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Feature/spectra correlations #306

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merged 13 commits into from
Jun 17, 2024
Merged

Feature/spectra correlations #306

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12359ad
update the ncv values
atrayees Jun 10, 2024
742df12
include spectra routine
atrayees Jun 10, 2024
6e0a6bc
function to check for a correlation matrix
atrayees Jun 10, 2024
b36ea3d
run sampling for matrices with greater dimensions
atrayees Jun 10, 2024
93e88c8
remove blank space lines
atrayees Jun 10, 2024
e7e8252
fix indentations
atrayees Jun 12, 2024
322f794
fixed indentation and code style
atrayees Jun 12, 2024
56ea104
updated tol as a function parameter
atrayees Jun 12, 2024
594e1d0
fix indentations
atrayees Jun 12, 2024
91b10d4
update comments about the ncv parameter
atrayees Jun 12, 2024
f872b12
Update comment regarding computing of the minimum positive eigenvalue…
atrayees Jun 12, 2024
2b52486
reuse function isPositiveSemidefinite()
atrayees Jun 14, 2024
8128efa
fix indentation
atrayees Jun 14, 2024
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62 changes: 49 additions & 13 deletions examples/correlation_matrices/sampler.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -17,6 +17,7 @@
#include "convex_bodies/spectrahedra/spectrahedron.h"
#include "random_walks/random_walks.hpp"
#include "sampling/sample_correlation_matrices.hpp"
#include "matrix_operations/EigenvaluesProblems.h"

typedef double NT;
typedef Eigen::Matrix<NT, Eigen::Dynamic, Eigen::Dynamic> MT;
Expand Down Expand Up @@ -89,6 +90,28 @@ void write_to_file(std::string filename, std::vector<PointType> const& randPoint
std::cout.rdbuf(coutbuf);
}

bool is_correlation_matrix(const MT& matrix, const double tol = 1e-8){
//check if all the diagonal elements are ones
for(int i=0 ; i<matrix.rows() ; i++)
{
if(std::abs(matrix(i, i)-1.0) > tol)
{
return false;
}
}

//check if the matrix is positive semidefinite
using NT = double;
using MatrixType = Eigen::Matrix<NT, Eigen::Dynamic, Eigen::Dynamic>;
EigenvaluesProblems<NT, MatrixType, Eigen::Matrix<NT, Eigen::Dynamic, 1>> solver;

if(solver.isPositiveSemidefinite(matrix))
{
return true;
}
return false;
}

template<typename WalkType>
void correlation_matrix_uniform_sampling(const unsigned int n, const unsigned int num_points, std::string walkname){

Expand All @@ -106,7 +129,7 @@ void correlation_matrix_uniform_sampling(const unsigned int n, const unsigned in
time = std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count();
std::cout << "Elapsed time : " << time << " (ms)" << std::endl;

write_to_file<Point>(walkname + "_matrices.txt", randPoints);
write_to_file<Point>(walkname + "_matrices" + std::to_string(n) + ".txt", randPoints);
}

template<typename WalkType>
Expand All @@ -126,7 +149,15 @@ void correlation_matrix_uniform_sampling_MT(const unsigned int n, const unsigned
time = std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count();
std::cout << "Elapsed time : " << time << " (ms)" << std::endl;

write_to_file<PointMT>(walkname + "_matrices_MT.txt", randPoints);
int valid_points = 0;
for(const auto& points : randPoints){
if(is_correlation_matrix(points.mat)){
valid_points++;
}
}
std::cout << "Number of valid points = " << valid_points << std::endl;

write_to_file<PointMT>(walkname + "_matrices_MT" + std::to_string(n) + ".txt", randPoints);
}

int main(int argc, char const *argv[]){
Expand All @@ -146,25 +177,30 @@ int main(int argc, char const *argv[]){
printf("\n");
#endif

unsigned int n = 3, num_points = 5000;
unsigned int num_points = 5000;

std::vector<unsigned int> dimensions = {3, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100};

old_uniform_sampling<BilliardWalk>(n, num_points);
for(unsigned int n : dimensions){

correlation_matrix_uniform_sampling<BallWalk>(n, num_points, "BallWalk");
old_uniform_sampling<BilliardWalk>(n, num_points);

correlation_matrix_uniform_sampling<RDHRWalk>(n, num_points, "RDHRWalk");
correlation_matrix_uniform_sampling<BallWalk>(n, num_points, "BallWalk");

correlation_matrix_uniform_sampling<BilliardWalk>(n, num_points, "BilliardWalk");
correlation_matrix_uniform_sampling<RDHRWalk>(n, num_points, "RDHRWalk");

correlation_matrix_uniform_sampling<AcceleratedBilliardWalk>(n, num_points, "AcceleratedBilliardWalk");
correlation_matrix_uniform_sampling<BilliardWalk>(n, num_points, "BilliardWalk");

correlation_matrix_uniform_sampling_MT<BallWalk>(n, num_points, "BallWalk");
correlation_matrix_uniform_sampling<AcceleratedBilliardWalk>(n, num_points, "AcceleratedBilliardWalk");

