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opencv/modules/core/src/lda.cpp

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/*
* Copyright (c) 2011. Philipp Wagner <bytefish[at]gmx[dot]de>.
* Released to public domain under terms of the BSD Simplified license.
*
* 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 organization nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* See <http://www.opensource.org/licenses/bsd-license>
*/
#include "precomp.hpp"
#include <iostream>
#include <map>
#include <set>
namespace cv
{
// Removes duplicate elements in a given vector.
template<typename _Tp>
inline std::vector<_Tp> remove_dups(const std::vector<_Tp>& src) {
typedef typename std::set<_Tp>::const_iterator constSetIterator;
typedef typename std::vector<_Tp>::const_iterator constVecIterator;
std::set<_Tp> set_elems;
for (constVecIterator it = src.begin(); it != src.end(); ++it)
set_elems.insert(*it);
std::vector<_Tp> elems;
for (constSetIterator it = set_elems.begin(); it != set_elems.end(); ++it)
elems.push_back(*it);
return elems;
}
static Mat argsort(InputArray _src, bool ascending=true)
{
Mat src = _src.getMat();
if (src.rows != 1 && src.cols != 1) {
String error_message = "Wrong shape of input matrix! Expected a matrix with one row or column.";
CV_Error(Error::StsBadArg, error_message);
}
int flags = SORT_EVERY_ROW | (ascending ? SORT_ASCENDING : SORT_DESCENDING);
Mat sorted_indices;
sortIdx(src.reshape(1,1),sorted_indices,flags);
return sorted_indices;
}
static Mat asRowMatrix(InputArrayOfArrays src, int rtype, double alpha=1, double beta=0) {
// make sure the input data is a vector of matrices or vector of vector
if(src.kind() != _InputArray::STD_VECTOR_MAT && src.kind() != _InputArray::STD_ARRAY_MAT &&
src.kind() != _InputArray::STD_VECTOR_VECTOR) {
String error_message = "The data is expected as InputArray::STD_VECTOR_MAT (a std::vector<Mat>) or _InputArray::STD_VECTOR_VECTOR (a std::vector< std::vector<...> >).";
CV_Error(Error::StsBadArg, error_message);
}
// number of samples
size_t n = src.total();
// return empty matrix if no matrices given
if(n == 0)
return Mat();
// dimensionality of (reshaped) samples
size_t d = src.getMat(0).total();
// create data matrix
Mat data((int)n, (int)d, rtype);
// now copy data
for(int i = 0; i < (int)n; i++) {
// make sure data can be reshaped, throw exception if not!
if(src.getMat(i).total() != d) {
String error_message = format("Wrong number of elements in matrix #%d! Expected %d was %d.", i, (int)d, (int)src.getMat(i).total());
CV_Error(Error::StsBadArg, error_message);
}
// get a hold of the current row
Mat xi = data.row(i);
// make reshape happy by cloning for non-continuous matrices
if(src.getMat(i).isContinuous()) {
src.getMat(i).reshape(1, 1).convertTo(xi, rtype, alpha, beta);
} else {
src.getMat(i).clone().reshape(1, 1).convertTo(xi, rtype, alpha, beta);
}
}
return data;
}
static void sortMatrixColumnsByIndices(InputArray _src, InputArray _indices, OutputArray _dst) {
if(_indices.getMat().type() != CV_32SC1) {
CV_Error(Error::StsUnsupportedFormat, "cv::sortColumnsByIndices only works on integer indices!");
}
Mat src = _src.getMat();
std::vector<int> indices = _indices.getMat();
_dst.create(src.rows, src.cols, src.type());
Mat dst = _dst.getMat();
for(size_t idx = 0; idx < indices.size(); idx++) {
Mat originalCol = src.col(indices[idx]);
Mat sortedCol = dst.col((int)idx);
originalCol.copyTo(sortedCol);
}
}
static Mat sortMatrixColumnsByIndices(InputArray src, InputArray indices) {
Mat dst;
sortMatrixColumnsByIndices(src, indices, dst);
return dst;
}
template<typename _Tp> static bool
isSymmetric_(InputArray src) {
Mat _src = src.getMat();
if(_src.cols != _src.rows)
return false;
for (int i = 0; i < _src.rows; i++) {
for (int j = 0; j < _src.cols; j++) {
_Tp a = _src.at<_Tp> (i, j);
