public void Regression_Solve_OLS_Partials()
{
// Boston dataset downloaded from http://lib.stat.cmu.edu/datasets/boston
// validating results against values from https://towardsdatascience.com/simple-and-multiple-linear-regression-in-python-c928425168f9
Matrix A = new Matrix(
new decimal[, ]
{
{ 12, -51, 4 },
{ 6, 167, -68 },
{ -4, 24, -41 }
});
// don't alter a1 or it will alter A
ColumnVector a1 = A.GetColumnVector(
0,
0,
A.Height);
decimal norm = a1.GetNorm();
// create copy of vector that can be edited
Matrix u = a1.AsMatrix();
Assert.AreEqual(
new decimal[, ]
{
{ 12 },
{ 6 },
{ -4 }
},
a1.AsMatrix().Array);
// subtract norm * e vector
// the sign is selected so it has the opposite sign of u1
decimal u1 = u[0, 0];
u[0, 0] -= Math.Sign(u1) * norm;
u.DivideBy(2);
Matrix uT = u.GetTranspose();
Matrix uuT = Matrices.Multiply(
u,
uT);
Matrix I = Matrices.GetIdentity(
uuT.Width);
uuT.MultiplyBy(
2 / norm);
Matrix H = Matrices.Subtract(
I,
uuT);
Matrix HA = Matrices.Multiply(
H,
A);
decimal[,] expected = new decimal[, ]
{
{ 6 / 7m, 3 / 7m, -2 / 7m },
{ 3 / 7m, -2 / 7m, 6 / 7m },
{ -2 / 7m, 6 / 7m, 3 / 7m }
};
Assert.AreEqual(
expected,
H.Array);
A = new Matrix(
new decimal[, ]
{
{ 4, 1, -2, 2 },
{ 1, 2, 0, 1 },
{ -2, 0, 3, -2 },
{ 2, 1, -2, -1 }
});
//Q1 = A.GetHouseholderMatrix();
//expected = new decimal[,]
// {
// {1, 0, 0, 0},
// {0, -1/3m, 2/3m, -2/3m},
// {0, 2/3m, 2/3m, 1/3m},
// {0, -2/3m, 1/3m, 2/3m}
// };
}