I think that this algorithm is not good, at least for calculation of 5x5 matrices. Even If we correct this
for (j = i + 1; j < n + 1; j++)
to be like this
for (j = i + 1; j < n; j++)
And then write a complete code such as:
using System;
public class Matrix
{
private int row_matrix; //number of rows for matrix
private int column_matrix; //number of colums for matrix
private double[,] matrix; //holds values of matrix itself
//create r*c matrix and fill it with data passed to this constructor
public Matrix(double[,] double_array)
{
matrix = double_array;
row_matrix = matrix.GetLength(0);
column_matrix = matrix.GetLength(1);
Console.WriteLine("Contructor which sets matrix size {0}*{1} and fill it with initial data executed.", row_matrix, column_matrix);
}
//returns total number of rows
public int countRows()
{
return row_matrix;
}
//returns total number of columns
public int countColumns()
{
return column_matrix;
}
//returns value of an element for a given row and column of matrix
public double readElement(int row, int column)
{
return matrix[row, column];
}
//sets value of an element for a given row and column of matrix
public void setElement(double value, int row, int column)
{
matrix[row, column] = value;
}
public double deterMatrix()
{
double det = 0;
double value = 0;
int i, j, k;
i = row_matrix;
j = column_matrix;
int n = i;
if (i != j)
{
Console.WriteLine("determinant can be calculated only for sqaure matrix!");
return det;
}
for (i = 0; i < n - 1; i++)
{
for (j = i + 1; j < n; j++)
{
det = (this.readElement(j, i) / this.readElement(i, i));
for (k = i; k < n; k++)
{
value = this.readElement(j, k) - det * this.readElement(i, k);
this.setElement(value, j, k);
}
}
}
det = 1;
for (i = 0; i < n; i++)
det = det * this.readElement(i, i);
return det;
}
}
internal class Program
{
private static void Main(string[] args)
{
Matrix mat03 = new Matrix(new[,]
{
{1.0, 2.0, -1.0},
{-2.0, -5.0, -1.0},
{1.0, -1.0, -2.0},
});
Matrix mat04 = new Matrix(new[,]
{
{1.0, 2.0, 1.0, 3.0},
{-2.0, -5.0, -2.0, 1.0},
{1.0, -1.0, -3.0, 2.0},
{4.0, -1.0, -3.0, 1.0},
});
Matrix mat05 = new Matrix(new[,]
{
{1.0, 2.0, 1.0, 2.0, 3.0},
{2.0, 1.0, 2.0, 2.0, 1.0},
{3.0, 1.0, 3.0, 1.0, 2.0},
{1.0, 2.0, 4.0, 3.0, 2.0},
{2.0, 2.0, 1.0, 2.0, 1.0},
});
double determinant = mat03.deterMatrix();
Console.WriteLine("determinant is: {0}", determinant);
determinant = mat04.deterMatrix();
Console.WriteLine("determinant is: {0}", determinant);
determinant = mat05.deterMatrix();
Console.WriteLine("determinant is: {0}", determinant);
}
}
Result is:
determinant is: -8
determinant is: -142
determinant is: -NaN
NaN occurs because of division by zero (I debugged it)
It could be possible that for some very specific input this works OK, but in general case this is NOT a good algorithm.
So, it works for 3x3 and 4x4 but NOT for 5x5
I wrote this to anyone who might come across this question to avoid losing few hours in trying to implement or fix something that has wrong algorithm in the first place.