_Tp b = _src.at<_Tp> (j, i);
if (a != b) {
return false;
}
}
}
return true;
}
template<typename _Tp> static bool
isSymmetric_(InputArray src, double eps) {
Mat _src = src.getMat();
if(_src.cols != _src.rows)
return false;
for (int i = 0; i < _src.rows; i++) {
for (int j = 0; j < _src.cols; j++) {
_Tp a = _src.at<_Tp> (i, j);
_Tp b = _src.at<_Tp> (j, i);
if (std::abs(a - b) > eps) {
return false;
}
}
}
return true;
}
static bool isSymmetric(InputArray src, double eps=1e-16)
{
Mat m = src.getMat();
switch (m.type()) {
case CV_8SC1: return isSymmetric_<char>(m); break;
case CV_8UC1:
return isSymmetric_<unsigned char>(m); break;
case CV_16SC1:
return isSymmetric_<short>(m); break;
case CV_16UC1:
return isSymmetric_<unsigned short>(m); break;
case CV_32SC1:
return isSymmetric_<int>(m); break;
case CV_32FC1:
return isSymmetric_<float>(m, eps); break;
case CV_64FC1:
return isSymmetric_<double>(m, eps); break;
default:
break;
}
return false;
}
//------------------------------------------------------------------------------
// cv::subspaceProject
//------------------------------------------------------------------------------
Mat LDA::subspaceProject(InputArray _W, InputArray _mean, InputArray _src) {
// get data matrices
Mat W = _W.getMat();
Mat mean = _mean.getMat();
Mat src = _src.getMat();
// get number of samples and dimension
int n = src.rows;
int d = src.cols;
// make sure the data has the correct shape
if(W.rows != d) {
String error_message = format("Wrong shapes for given matrices. Was size(src) = (%d,%d), size(W) = (%d,%d).", src.rows, src.cols, W.rows, W.cols);
CV_Error(Error::StsBadArg, error_message);
}
// make sure mean is correct if not empty
if(!mean.empty() && (mean.total() != (size_t) d)) {
String error_message = format("Wrong mean shape for the given data matrix. Expected %d, but was %zu.", d, mean.total());
CV_Error(Error::StsBadArg, error_message);
}
// create temporary matrices
Mat X, Y;
// make sure you operate on correct type
src.convertTo(X, W.type());
// safe to do, because of above assertion
if(!mean.empty()) {
for(int i=0; i<n; i++) {
Mat r_i = X.row(i);
subtract(r_i, mean.reshape(1,1), r_i);
}
}
// finally calculate projection as Y = (X-mean)*W
gemm(X, W, 1.0, Mat(), 0.0, Y);
return Y;
}
//------------------------------------------------------------------------------
// cv::subspaceReconstruct
//------------------------------------------------------------------------------
Mat LDA::subspaceReconstruct(InputArray _W, InputArray _mean, InputArray _src)
{
// get data matrices
Mat W = _W.getMat();
Mat mean = _mean.getMat();
Mat src = _src.getMat();
// get number of samples and dimension
int n = src.rows;
int d = src.cols;
// make sure the data has the correct shape
if(W.cols != d) {
String error_message = format("Wrong shapes for given matrices. Was size(src) = (%d,%d), size(W) = (%d,%d).", src.rows, src.cols, W.rows, W.cols);
CV_Error(Error::StsBadArg, error_message);
}
// make sure mean is correct if not empty
if(!mean.empty() && (mean.total() != (size_t) W.rows)) {
String error_message = format("Wrong mean shape for the given eigenvector matrix. Expected %d, but was %zu.", W.cols, mean.total());
CV_Error(Error::StsBadArg, error_message);
}
// initialize temporary matrices
Mat X, Y;
// copy data & make sure we are using the correct type
src.convertTo(Y, W.type());
// calculate the reconstruction
gemm(Y, W, 1.0, Mat(), 0.0, X, GEMM_2_T);
// safe to do because of above assertion
if(!mean.empty()) {
for(int i=0; i<n; i++) {
Mat r_i = X.row(i);
add(r_i, mean.reshape(1,1), r_i);
}
}
return X;
}
class EigenvalueDecomposition {
private:
// Holds the data dimension.
int n;
// Pointer to internal memory.
double *d, *e, *ort;
double **V, **H;
// Holds the computed eigenvalues.
Mat _eigenvalues;
// Holds the computed eigenvectors.
