isMatrixSymmetric

C++ Function Reference

1 Signature

bool BigDataStatMeth::isMatrixSymmetric(const Eigen::MatrixXd &X, int sample_size=100)

2 Description

Improved matrix symmetry detection for big-omics data.

3 Parameters

  • X (const Eigen::MatrixXd &): Input matrix to check for symmetry
  • sample_size (int): Number of elements to sample for symmetry check (default 100)

4 Returns

True if matrix is approximately symmetric within tolerance

5 Details

XInput matrix to check for symmetry sample_sizeNumber of elements to sample for symmetry check (default 100) True if matrix is approximately symmetric within tolerance Optimized for large biological matrices with potential noise

6 Caller Graph

Function dependencies

7 Source Code

File: inst/include/hdf5Algebra/matrixEigenDecomposition.hpp • Lines 101-142

inline bool isMatrixSymmetric(const Eigen::MatrixXd& X, int sample_size = 100) {
        if (X.rows() != X.cols()) return false;
        
        int n = X.rows();
        if (n <= 3) return true; // Too small to meaningfully check
        
        // For small matrices, check all elements
        if (n <= 50) {
            double max_diff = (X - X.transpose()).cwiseAbs().maxCoeff();
            double matrix_scale = X.cwiseAbs().maxCoeff();
            return max_diff <= 1e-12 * std::max(1.0, matrix_scale);
        }
        
        // For large matrices, use optimized sampling with vectorized operations
        sample_size = std::min(sample_size, n * n / 4);
        
        // Sample diagonal and off-diagonal elements efficiently
        Eigen::VectorXd diffs(sample_size);
        int count = 0;
        
        // Random sampling with good coverage
        std::random_device rd;
        std::mt19937 gen(rd());
        std::uniform_int_distribution<> dis(0, n - 1);
        
        for (int s = 0; s < sample_size && count < sample_size; ++s) {
            int i = dis(gen);
            int j = dis(gen);
            if (i != j) {
                diffs(count++) = std::abs(X(i, j) - X(j, i));
            }
        }
        
        if (count == 0) return true;
        
        // Use vectorized operations to compute statistics
        double max_diff = diffs.head(count).maxCoeff();
        double matrix_scale = X.cwiseAbs().maxCoeff();
        double tolerance = 1e-12 * std::max(1.0, matrix_scale);
        
        return max_diff <= tolerance;
    }

8 Usage Example

#include "BigDataStatMeth.hpp"

// Example usage
auto result = isMatrixSymmetric(...);