public static bool DiscrepancyIsSmall()
{
Random rand = new Random();
double changingEntry = rand.Next() % 10;
double[] entries1 = new double[3] {
-1, 3, 4
};
double[] entries2 = new double[3] {
-7, 11, changingEntry
};
Vector vector1 = new Vector(entries1);
Vector vector2 = new Vector(entries2);
Vector[] inputVectors = { vector1, vector2 };
Basis inputBasis = new Basis(inputVectors);
Compute compute = new Compute();
compute.Gram_Schmidt_Process(inputBasis);
Vector[] result = Basis.VectorsOfBasis(compute.orthogonalBasis);
double innerProduct = Vector.FindInnerProduct(result[0], result[1]);
bool discrepancyIsSmall = (innerProduct <= 0.01);
return(discrepancyIsSmall);
}
public void Gram_Schmidt_Process(Basis inputBasis)
{
orthogonalBasis = new Basis(inputBasis.dim, inputBasis.vectors[0].n);
orthogonalBasis.dim = inputBasis.dim;
Vector[] u = Basis.VectorsOfBasis(inputBasis);
Vector[] v = new Vector[u.Length];
v[0] = inputBasis.vectors[0];
double[] zeroVector = Vector.ZeroVector(u[0].n);
for (int i = 1; i < inputBasis.dim; ++i)
{
Vector deduct = new Vector(zeroVector);
Vector[] deductVectors = new Vector[i];
for (int j = 0; j < i; ++j)
{
double innerProduct = Vector.FindInnerProduct(u[i], v[j]);
double normSquare = Vector.FindNormSquare(v[j]);
deductVectors[j] = Vector.ScalarMultiplication(v[j], (innerProduct / normSquare));
}
deduct = Vector.VectorArrayAddition(deductVectors);
v[i] = Vector.VectorAddition(u[i], Vector.ScalarMultiplication(deduct, (-1)));
}
for (int i = 0; i < inputBasis.dim; ++i)
{
orthogonalBasis.vectors[i] = v[i];
}
}