public void TestOrthogonalization()
{
List<IVector> Acols = MatrixUtils.GetColumnVectors(A);
List<IVector> vstarlist = Orthogonalization.Orthogonalize(Acols);
for (int i = 0; i < vstarlist.Count-1; ++i)
{
for (int j = i + 1; j < vstarlist.Count; ++j)
{
Assert.True(vstarlist[i].Multiply(vstarlist[j]) < 1e-10);
}
}
}
public void TestOrthoNormal()
{
List<IVector> Rcols;
List<IVector> Acols = MatrixUtils.GetColumnVectors(A);
List<IVector> vstarlist = Orthogonalization.Orthogonalize(Acols, out Rcols);
for (int i = 0; i < Rcols.Count; ++i)
{
int count = 0;
for (int j = 0; j < Rcols[i].Dimension; ++j)
{
count += (System.Math.Abs(Rcols[i][j]) > 1e-10) ? 1 : 0;
}
Assert.Equal(i + 1, count);
}
for (int i = 0; i < Acols.Count; ++i)
{
IVector pi = new SparseVector(Acols[i].Dimension);
for (int j = 0; j < vstarlist.Count; ++j)
{
pi = pi.Add(vstarlist[j].Multiply(Rcols[i][j]));
}
for (int d = 0; d < Acols[i].Dimension; ++d)
{
Assert.Equal(Acols[i][d], pi[d]);
}
Assert.True(Acols[i].Equals(pi));
}
List<double> norms;
List<IVector> qlist = VectorUtils.Normalize(vstarlist, out norms);
for (int i = 0; i < qlist.Count - 1; ++i)
{
for (int j = i + 1; j < vstarlist.Count; ++j)
{
Assert.True(qlist[i].Multiply(qlist[j]) < 1e-10);
}
Assert.True(qlist[i].Norm(2) - 1 < 1e-10);
}
for (int i = 0; i < vstarlist.Count; ++i)
{
Assert.Equal(norms[i], vstarlist[i].Norm(2));
}
IMatrix R = MatrixUtils.GetMatrix(Rcols);
foreach (int r in R.RowKeys)
{
R[r] = R[r].Multiply(norms[r]);
}
for (int i = 0; i < A.RowCount; ++i)
{
for (int j = 0; j < A.ColCount; ++j)
{
Assert.Equal(R[i][j], Rcols[j][i] * norms[i]);
}
}
}