public EpMatrix ParseEquations()
{
// Look: an example set
// 3x + 7z = 9
// x + y + z = 10
// y + 2z = 6
int numOfEquals = NumberOf (originalText, "=");
int numOfNewline = NumberOf (originalText, "\n");
if (numOfEquals != numOfNewline)
return null;
string[] lines = originalText.Split ('\n');
System.Text.RegularExpressions.MatchCollection unknowns =
System.Text.RegularExpressions.Regex.Matches (originalText, "[a-z]",
System.Text.RegularExpressions.RegexOptions.IgnorePatternWhitespace);
string[] unknownsString = new string[unknowns.Count - 1];
unknowns.CopyTo (unknownsString, 0);
unknownsString = RemoveDuplicates (unknownsString);
if (unknownsString.GetLength (0) != lines.GetLength (0)) {
return null;
}
// Let's get started splitting lines into an array
EpMatrix result = new EpMatrix(new int[lines.GetUpperBound (0),unknownsString.GetUpperBound (0)]);
char[] delimiterChars = { '+', '-', '=' };
string[,] setSplit = new string[numOfNewline, unknownsString.GetUpperBound (0)];
for (int i = 0; i < lines.GetLength (0); i++) {
string[] currentBits = lines [i].Split (delimiterChars);
for (int j = 0; j < currentBits.GetLength (0); j++) {
setSplit[i, j] = currentBits [j];
}
}
// by now, we have an array that, for the example set up top, now looks like this:
// {(3x , 7z, 9),
// (x, y, z, 10),
// (y, 2z, 6)}
// We now need to replace nx with n, where n is a number and x is an unknown,
// so that every unknown appears exactly once in every row
return result; // random return to statisfy commpiler
}
/// <summary>
/// Swaps the two given rows
/// </summary>
/// <returns>An EpMatrix with the swap performed</returns>
/// <param name="matrix">Matrix.</param>
/// <param name="rowOne">Zero-based index for the first row.</param>
/// <param name="rowTwo">Zero-based index for the second row.</param>
public static EpMatrix SwapRows (EpMatrix matrix, int rowOne, int rowTwo)
{
// tempstore the two rows, then swap them in TheMatrix
int[] firstRow = new int[matrix.GetNumOfColumns()-1];
for (int i = 0; i < matrix.GetNumOfColumns (); i++) {
firstRow [i] = matrix.GetElement (rowOne, i);
}
// Copy the second row into the first one
for (int i = 0; i < matrix.GetNumOfColumns (); i++) {
matrix.SetElement (rowOne, i, matrix.GetElement (rowTwo, i));
}
// And now the temp into the second row
for (int i = 0; i < matrix.GetNumOfColumns (); i++) {
matrix.SetElement (rowOne, i, firstRow [i]);
}
return matrix;
}
/// <summary>
/// Turns the given matrix into it's row reduced echelon form.
/// </summary>
/// <param name="matrix">An EpMatrix to perform the operation on.</param>
public static EpMatrix Rref (EpMatrix matrix)
{
int[,] rrem = matrix.GetMatrix ();
int lead = 0, rowCount = rrem.GetLength(0), columnCount = rrem.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (rrem[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = rrem[r, j];
rrem[r, j] = rrem[i, j];
rrem[i, j] = temp;
}
int div = rrem[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) rrem[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = rrem[j, lead];
for (int k = 0; k < columnCount; k++) rrem[j, k] -= (sub * rrem[r, k]);
}
}
lead++;
}
// Done!
return new EpMatrix(rrem);
}
/// <summary>
/// Performs a linear combination on two rows. Stores the result in the first row by convention.
/// </summary>
/// <returns>EpMatrix with the combination performed on it</returns>
/// <param name="matrix">Matrix.</param>
/// <param name="rowOne">Zero-based index for the first row</param>
/// <param name="factorOne">Factor to multiply the first rwo by</param>
/// <param name="rowTwo">Zero-based index for the second row</param>
/// <param name="factorTwo">Factor to multiply the second row by</param>
public static EpMatrix LinearCombination (EpMatrix matrix, int rowOne, int factorOne, int rowTwo, int factorTwo)
{
for (int i = 0; i < matrix.GetNumOfColumns (); i++) {
matrix.SetElement (rowOne, i,
factorOne * matrix.GetElement (rowOne, i) + factorTwo * matrix.GetElement (rowTwo, i));
}
return matrix;
}
/// <summary>
/// Adds two rows from the given matrix together. Stores the result in the first row by convention
/// </summary>
/// <returns>An EpMatrix with the rows added</returns>
/// <param name="matrix">Matrix.</param>
/// <param name="rowOne">Zero-based index for the first row. The result goes in here as well.</param>
/// <param name="rowTwo">Zero-based index for the second row.</param>
public static EpMatrix AddRows (EpMatrix matrix, int rowOne, int rowTwo)
{
for (int i = 0; i < matrix.GetNumOfColumns (); i++) {
matrix.SetElement (rowOne, i, matrix.GetElement (rowTwo, i) + matrix.GetElement (rowOne, i));
}
return matrix;
}
/// <summary>
/// Multiplies two rows together.
/// </summary>
/// <returns>An EpMatrix with the operation performed on it.</returns>
/// <param name="matrix">Matrix.</param>
/// <param name="theRow">Zero-based index for the row.</param>
/// <param name="factor">Factor.</param>
public static EpMatrix MultiplyRow (EpMatrix matrix, int theRow, int factor)
{
for (int i = 0; i < matrix.GetNumOfColumns (); i++) {
matrix.SetElement (theRow, i, matrix.GetElement (theRow, i) * factor);
}
return matrix;
}