private static void ScalaRow(Matrix m, int r, Fraction s)
{
for (int i = 0; i < m.columns; i++)
{
m.data[r, i] = FractionOperators.Multiply(m.data[r, i], s);
}
}
private static void ScalaAdd(Matrix m, int src, int dst, Fraction s)
{
for (int i = 0; i < m.columns; i++)
{
m.data[dst, i] = FractionOperators.Add(m.data[dst, i], FractionOperators.Multiply(s, m.data[src, i]));
}
}
public static Fraction Length(List <TokenType> parameters)
{
Vector v = parameters[0] as Vector;
Vector.CheckNumberic(v);
if (v is Vec2 vec2)
{
return(Fraction.Sqrt(FractionOperators.Add(FractionOperators.Multiply(vec2.X, vec2.X), FractionOperators.Multiply(vec2.Y, vec2.Y))));
}
if (v is Vec3 vec3)
{
return(Fraction.Sqrt(FractionOperators.Add(FractionOperators.Add(FractionOperators.Multiply(vec3.X, vec3.X), FractionOperators.Multiply(vec3.Y, vec3.Y)), FractionOperators.Multiply(vec3.Z, vec3.Z))));
}
return(null);
}
public static Fraction Det(List <TokenType> parameters)
{
Matrix m = parameters[0] as Matrix;
Matrix.CheckNumbericMatrix(m);
Matrix.CheckSquareMatrix(m);
m = GaussBot(m, true, true);
Fraction det = 1;
for (int i = 0; i < m.rows; i++)
{
det = FractionOperators.Multiply(det, m.data[i, i]);
}
return(det);
}
public static Matrix Inverse(List <TokenType> parameters)
{
Matrix m = parameters[0] as Matrix;
Matrix.CheckNumbericMatrix(m);
Matrix.CheckSquareMatrix(m);
Matrix mat = Matrix.CreateUnsafeMatrix(m.rows, m.columns * 2);
for (int r = 0; r < m.rows; r++)
{
for (int c = 0; c < m.columns; c++)
{
mat.data[r, c] = m.data[r, c];
}
for (int c = m.columns; c < m.columns * 2; c++)
{
if (c == r + m.columns)
{
mat.data[r, c] = new Fraction(1);
}
else
{
mat.data[r, c] = new Fraction(0);
}
}
}
GaussBot(mat, false, false);
Fraction det = 1;
for (int i = 0; i < mat.rows; i++)
{
det = FractionOperators.Multiply(det, mat.data[i, i]);
}
if (det.GetValue() == 0)
{
throw new ExprCoreException("행렬식이 0인 행렬은 inverse를 구할 수 없습니다.");
}
for (int i = mat.rows - 1; i >= 0; i--)
{
for (int j = i - 1; j >= 0; j--)
{
ScalaAdd(mat, i, j, FractionOperators.Negative(FractionOperators.Divide(mat.data[j, i], mat.data[i, i])));
}
ScalaRow(mat, i, FractionOperators.Divide(new Fraction(1), mat.data[i, i]));
}
Matrix ret = Matrix.CreateUnsafeMatrix(m.rows, m.columns);
for (int r = 0; r < m.rows; r++)
{
for (int c = 0; c < m.columns; c++)
{
ret.data[r, c] = mat.data[r, m.rows + c];
}
}
return(ret);
}