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]));
}
}
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);
}
}
// copy = 행렬을 copy후 계산할것인가?
// allowMulNeg = Switching이 홀수번 이루어지면 자동으로 첫 행에 * -1
public static Matrix GaussBot(Matrix m, bool copy, bool allowMulNeg)
{
bool found = false, neg = false;
int r = 0, c = 0;
Matrix ret = copy ? new Matrix(m) : m;
while (r < m.rows && c < m.columns)
{
for (int i = r; i < m.rows; i++)
{
if (((Fraction)m.data[i, c]).GetValue() != 0)
{
if (i != r)
{
Switching(ret, i, r);
Console.WriteLine("Switch " + i + ", " + r);
neg = !neg;
}
found = true;
break;
}
}
if (!found)
{
c++;
continue;
}
else
{
Fraction src = ret.data[r, c] as Fraction;
for (int j = r + 1; j < m.rows; j++)
{
Fraction val = ret.data[j, c] as Fraction;
if (val.GetValue() != 0)
{
Fraction frac = FractionOperators.Negative(FractionOperators.Divide(val, src));
ScalaAdd(ret, r, j, frac);
Console.WriteLine("Add " + r + "*" + frac + " -> " + j);
}
}
}
r++; c++;
}
if (neg && allowMulNeg)
{
ScalaRow(ret, 0, -1);
}
return(ret);
}
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 Vector Normalize(List <TokenType> parameters)
{
Vector v = parameters[0] as Vector;
Vector.CheckNumberic(v);
Fraction len = Length(parameters);
if (v is Vec2 vec2)
{
return(new Vec2(FractionOperators.Divide(vec2.X, len), FractionOperators.Divide(vec2.Y, len)));
}
if (v is Vec3 vec3)
{
return(new Vec3(FractionOperators.Divide(vec3.X, len), FractionOperators.Divide(vec3.Y, len), FractionOperators.Divide(vec3.Z, len)));
}
return(null);
}
public static Matrix GaussTop(Matrix m, bool copy)
{
int r = m.rows - 1, c = m.columns - 1;
Matrix ret = copy ? new Matrix(m) : m;
while (r >= 0 && c >= 0)
{
int swcnt = 0;
for (int i = r; i >= 0; i--)
{
if (((Fraction)ret.data[i, c]).GetValue() != 0)
{
if (i != r)
{
Switching(ret, i, r);
}
swcnt++;
break;
}
}
if (swcnt == 0)
{
c--;
continue;
}
else
{
Fraction src = ret.data[r, c] as Fraction;
for (int j = r - 1; j >= 0; j--)
{
Fraction val = ret.data[j, c] as Fraction;
if (val.GetValue() != 0)
{
ScalaAdd(ret, r, j, FractionOperators.Negative(FractionOperators.Divide(val, src)));
}
}
}
r--; c--;
}
return(ret);
}
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);
}
