Function/is correlation (#315)

* new function is_correlation_matrix

* update example function call

this example calls the is_correlation_matrix() function that is present in include/matrix_operations/EigenvaluesProblems.h

* remove blank line

* remove blank line

* fix spaces, add function parameter

Author: atrayees

examples/correlation_matrices/sampler.cpp

@@ -150,10 +150,11 @@ void correlation_matrix_uniform_sampling_MT(const unsigned int n, const unsigned
     std::cout << "Elapsed time : " << time << " (ms)" << std::endl;
 
     int valid_points = 0;
+    EigenvaluesProblems<NT, MT, Eigen::Matrix<NT, Eigen::Dynamic, 1>> solver;
     for(const auto& points : randPoints){
-    	if(is_correlation_matrix(points.mat)){
-    	    valid_points++;
-    	}
+        if(solver.is_correlation_matrix(points.mat)){
+            valid_points++;
+        }
     }
     std::cout << "Number of valid points = " << valid_points << std::endl;
 

include/matrix_operations/EigenvaluesProblems.h

@@ -439,6 +439,24 @@ class EigenvaluesProblems<NT, Eigen::Matrix<NT,Eigen::Dynamic,Eigen::Dynamic>, E
         return false;
     }
 
+    /// Check if a matrix is indeed a correlation matrix
+    /// return true if input matrix is found to be a correlation matrix
+    /// |param[in] matrix
+    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 definite
+        if (isPositiveSemidefinite(matrix)) return true;
+    
+        return false;
+    }
+
     /// Minimum positive eigenvalue of the generalized eigenvalue problem A - lB
     /// Use Eigen::GeneralizedSelfAdjointEigenSolver<MT> ges(B,A) (faster)
     /// \param[in] A: symmetric positive definite matrix