public void GetMatrixTest()
{
var matrix = Walsh.GetMatrix(0);
Assert.AreEqual(1, matrix.GetLength(0));
Assert.AreEqual(1, matrix.GetLength(1));
Assert.AreEqual(1, matrix[0, 0]);
matrix = Walsh.GetMatrix(1);
Assert.AreEqual(2, matrix.GetLength(0));
Assert.AreEqual(2, matrix.GetLength(1));
Assert.AreEqual(new sbyte[, ] {
{ 1, 1 }, { 1, -1 }
}, matrix);
matrix = Walsh.GetMatrix(2);
Assert.AreEqual(4, matrix.GetLength(0));
Assert.AreEqual(4, matrix.GetLength(1));
Assert.AreEqual(new sbyte[, ] {
{ 1, 1, 1, 1 }, { 1, 1, -1, -1 }, { 1, -1, 1, -1 }, { 1, -1, -1, 1 }
}, matrix);
matrix = Walsh.GetMatrix(3);
Assert.AreEqual(8, matrix.GetLength(0));
Assert.AreEqual(8, matrix.GetLength(1));
Assert.AreEqual(-1, matrix[5, 4]);
}
/// <summary>
/// coeff(n)=c_{1,n}(f), n > 0
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
private double coeff(Func <double, double> f, int n)
{
// we use formula c_{1,n}(f) = c_n(f')
--n;
if (n == 0)
{
return(f(1) - f(0));
}
var k = (int)Log(n, 2) + 1;
var w = Walsh.GetMatrix(k);
var pow2k = Pow(2, k);
var s = 0d;
for (int j = 0; j <= pow2k - 1; j++)
{
s += w[n, j] * (f((j + 1) / pow2k) - f(j / pow2k));
}
return(s);
}