public SafeMatrix Transpose()
{
SafeMatrix M = new SafeMatrix(m_ColumnCount, m_RowCount);
for (int i = 0; i < m_ColumnCount; i++)
{
for (int j = 0; j < m_RowCount; j++)
{
M.m_Elements[i * M.m_ColumnCount + j] = m_Elements[j * m_ColumnCount + i];
}
}
return M;
}
/// <summary>
/// Inverts square matrix as long as det != 0.
/// </summary>
/// <returns>Inverse of matrix.</returns>
public SafeMatrix Inverse()
{
if (!this.IsSquare())
throw new InvalidOperationException("Cannot invert non-square matrix.");
double det = this.Determinant();
if (det == 0)
throw new InvalidOperationException("Cannot invert (nearly) singular matrix.");
SafeMatrix buf = new SafeMatrix(m_ColumnCount, m_ColumnCount);
for (int i = 0; i < m_ColumnCount; i++)
{
for (int j = 0; j < m_ColumnCount; j++)
{
buf.m_Elements[i * buf.m_ColumnCount + j] = (Math.Pow(-1, i + j) * this.Minor(j, i).Determinant()) / det;
}
}
return buf;
}
public SafeMatrix Minor(int row, int col)
{
// THIS IS THE LOW-LEVEL SOLUTION ~ O(n^2)
SafeMatrix buf = new SafeMatrix(m_RowCount - 1, m_ColumnCount - 1);
int r = 0;
int c = 0;
for (int i = 0; i < m_RowCount; i++)
{
if (i != row)
{
for (int j = 0; j < m_ColumnCount; j++)
{
if (j != col)
{
buf.m_Elements[r * buf.m_ColumnCount + c] = m_Elements[i * m_ColumnCount + j];
c++;
}
}
c = 0;
r++;
}
}
return buf;
}
public SafeMatrix Clone()
{
SafeMatrix A = new SafeMatrix(m_RowCount, m_ColumnCount);
for (int i = 0; i < m_MatrixSize; i++)
A.m_Elements[i] = m_Elements[i];
return A;
}
public static double Dot(SafeMatrix v, int vRow, SafeMatrix w, int wCol)
{
if (v.ColumnCount != w.RowCount)
throw new ArgumentException("Vectors must be of the same length.");
double buf = 0;
for (int i = 0; i < v.ColumnCount; i++)
{
buf += v.m_Elements[vRow * v.m_ColumnCount + i] * w.m_Elements[i * w.m_ColumnCount + wCol];
}
return buf;
}
public static SafeMatrix operator *(double x, SafeMatrix A)
{
SafeMatrix B = new SafeMatrix(A.RowCount, A.ColumnCount);
for (int i = 0; i < A.m_MatrixSize; i++)
{
B.m_Elements[i] = A.m_Elements[i] * x;
}
return B;
}
public static SafeMatrix operator *(SafeMatrix A, SafeMatrix B)
{
if (A.ColumnCount != B.RowCount)
throw new ArgumentException("Inner matrix dimensions must agree.");
SafeMatrix C = new SafeMatrix(A.RowCount, B.ColumnCount);
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < B.ColumnCount; j++)
{
C.m_Elements[i * C.m_ColumnCount + j] = Dot(A, i, B, j);
}
}
return C;
}
public void Solve()
{
if (m_XValues.Count < 3)
throw new InvalidOperationException("Cannot get a linear fit from less than 3 points.");
SafeMatrix A = new SafeMatrix(m_XValues.Count, 3);
SafeMatrix X = new SafeMatrix(m_XValues.Count, 1);
for (int i = 0; i < m_XValues.Count; i++)
{
A[i, 0] = m_XValues[i] * m_XValues[i];
A[i, 1] = m_XValues[i];
A[i, 2] = 1;
X[i, 0] = m_YValues[i];
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
m_A = bx[0, 0];
m_B = bx[1, 0];
m_C = bx[2, 0];
m_IsSolved = true;
}