Gaussian Elimination and back-substitution algorithm

Gauss-Elim/GEtest.cpp

@@ -0,0 +1,41 @@
+// GEtest.cpp
+// Author: Isaac Stone
+// Language: C++
+//
+// Synopsis: This program simply tests the return
+// value of the gaussElim() function described in
+// "gaussElim.h". The mat_gen() function generates
+// an augmented matrix that is stored into A. Both 
+// the matrix and the solution to Ax=b are printed
+// to the screen
+
+#include <stdlib.h>
+#include <stdio.h>
+#include "matrix.h"
+#include "vectorCode.h"
+#include "mat_gen.h"
+#include "gaussElim.h"
+
+using namespace std;
+
+int main(  int argc, char **argv ) {
+
+  Matrix A;
+  vector<double> a_sols;
+
+  A = mat_gen();
+  a_sols.resize( A.size(), 0 );
+
+  // Perform Gussian Elimination with 
+  // back substitution
+  a_sols = gaussElim( A );
+
+  // Print augmented matrix A
+  printMatrix(A);
+  printf( "\n" );
+
+  // Printf solutions to Ax=b
+  printVector( a_sols );
+
+  return 0;
+}

Gauss-Elim/README.md

@@ -0,0 +1,26 @@
+### Gaussian Elimination and Back-Substution Algorithm - gaussElim.h
+
+#### Author: Isaac Stone, University of Tennessee Undergrad of Computer Science
+
+### gaussElim.h
+gaussElim.h - Included is gaussElim.h, which implements the Gaussian Elimination and back-substituion method for an augmented matrix. The functionality is fairly simple. The function gaussElim() can be called by any c++ program that includes "gaussElim.h". It takes as its only argument a Matrix ( described in matrix.cpp ) and returns a Vector ( described in vectorCode.cpp ) that is the solution to Ax=b. If no solution exists, or only the trivial solution exists, the program prints an error and exits. 
+
+#### Other files worth noting:
+
+mat_gen.h - Generates an augmented matrix using pseudorandom values. It returns a Matrix and can be included via "mat_gen.h". For more, see commments in file.
+
+GEtest.cpp - Used to test gaussElim.h with various inputs from mat_gen.h.
+
+makefile - If working on a linux system, make sure all files are in working directory and type "make" to compile.
+
+iterativeSolvers.h, iterativeSolver.cpp, matrix.h, matrix.cpp, vectorCode.h, VectorCode.cpp -
+All these files are dependencies for Matrix and Vector data structures needed for gaussElim.h and mat_gen.h to function as-is. They are written and developed by Christopher Johnson and obtained via GitHub at:
+
+### https://github.com/Christopher42/computational-mathematics
+
+where extensive documentation can be found, along with examples and testing information.
+
+Project was compiled on a linux machine using g++ -std=11 and was produced under the GNU GeneralPublic License, version 3. Feel free to modify, include, and improve gaussElim.h and mat_gen.h under the GGPL. Thank you. 
+
+
+Acknowledgements to Christopher Johnson, the author of the computational-mathematics repository on GitHhub.

Gauss-Elim/gaussElim.cpp

@@ -0,0 +1,89 @@
+// GEtest.cpp
+// Author: Isaac Stone
+// Language: C++
+//
+// Synopsis: This .cpp file implements Guassin Elimination with
+// back-substitution for an augmented matrix. The function
+// gaussElim() takes a Matrix ( matrix.h ) as an argument and returns a
+// solution to Ax=b in the form of a Vector ( vectorCode.h ). If no solution or 
+// only the trivial solution exists, a message is printed 
+// to the screen and the program exits.
+
+#include <vector>
+#include <cstdio>
+#include <cstdlib>
+#include "matrix.h"
+#include "vectorCode.h"
+
+using namespace std;
+
+// Elimination step
+void Elim( double x, Vector &a, Vector &b ) {
+
+  for ( unsigned i = 0; i < a.size(); i++ )
+	  a[i] = a[i] - ( x * b[i] );
+}
+
+Vector gaussElim( Matrix A ) {
+
+  int i, j, p, n;
+  double sum, xn, x;
+  Vector tmp, sols;
+
+  x = 0.0;
+  p = 0;
+  n = A.size();
+
+  // Guassian Elimination
+  for ( i = 0; i < (n - 1) ; i++ )
+  {
+	p = i;
+	while( A[p][i] == 0 )
+	{
+	  p++;
+	  if ( p >  n )
+	  {
+		printf( "No solution or trivial solution\n" );
+		exit(1);
+	  }
+	}
+
+	// Swap rows
+	if ( p != i ) {
+	  tmp = A[p];
+	  A[p] = A[i];
+	  A[i] = tmp;
+	}
+
+	for ( j = i+1; j < n; j++ )
+	{
+	  x = A[j][i] / A[i][i];
+	  Elim( x, A[j], A[i] );
+	}
+  }
+
+  // Test for no solution
+  if ( A[ n - 1 ][ n - 1 ] == 0 )
+  {
+    printf( "No solution or trivial solution\n" );
+	exit(1);
+  }
+
+  // Perform back-substitution
+  sols.resize( n, 0 );
+
+  xn = A[n-1][n] / A[n-1][n-1];
+  sols[n-1] = xn;
+
+  for ( int i = n-1; i >= 0; i-- )
+  {
+	sum = 0;
+	for ( j = i+1; j < n+1; j++ ) {
+	  sum += ( A[i][j] * sols[j] );
+	}
+	xn = ( A[i][n] - sum ) / A[i][i];
+	sols[i] = xn;
+  }
+
+  return sols;
+}

Gauss-Elim/gaussElim.h

@@ -0,0 +1,19 @@
+// GEtest.cpp
+// Author: Isaac Stone
+// Language: C++
+//
+// Synopsis: This file includes headers gaussElim.cpp to implement
+// Guassin Elimination with back-substitution for an augmented matrix. The function
+// gaussElim() takes a Matrix ( matrix.h ) as an argument and returns a
+// solution to Ax=b in the form of a Vector ( vectorCode.h ). If no solution or 
+// only the trivial solution exists, a message is printed 
+// to the screen and the program exits.
+//
+// Check "gaassElim.cpp" for more information.
+
+#include <vector>
+#include <cstdlib>
+#include "matrix.h"
+#include "vectorCode.h"
+
+Vector gaussElim( Matrix A );