matrix becomes singular
|
|
|
|
if (N < D)
|
|
|
|
cout << "Warning: Less observations than feature dimension given!"
|
|
|
|
<< "Computation will probably fail."
|
|
|
|
<< endl;
|
|
|
|
// clip number of components to be a valid number
|
|
|
|
if ((_num_components <= 0) || (_num_components > (C - 1)))
|
|
|
|
_num_components = (C - 1);
|
|
|
|
// holds the mean over all classes
|
|
|
|
Mat meanTotal = Mat::zeros(1, D, data.type());
|
|
|
|
// holds the mean for each class
|
|
|
|
vector<Mat> meanClass(C);
|
|
|
|
vector<int> numClass(C);
|
|
|
|
// initialize
|
|
|
|
for (int i = 0; i < C; i++) {
|
|
|
|
numClass[i] = 0;
|
|
|
|
meanClass[i] = Mat::zeros(1, D, data.type()); //! Dx1 image vector
|
|
|
|
}
|
|
|
|
// calculate sums
|
|
|
|
for (int i = 0; i < N; i++) {
|
|
|
|
Mat instance = data.row(i);
|
|
|
|
int classIdx = mapped_labels[i];
|
|
|
|
add(meanTotal, instance, meanTotal);
|
|
|
|
add(meanClass[classIdx], instance, meanClass[classIdx]);
|
|
|
|
numClass[classIdx]++;
|
|
|
|
}
|
|
|
|
// calculate means
|
|
|
|
meanTotal.convertTo(meanTotal, meanTotal.type(),
|
|
|
|
1.0 / static_cast<double> (N));
|
|
|
|
for (int i = 0; i < C; i++)
|
|
|
|
meanClass[i].convertTo(meanClass[i], meanClass[i].type(),
|
|
|
|
1.0 / static_cast<double> (numClass[i]));
|
|
|
|
// subtract class means
|
|
|
|
for (int i = 0; i < N; i++) {
|
|
|
|
int classIdx = mapped_labels[i];
|
|
|
|
Mat instance = data.row(i);
|
|
|
|
subtract(instance, meanClass[classIdx], instance);
|
|
|
|
}
|
|
|
|
// calculate within-classes scatter
|
|
|
|
Mat Sw = Mat::zeros(D, D, data.type());
|
|
|
|
mulTransposed(data, Sw, true);
|
|
|
|
// calculate between-classes scatter
|
|
|
|
Mat Sb = Mat::zeros(D, D, data.type());
|
|
|
|
for (int i = 0; i < C; i++) {
|
|
|
|
Mat tmp;
|
|
|
|
subtract(meanClass[i], meanTotal, tmp);
|
|
|
|
mulTransposed(tmp, tmp, true);
|
|
|
|
add(Sb, tmp, Sb);
|
|
|
|
}
|
|
|
|
// invert Sw
|
|
|
|
Mat Swi = Sw.inv();
|
|
|
|
// M = inv(Sw)*Sb
|
|
|
|
Mat M;
|
|
|
|
gemm(Swi, Sb, 1.0, Mat(), 0.0, M);
|
|
|
|
EigenvalueDecomposition es(M);
|
|
|
|
_eigenvalues = es.eigenvalues();
|
|
|
|
_eigenvectors = es.eigenvectors();
|
|
|
|
// reshape eigenvalues, so they are stored by column
|
|
|
|
_eigenvalues = _eigenvalues.reshape(1, 1);
|
|
|
|
// get sorted indices descending by their eigenvalue
|
|
|
|
vector<int> sorted_indices = argsort(_eigenvalues, false);
|
|
|
|
// now sort eigenvalues and eigenvectors accordingly
|
|
|
|
_eigenvalues = sortMatrixColumnsByIndices(_eigenvalues, sorted_indices);
|
|
|
|
_eigenvectors = sortMatrixColumnsByIndices(_eigenvectors, sorted_indices);
|
|
|
|
// and now take only the num_components and we're out!
|
|
|
|
_eigenvalues = Mat(_eigenvalues, Range::all(), Range(0, _num_components));
|
|
|
|
_eigenvectors = Mat(_eigenvectors, Range::all(), Range(0, _num_components));
|
|
|
|
}
|
|
|
|
|
|
|
|
void LDA::compute(InputArray _src, InputArray _lbls) {
|
|
|
|
switch(_src.kind()) {
|
|
|
|
case _InputArray::STD_VECTOR_MAT:
|
|
|
|
lda(asRowMatrix(_src, CV_64FC1), _lbls);
|
|
|
|
break;
|
|
|
|
case _InputArray::MAT:
|
|
|
|
lda(_src.getMat(), _lbls);
|
|
|
|
break;
|
|
|
|
default:
|
|
|
|
CV_Error(CV_StsNotImplemented, "This data type is not supported by subspace::LDA::compute.");
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Projects samples into the LDA subspace.
|
|
|
|
Mat LDA::project(InputArray src) {
|
|
|
|
return subspaceProject(_eigenvectors, Mat(), _dataAsRow ? src : src.getMat().t());
|
|
|
|
}
|
|
|
|
|
|
|
|
// Reconstructs projections from the LDA subspace.
|
|
|
|
Mat LDA::reconstruct(InputArray src) {
|
|
|
|
return subspaceReconstruct(_eigenvectors, Mat(), _dataAsRow ? src : src.getMat().t());
|
|
|
|
}
|
|
|
|
|
|
|
|
}
|
|
|
|
|