correlation_matrix_uniform_sampling_MT<RDHRWalk>(n, num_points, "RDHRWalk");
correlation_matrix_uniform_sampling_MT<BallWalk>(n, num_points, "BallWalk");

correlation_matrix_uniform_sampling_MT<BilliardWalk>(n, num_points, "BilliardWalk");
correlation_matrix_uniform_sampling_MT<RDHRWalk>(n, num_points, "RDHRWalk");

correlation_matrix_uniform_sampling_MT<AcceleratedBilliardWalk>(n, num_points, "AcceleratedBilliardWalk");
correlation_matrix_uniform_sampling_MT<BilliardWalk>(n, num_points, "BilliardWalk");

correlation_matrix_uniform_sampling_MT<AcceleratedBilliardWalk>(n, num_points, "AcceleratedBilliardWalk");
}

return 0;
}
}
43 changes: 39 additions & 4 deletions include/matrix_operations/EigenvaluesProblems.h
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Expand Up @@ -167,9 +167,12 @@ class EigenvaluesProblems<NT, Eigen::Matrix<NT,Eigen::Dynamic,Eigen::Dynamic>, E
Spectra::DenseSymMatProd<NT> op(B);
Spectra::DenseCholesky<NT> Bop(-A);

// Construct generalized eigen solver object, requesting the largest three generalized eigenvalues
// Construct generalized eigen solver object, computing the minimum positive eigenvalue by computing the largest eigenvalue of the inverse Generalized Eigenvalue Problem
// An empirical value of ncv that gives a better performance
// TODO: tune this implementation by tuning the parameters like ncv
int ncv = std::min(std::max(10, matrixDim/20), matrixDim);
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Could you please comment on where those numbers come from? 10, 20, 15 ?

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This is an empirical value I gave to @atrayees. We left as a task after the R interface to tune this implementation (not only ncv value).

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Thanks @TolisChal for the explanations. @atrayees could you please add a comment with this explanation and mention that as a TODO?

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yes, done

Spectra::SymGEigsSolver<NT, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<NT>, Spectra::DenseCholesky<NT>, Spectra::GEIGS_CHOLESKY>
geigs(&op, &Bop, 1, 15 < matrixDim ? 15 : matrixDim);
geigs(&op, &Bop, 1, ncv);

// Initialize and compute
geigs.init();
Expand Down Expand Up @@ -324,9 +327,12 @@ class EigenvaluesProblems<NT, Eigen::Matrix<NT,Eigen::Dynamic,Eigen::Dynamic>, E
Spectra::DenseSymMatProd<NT> op(B);
Spectra::DenseCholesky<NT> Bop(-A);

// Construct generalized eigen solver object, requesting the largest three generalized eigenvalues
// Construct generalized eigen solver object, requesting the largest generalized eigenvalue
// an empirical value of ncv that gives a better performance
// TODO: tune this implementation by tuning the parameters like ncv
int ncv = std::min(std::max(10, matrixDim/20), matrixDim);
Spectra::SymGEigsSolver<NT, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<NT>, Spectra::DenseCholesky<NT>, Spectra::GEIGS_CHOLESKY>
geigs(&op, &Bop, 1, 15 < matrixDim ? 15 : matrixDim);
geigs(&op, &Bop, 1, ncv);

// Initialize and compute
geigs.init();
Expand Down Expand Up @@ -439,10 +445,39 @@ class EigenvaluesProblems<NT, Eigen::Matrix<NT,Eigen::Dynamic,Eigen::Dynamic>, E
/// \param[in] B: symmetric matrix
/// \return The minimum positive eigenvalue and the corresponding eigenvector
NT minPosLinearEigenvalue_EigenSymSolver(MT const & A, MT const & B, VT &eigvec) const {

#if defined(SPECTRA_EIGENVALUES_SOLVER)
int matrixDim = A.rows();
NT lambdaMinPositive;

Spectra::DenseSymMatProd<NT> op(B);
Spectra::DenseCholesky<NT> Bop(A);

//construct generalized eigen solver object, requesting the smallest eigenvalue
int ncv = std::min(std::max(10, matrixDim/20), matrixDim);
Spectra::SymGEigsSolver<NT, Spectra::LARGEST_ALGE, Spectra::DenseSymMatProd<NT>, Spectra::DenseCholesky<NT>, Spectra::GEIGS_CHOLESKY>
geigs(&op, &Bop, 1, ncv);

//initialize and compute
geigs.init();
int nconv = geigs.compute();

//retrieve results
VT evalues;

if(geigs.info() == Spectra::SUCCESSFUL){
evalues = geigs.eigenvalues();
eigvec = geigs.eigenvectors().col(0);
}

lambdaMinPositive = NT(1)/evalues(0);

#elif
NT lambdaMinPositive = NT(0);
Eigen::GeneralizedSelfAdjointEigenSolver<MT> ges(B,A);
lambdaMinPositive = 1/ges.eigenvalues().reverse()[0];
eigvec = ges.eigenvectors().reverse().col(0).reverse();
#endif
return lambdaMinPositive;
}
};
Expand Down
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