public RationalNumber Determinant()
{
int D = Dimension;
RationalNumber result = 0;
RationalMatrix A = Clone();
for (int i = 0; i < D; i++)
{
RationalNumber pivot = A[i, i];
for (int j = 0; j < D; j++)
{
if (i != j)
{
for (int k = i + 1; k < D; k++)
{
RationalNumber divider = i == 0 ? 1 : A[i - 1, i - 1];
RationalNumber a = pivot * A[j, k];
RationalNumber b = A[j, i] * A[i, k];
RationalNumber ab = a - b;
ab = ab / divider;
A[j, k] = ab;
}
}
}
}
return(A[D - 1, D - 1]);
}
public static RationalMatrix From(double[,] a)
{
RationalMatrix M = new RationalMatrix(a.GetLength(0));
M = a;
return(M);
}
public static RationalMatrix IdentityMatrix(int D)
{
RationalMatrix I = new RationalMatrix(D);
for (int i = 0; i < D; i++)
{
I[i, i] = 1;
}
return(I);
}
public static RationalMatrix operator /(RationalMatrix a, RationalNumber b)
{
RationalMatrix M = new RationalMatrix(a.Dimension);
for (int r = 0; r < M.Dimension; r++)
{
for (int c = 0; c < M.Dimension; c++)
{
M[r, c] = a[r, c] / b;
}
}
return(M);
}
public static RationalMatrix operator *(RationalNumber a, RationalMatrix b)
{
RationalMatrix M = new RationalMatrix(b.Dimension);
for (int r = 0; r < M.Dimension; r++)
{
for (int c = 0; c < M.Dimension; c++)
{
M[r, c] = a * b[r, c];
}
}
return(M);
}
public RationalMatrix Clone()
{
int D = Dimension;
RationalMatrix M = new RationalMatrix(D);
for (int r = 0; r < D; r++)
{
for (int c = 0; c < D; c++)
{
M[r, c] = this[r, c];
}
}
return(M);
}
public RationalMatrix TransposeMatrix()
{
int D = Dimension;
RationalMatrix T = new RationalMatrix(D);
for (int r = 0; r < D; r++)
{
for (int c = 0; c < D; c++)
{
T[c, r] = this[r, c];
}
}
return(T);
}
public static RationalMatrix operator ^(RationalMatrix a, int exponent)
{
if (exponent < 0)
{
throw new System.NotSupportedException();
}
RationalMatrix R = a.IdentityMatrix();
while (exponent > 0)
{
R *= a;
exponent--;
}
return(R);
}
public static RationalMatrix operator -(RationalMatrix a, RationalMatrix b)
{
if (a.Dimension != b.Dimension)
{
throw new System.NotSupportedException();
}
RationalMatrix M = new RationalMatrix(a.Dimension);
for (int r = 0; r < M.Dimension; r++)
{
for (int c = 0; c < M.Dimension; c++)
{
M[r, c] = a[r, c] - b[r, c];
}
}
return(M);
}
public static RationalMatrix operator *(RationalMatrix a, RationalMatrix b)
{
if (a.Dimension != b.Dimension)
{
throw new System.NotSupportedException();
}
RationalMatrix M = new RationalMatrix(a.Dimension);
for (int i = 0; i < a.Dimension; i++)
{
for (int j = 0; j < a.Dimension; j++)
{
for (int k = 0; k < a.Dimension; k++)
{
M[i, j] += a[i, k] * b[k, j];
}
}
}
return(M);
}
public RationalMatrix CofactorMatrix()
{
int D = Dimension;
RationalMatrix CF = new RationalMatrix(D);
if (D == 1)
{
CF[0, 0] = 1;
return(CF);
}
int sign;
for (int i = 0; i < D; i++)
{
for (int j = 0; j < D; j++)
{
sign = ((i + j) % 2 == 0) ? 1 : -1;;
CF[i, j] = MinorMatrix(i, j).Determinant() * sign;
}
}
return(CF);
}
private RationalMatrix MinorMatrix(int row, int col)
{
int D = Dimension;
RationalMatrix M = new RationalMatrix(D - 1);
int i = 0;
int j = 0;
for (int r = 0; r < D; r++)
{
for (int c = 0; c < D; c++)
{
if (r != row && c != col)
{
M[i, j++] = this[r, c];
if (j == D - 1)
{
j = 0;
i++;
}
}
}
}
return(M);
}
public static RationalMatrix ZeroMatrix(int D)
{
RationalMatrix I = new RationalMatrix(D);
return(I);
}