Mat _eigenvectors;
// Allocates memory.
template<typename _Tp>
_Tp *alloc_1d(int m) {
return new _Tp[m];
}
// Allocates memory.
template<typename _Tp>
_Tp *alloc_1d(int m, _Tp val) {
_Tp *arr = alloc_1d<_Tp> (m);
for (int i = 0; i < m; i++)
arr[i] = val;
return arr;
}
// Allocates memory.
template<typename _Tp>
_Tp **alloc_2d(int m, int _n) {
_Tp **arr = new _Tp*[m];
for (int i = 0; i < m; i++)
arr[i] = new _Tp[_n];
return arr;
}
// Allocates memory.
template<typename _Tp>
_Tp **alloc_2d(int m, int _n, _Tp val) {
_Tp **arr = alloc_2d<_Tp> (m, _n);
for (int i = 0; i < m; i++) {
for (int j = 0; j < _n; j++) {
arr[i][j] = val;
}
}
return arr;
}
static void complex_div(double xr, double xi, double yr, double yi, double& cdivr, double& cdivi) {
double r, dv;
CV_DbgAssert(std::abs(yr) + std::abs(yi) > 0.0);
if (std::abs(yr) > std::abs(yi)) {
r = yi / yr;
dv = yr + r * yi;
cdivr = (xr + r * xi) / dv;
cdivi = (xi - r * xr) / dv;
} else {
r = yr / yi;
dv = yi + r * yr;
cdivr = (r * xr + xi) / dv;
cdivi = (r * xi - xr) / dv;
}
}
// Nonsymmetric reduction from Hessenberg to real Schur form.
void hqr2() {
// This is derived from the Algol procedure hqr2,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
// Initialize
const int max_iters_count = 1000 * this->n;
const int nn = this->n; CV_Assert(nn > 0);
int n1 = nn - 1;
const int low = 0;
const int high = nn - 1;
const double eps = std::numeric_limits<double>::epsilon();
double exshift = 0.0;
// Store roots isolated by balanc and compute matrix norm
double norm = 0.0;
for (int i = 0; i < nn; i++) {
#if 0 // 'if' condition is always false
if (i < low || i > high) {
d[i] = H[i][i];
e[i] = 0.0;
}
#endif
for (int j = std::max(i - 1, 0); j < nn; j++) {
norm += std::abs(H[i][j]);
}
}
// Outer loop over eigenvalue index
int iter = 0;
while (n1 >= low) {
// Look for single small sub-diagonal element
int l = n1;
while (l > low) {
if (norm < FLT_EPSILON) {
break;
}
double s = std::abs(H[l - 1][l - 1]) + std::abs(H[l][l]);
if (s == 0.0) {
s = norm;
}
if (std::abs(H[l][l - 1]) < eps * s) {
break;
}
l--;
}
// Check for convergence
if (l == n1) {
// One root found
H[n1][n1] = H[n1][n1] + exshift;
d[n1] = H[n1][n1];
e[n1] = 0.0;
n1--;
iter = 0;
} else if (l == n1 - 1) {
// Two roots found
double w = H[n1][n1 - 1] * H[n1 - 1][n1];
double p = (H[n1 - 1][n1 - 1] - H[n1][n1]) * 0.5;
double q = p * p + w;
double z = std::sqrt(std::abs(q));
H[n1][n1] = H[n1][n1] + exshift;
H[n1 - 1][n1 - 1] = H[n1 - 1][n1 - 1] + exshift;
double x = H[n1][n1];
if (q >= 0) {
// Real pair
if (p >= 0) {
z = p + z;
} else {
z = p - z;
}
d[n1 - 1] = x + z;
d[n1] = d[n1 - 1];
if (z != 0.0) {
d[n1] = x - w / z;
}
e[n1 - 1] = 0.0;
e[n1] = 0.0;
x = H[n1][n1 - 1];
double s = std::abs(x) + std::abs(z);
p = x / s;
q = z / s;
double r = std::sqrt(p * p + q * q);
p = p / r;
q = q / r;
// Row modification
for (int j = n1 - 1; j < nn; j++) {
z = H[n1 - 1][j];
H[n1 - 1][j] = q * z + p * H[n1][j];
H[n1][j] = q * H[n1][j] - p * z;
}
// Column modification
for (int i = 0; i <= n1; i++) {
z = H[i][n1 - 1];
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;
}
} else {
// Complex pair
d[n1 - 1] = x + p;
d[n1] = x + p;
e[n1 - 1] = z;
e[n1] = -z;
}
n1 = n1 - 2;
iter = 0;
} else {
// No convergence yet
// Form shift
double x = H[n1][n1];
double y = 0.0;
double 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;
}
double 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) {
double s = (y - x) * 0.5;
s = s * s + w;
if (s > 0) {
s = std::sqrt(s);
if (y < x) {
s = -s;
}
s = x - w / ((y - x) * 0.5 + s);
for (int i = low; i <= n1; i++) {
H[i][i] -= s;
}
exshift += s;
x = y = w = 0.964;
}
}
iter = iter + 1;
if (iter > max_iters_count)
CV_Error(Error::StsNoConv, "Algorithm doesn't converge (complex eigen values?)");
double p = std::numeric_limits<double>::quiet_NaN();
