Sync public subset from Flux (private)

include/numerics/inverse/inverse_gauss_jordan.h

@@ -0,0 +1,100 @@
+#ifndef _inverse_gj_n_
+#define _inverse_gj_n_
+
+
+#include "./utils/vector.h"
+#include "./utils/matrix.h"
+
+#include "./numerics/initializers/eye.h"
+
+#include <omp.h>
+
+namespace numerics{
+	
+	template <typename T>
+   	void inverse_gj(utils::Matrix<T>& A){
+		//utils::Matrix<T> B(A.rows(),A.cols(), T{0});
+		utils::Matrix<T> B;
+		B = eye_omp_auto<T>(A.rows());
+
+
+		uint64_t icol{0}, irow{0}, rows{A.rows()}, cols{A.cols()};
+		double big, dum, pivinv, temp;
+		utils::Vi indxc(rows,0), indxr(rows,0), ipiv(rows,0);
+
+		//for (uint64_t j = 0; j < N; ++j){ ipiv[j] = 0;}
+
+		for (uint64_t i = 0; i < rows; i++){
+			big = 0.0;
+			for (uint64_t j = 0; j < rows; j++){
+				if (ipiv[j] != 1){
+					for (uint64_t k = 0; k < rows; k++){
+						if (ipiv[k] == 0){
+							if (abs(A(j,k)) >= big){
+								big = abs(A(j,k));
+								irow = j;
+								icol = k;
+							}
+						}
+					}
+				}
+			}
+			if (big <= T{1e-14}){
+				throw std::runtime_error("utill:inplace_inverse('Gauss-Jordan' - Singular Matrix");
+			}
+			ipiv[icol]++;
+			if (irow != icol){
+				for (uint64_t l = 0; l < rows; l++){ // SWAP 
+					temp = A(irow,l);
+					A(irow,l) = A(icol,l);
+					A(icol,l) = temp;
+				}
+				for (uint64_t l = 0; l < cols; l++){ // SWAP temp matrix
+					temp = B(irow,l);
+					B(irow,l) = B(icol,l);
+					B(icol,l) = temp;
+				}
+			}
+			indxr[i] = irow;
+			indxc[i] = icol;
+			if (A(icol,icol) == 0.0){
+				throw std::runtime_error("utill:inplace_inverse('Gauss-Jordan' - Singular Matrix");
+			}
+			pivinv= 1.0/A(icol,icol);
+			A(icol,icol)=1.0;
+		
+			for (uint64_t l = 0; l < rows; l++){
+				A(icol,l) *= pivinv;
+			}
+			for (uint64_t l = 0; l < cols; l++){
+				B(icol,l) *= pivinv;
+			}
+			for (uint64_t ll = 0; ll < rows; ll++){
+				if (ll != icol){
+					dum = A(ll,icol);
+					A(ll,icol) = 0;
+					for (uint64_t l = 0; l < rows; l++){
+						A(ll,l) -= A(icol,l)*dum;
+					}
+					for (uint64_t l = 0; l < rows; l++){
+						B(ll,l) -= B(icol,l)*dum;
+					}
+				}
+			}
+
+		}
+		//m = temp_m;
+		for (int64_t l = rows-1; l >= 0; l--){
+			if (indxr[l] != indxc[l]){
+				for (uint64_t k = 0; k < rows; k++){
+					temp = A(k,indxr[l]);
+				A(k,indxr[l]) = A(k,indxc[l]);
+				A(k,indxc[l]) = temp;
+				}
+			}
+		}
+	}
+
+} // namespace numerics
+
+#endif // _inverse_gj_n_