/// <summary> Create a transposed matrix </summary>
public MyMatrix Transpose()
{
MyMatrix result = new MyMatrix(this.cols, this.rows);
for (int row = 0; row < this.rows; row++)
{
for (int col = 0; col < this.cols; col++)
{
result[col, row] = this.data[row, col];
}
}
return(result);
}
/// <summary> Iteratively solve the coefficients using Gauss-Newton method </summary>
/// <remarks> http://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm </remarks>
public double[] Solve()
{
if (this.ys == null)
{
throw new InvalidOperationException("Not yet initialized");
}
double lastSSE = double.MaxValue;
double[] errors = new double[this.ys.Length];
// let C0 be the current coefficient guess, C1 be the better answer we are after
// let E0 be the error using current guess
// we have:
// JacT * Jac * (C1 - C0) = JacT * E0
//
MyMatrix jacobian = Jacobian();
MyMatrix jacobianT = jacobian.Transpose();
MyMatrix product = jacobianT * jacobian;
SquareMatrix inverse = SquareMatrix.FromMatrix(product).Inverse();
for (int iteration = 0; iteration < GaussNewton.MaxIteration; iteration++)
{
this.sse = 0;
for (int i = 0; i < this.ys.Length; i++)
{
double y = function(this.coefficients, this.xs[i]);
errors[i] = this.ys[i] - y;
sse += errors[i] * errors[i];
}
if (lastSSE - sse < GaussNewton.ConvergeThreshold)
{
this.solved = true;
return(this.coefficients);
}
double[] shift = inverse * (jacobianT * errors);
for (int i = 0; i < this.coefficientCount; i++)
{
this.coefficients[i] += shift[i];
}
lastSSE = sse;
}
throw new InvalidOperationException("No answer can be found");
}
/// <summary> Calculate a Jacobian matrix. </summary>
/// <remarks> http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant </remarks>
private MyMatrix Jacobian()
{
double[][] p = new double[this.coefficientCount][];
for (int i = 0; i < p.Length; i++)
{
p[i] = new double[this.coefficientCount];
p[i][i] = 1;
}
MyMatrix jacobian = new MyMatrix(this.ys.Length, this.coefficientCount);
for (int i = 0; i < this.ys.Length; i++)
{
for (int j = 0; j < this.coefficientCount; j++)
{
jacobian[i, j] = function(p[j], this.xs[i]);
}
}
return(jacobian);
}
/// <summary> Multiply by another matrix. The width of left matrix should equal the height of right matrix </summary>
public MyMatrix Multiply(MyMatrix m)
{
if (m == null || m.rows != this.cols)
{
throw new ArgumentException("Invalid matrix to multiply");
}
MyMatrix result = new MyMatrix(this.rows, m.cols);
int inner = this.cols;
for (int row = 0; row < result.rows; row++)
{
for (int col = 0; col < result.cols; col++)
{
double sum = 0;
for (int i = 0; i < inner; i++)
{
sum += this[row, i] * m[i, col];
}
result[row, col] = sum;
}
}
return(result);
}