double q = std::numeric_limits<double>::quiet_NaN();
double r = std::numeric_limits<double>::quiet_NaN();
// Look for two consecutive small sub-diagonal elements
int m = n1 - 2;
while (m >= l) {
double z = H[m][m];
r = x - z;
double 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; 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;
}
double s = std::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;
double 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] -= p * x;
H[k + 1][j] -= p * y;
}
// Column modification
for (int i = 0; i <= std::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] -= p;
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 < FLT_EPSILON) {
return;
}
for (n1 = nn - 1; n1 >= 0; n1--) {
double p = d[n1];
double q = e[n1];
if (q == 0) {
// Real vector
double z = std::numeric_limits<double>::quiet_NaN();
double s = std::numeric_limits<double>::quiet_NaN();
int l = n1;
H[n1][n1] = 1.0;
for (int i = n1 - 1; i >= 0; i--) {
double w = H[i][i] - p;
double 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);
}
} else {
// Solve real equations
CV_DbgAssert(!cvIsNaN(z));
double x = H[i][i + 1];
double y = H[i + 1][i];
q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
double 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 {
CV_DbgAssert(z != 0.0);
H[i + 1][n1] = (-s - y * t) / z;
}
}
// Overflow control
double t = std::abs(H[i][n1]);
if ((eps * t) * t > 1) {
double inv_t = 1.0 / t;
for (int j = i; j <= n1; j++) {
H[j][n1] *= inv_t;
}
}
}
}
} else if (q < 0) {
// Complex vector
double z = std::numeric_limits<double>::quiet_NaN();
double r = std::numeric_limits<double>::quiet_NaN();
double s = std::numeric_limits<double>::quiet_NaN();
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 {
complex_div(
0.0, -H[n1 - 1][n1],
H[n1 - 1][n1 - 1] - p, q,
H[n1 - 1][n1 - 1], H[n1 - 1][n1]
);
}
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];
}
double w = H[i][i] - p;
if (e[i] < 0.0) {
z = w;
r = ra;
s = sa;
} else {
l = i;
if (e[i] == 0) {
complex_div(
-ra, -sa,
w, q,
H[i][n1 - 1], H[i][n1]
);
} else {
// Solve complex equations
double x = H[i][i + 1];
double 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));
}
complex_div(
x * r - z * ra + q * sa, x * s - z * sa - q * ra,
vr, vi,
H[i][n1 - 1], H[i][n1]);
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 {
complex_div(
-r - y * H[i][n1 - 1], -s - y * H[i][n1],
z, q,
H[i + 1][n1 - 1], H[i + 1][n1]);
}
}
// Overflow control
double t = std::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
#if 0 // 'if' condition is always false
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];
}
}
}
#endif
// Back transformation to get eigenvectors of original matrix
for (int j = nn - 1; j >= low; j--) {
for (int i = low; i <= high; i++) {
double z = 0.0;
for (int k = low; k <= std::min(j, high); k++) {
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; 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 = std::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; 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; d = NULL;
delete[] e; e = NULL;
delete[] ort; ort = NULL;
for (int i = 0; i < n; i++) {
if (H) delete[] H[i];
if (V) delete[] V[i];
}
delete[] H; H = NULL;
delete[] V; V = NULL;
}
// 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:
// 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() :
n(0),
d(NULL), e(NULL), ort(NULL),
V(NULL), H(NULL)
{
// nothing
}
// 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, bool fallbackSymmetric = true)
{
CV_INSTRUMENT_REGION();
if(fallbackSymmetric && 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() { release(); }
// Returns the eigenvalues of the Eigenvalue Decomposition.
Mat eigenvalues() const { return _eigenvalues; }
// Returns the eigenvectors of the Eigenvalue Decomposition.
