[TEST]UPSTREAM: Pick some source changes from 48080d0a97

* Sync new folder structure

AMSS_NCKU_source/Surface_Integral/gaussj.C

@@ -0,0 +1,106 @@
+
+#ifdef newc
+#include <iostream>
+#include <iomanip>
+#include <fstream>
+#include <cstdlib>
+#include <cstring>
+#include <cmath>
+using namespace std;
+#else
+#include <iostream.h>
+#include <iomanip.h>
+#include <fstream.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <math.h>
+#endif
+
+// Intel oneMKL LAPACK interface
+#include <mkl_lapacke.h>
+/* Linear equation solution using Intel oneMKL LAPACK.
+a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
+containing the right-hand side vectors. On output a is
+replaced by its matrix inverse, and b is replaced by the
+corresponding set of solution vectors.
+
+Mathematical equivalence:
+  Solves: A * x = b  =>  x = A^(-1) * b
+  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
+  within numerical precision. */
+
+int gaussj(double *a, double *b, int n)
+{
+  // Allocate pivot array and workspace
+  lapack_int *ipiv = new lapack_int[n];
+  lapack_int info;
+
+  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
+  double *a_copy = new double[n * n];
+  for (int i = 0; i < n * n; i++) {
+    a_copy[i] = a[i];
+  }
+
+  // Step 1: Solve linear system A*x = b using LU decomposition
+  // LAPACKE_dgesv uses column-major by default, but we use row-major
+  info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  // Step 2: Compute matrix inverse A^(-1) using LU factorization
+  // First do LU factorization of original matrix a
+  info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  // Then compute inverse from LU factorization
+  info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  delete[] ipiv;
+  delete[] a_copy;
+
+  return 0;
+}
+// for check usage
+/*
+int main()
+{
+  double *A,*b;
+  A=new double[9];
+  b=new double[3];
+
+  A[0]=0.5; A[1]=1.0/3; A[2]=1;
+  A[3]=1;   A[4]=5.0/3; A[5]=3;
+  A[6]=2;   A[7]=4.0/3; A[8]=5;
+
+  b[0]=1; b[1]=3; b[2]=2;
+
+  cout<<"initial data:"<<endl;
+  for(int i=0;i<3;i++) cout<<A[i*3]<<" "<<A[i*3+1]<<" "<<A[i*3+2]<<" "<<b[i]<<endl;
+
+  gaussj(A, b, 3);
+
+  cout<<"final data:"<<endl;
+  for(int i=0;i<3;i++) cout<<A[i*3]<<" "<<A[i*3+1]<<" "<<A[i*3+2]<<" "<<b[i]<<endl;
+
+  delete[] A; delete[] b;
+}
+*/