Mat eigenvectors() const { return _eigenvectors; }
};
void eigenNonSymmetric(InputArray _src, OutputArray _evals, OutputArray _evects)
{
CV_INSTRUMENT_REGION();
Mat src = _src.getMat();
int type = src.type();
size_t n = (size_t)src.rows;
CV_Assert(src.rows == src.cols);
CV_Assert(type == CV_32F || type == CV_64F);
Mat src64f;
if (type == CV_32F)
src.convertTo(src64f, CV_32FC1);
else
src64f = src;
EigenvalueDecomposition eigensystem;
eigensystem.compute(src64f, false);
// EigenvalueDecomposition returns transposed and non-sorted eigenvalues
std::vector<double> eigenvalues64f;
eigensystem.eigenvalues().copyTo(eigenvalues64f);
CV_Assert(eigenvalues64f.size() == n);
std::vector<int> sort_indexes(n);
cv::sortIdx(eigenvalues64f, sort_indexes, SORT_EVERY_ROW | SORT_DESCENDING);
std::vector<double> sorted_eigenvalues64f(n);
for (size_t i = 0; i < n; i++) sorted_eigenvalues64f[i] = eigenvalues64f[sort_indexes[i]];
Mat(sorted_eigenvalues64f).convertTo(_evals, type);
if( _evects.needed() )
{
Mat eigenvectors64f = eigensystem.eigenvectors().t(); // transpose
CV_Assert((size_t)eigenvectors64f.rows == n);
CV_Assert((size_t)eigenvectors64f.cols == n);
Mat_<double> sorted_eigenvectors64f((int)n, (int)n, CV_64FC1);
for (size_t i = 0; i < n; i++)
{
double* pDst = sorted_eigenvectors64f.ptr<double>((int)i);
double* pSrc = eigenvectors64f.ptr<double>(sort_indexes[(int)i]);
CV_Assert(pSrc != NULL);
memcpy(pDst, pSrc, n * sizeof(double));
}
sorted_eigenvectors64f.convertTo(_evects, type);
}
}
//------------------------------------------------------------------------------
// Linear Discriminant Analysis implementation
//------------------------------------------------------------------------------
LDA::LDA(int num_components) : _num_components(num_components) { }
LDA::LDA(InputArrayOfArrays src, InputArray labels, int num_components) : _num_components(num_components)
{
this->compute(src, labels); //! compute eigenvectors and eigenvalues
}
LDA::~LDA() {}
void LDA::save(const String& filename) const
{
FileStorage fs(filename, FileStorage::WRITE);
if (!fs.isOpened()) {
CV_Error(Error::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(Error::StsError, "File can't be opened for reading!");
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(InputArrayOfArrays _src, InputArray _lbls) {
// get data
Mat src = _src.getMat();
std::vector<int> labels;
// safely copy the labels
{
Mat tmp = _lbls.getMat();
for(unsigned int i = 0; i < tmp.total(); i++) {
labels.push_back(tmp.at<int>(i));
}
}
// 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]
std::vector<int> mapped_labels(labels.size());
std::vector<int> num2label = remove_dups(labels);
std::map<int, int> label2num;
for (int i = 0; i < (int)num2label.size(); i++)
label2num[num2label[i]] = 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();
// we can't do a LDA on one class, what do you
// want to separate from each other then?
if(C == 1) {
String error_message = "At least two classes are needed to perform a LDA. Reason: Only one class was given!";
CV_Error(Error::StsBadArg, error_message);
}
// throw error if less labels, than samples
if (labels.size() != static_cast<size_t>(N)) {
String error_message = format("The number of samples must equal the number of labels. Given %zu labels, %d samples. ", labels.size(), N);
CV_Error(Error::StsBadArg, error_message);
}
// warn if within-classes scatter matrix becomes singular
if (N < D) {
std::cout << "Warning: Less observations than feature dimension given!"
<< "Computation will probably fail."
<< std::endl;
}
// clip number of components to be a valid number
if ((_num_components <= 0) || (_num_components >= C)) {
_num_components = (C - 1);
}
// holds the mean over all classes
Mat meanTotal = Mat::zeros(1, D, data.type());
// holds the mean for each class
std::vector<Mat> meanClass(C);
std::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 total mean
meanTotal.convertTo(meanTotal, meanTotal.type(), 1.0 / static_cast<double> (N));
// calculate class means
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;
es.compute(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
std::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(InputArrayOfArrays _src, InputArray _lbls) {
switch(_src.kind()) {
case _InputArray::STD_VECTOR_MAT:
case _InputArray::STD_ARRAY_MAT:
lda(asRowMatrix(_src, CV_64FC1), _lbls);
break;
case _InputArray::MAT:
lda(_src.getMat(), _lbls);
break;
default:
String error_message= format("InputArray Datatype %d is not supported.", _src.kind());
CV_Error(Error::StsBadArg, error_message);
break;
}
}
// Projects one or more row aligned samples into the LDA subspace.
Mat LDA::project(InputArray src) {
return subspaceProject(_eigenvectors, Mat(), src);
}
// Reconstructs projections from the LDA subspace from one or more row aligned samples.
Mat LDA::reconstruct(InputArray src) {
return subspaceReconstruct(_eigenvectors, Mat(), src);
}
}
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