public void Transform2D()
{
// Transform forward and inverse and compare with initial values.
var random = new Random(1234567);
var s = new Vector2F[16, 8];
var t = new Vector2F[16, 8];
for (int i = 0; i < s.GetLength(0); i++)
{
for (int j = 0; j < s.GetLength(1); j++)
{
s[i, j] = random.NextVector2F(-10, 10);
t[i, j] = s[i, j];
}
}
var fft = new FastFourierTransformF(16);
fft.Transform2D(t, true);
Assert.IsFalse(Vector2F.AreNumericallyEqual(s[0, 0], t[0, 0]));
fft.Transform2D(t, false);
for (int i = 0; i < s.GetLength(0); i++)
{
for (int j = 0; j < s.GetLength(1); j++)
{
Assert.IsTrue(Vector2F.AreNumericallyEqual(s[i, j], t[i, j]));
}
}
}
public void Transform1DArguments()
{
Assert.Throws <ArgumentNullException>(() => FastFourierTransformF.Transform1D(null, true));
Assert.Throws <ArgumentNullException>(() => FastFourierTransformF.Transform1D(null, 2, true));
Assert.Throws <ArgumentException>(() => FastFourierTransformF.Transform1D(new Vector2F[0], true));
Assert.Throws <ArgumentException>(() => FastFourierTransformF.Transform1D(new Vector2F[13], true));
FastFourierTransformF.Transform1D(new Vector2F[1], true);
// This is ok.
FastFourierTransformF.Transform1D(new Vector2F[2], true);
FastFourierTransformF.Transform1D(new Vector2F[16], false);
}
public void Transform1DAs2DColumn()
{
// Result of 2D with one row/column must be the same as 1D.
var fft = new FastFourierTransformF(16);
var random = new Random(1234567);
var s1D = new Vector2F[16];
var s2D = new Vector2F[16, 1];
for (int i = 0; i < s1D.Length; i++)
{
s1D[i] = random.NextVector2F(-10, 10);
s2D[i, 0] = s1D[i];
}
FastFourierTransformF.Transform1D(s1D, true);
fft.Transform2D(s2D, true);
for (int i = 0; i < s1D.Length; i++)
Assert.AreEqual(s1D[i], s2D[i, 0]);
}
public void Transform2DArguments()
{
var fft = new FastFourierTransformF(16);
Assert.Throws <ArgumentNullException>(() => fft.Transform2D(null, true));
// Senseless.
Assert.Throws <ArgumentException>(() => fft.Transform2D(new Vector2F[0, 0], true));
// Not POT.
Assert.Throws <ArgumentException>(() => fft.Transform2D(new Vector2F[13, 2], true));
Assert.Throws <ArgumentException>(() => fft.Transform2D(new Vector2F[2, 6], true));
// Too large for capacity.
Assert.Throws <ArgumentException>(() => fft.Transform2D(new Vector2F[32, 6], true));
fft.Transform2D(new Vector2F[1, 1], true);
// This is ok.
fft.Transform2D(new Vector2F[2, 4], true);
fft.Transform2D(new Vector2F[16, 1], false);
}
public void Transform1DComparedWithDft()
{
// Transform forward and inverse and compare with initial values.
var random = new Random(1234567);
var s = new Vector2F[16];
var t = new Vector2F[16];
for (int i = 0; i < s.Length; i++)
{
s[i] = random.NextVector2F(-10, 10);
t[i] = s[i];
}
FastFourierTransformF.DFT(s, true);
FastFourierTransformF.Transform1D(t, true);
for (int i = 0; i < s.Length; i++)
{
Assert.IsTrue(Vector2F.AreNumericallyEqual(s[i], t[i]));
}
}
public void Transform1DAs2DRow()
{
// Result of 2D with one row/column must be the same as 1D.
var fft = new FastFourierTransformF(16);
var random = new Random(1234567);
var s1D = new Vector2F[8];
var s2D = new Vector2F[1, 8];
for (int i = 0; i < s1D.Length; i++)
{
s1D[i] = random.NextVector2F(-10, 10);
s2D[0, i] = s1D[i];
}
FastFourierTransformF.Transform1D(s1D, true);
fft.Transform2D(s2D, true);
for (int i = 0; i < s1D.Length; i++)
{
Assert.AreEqual(s1D[i], s2D[0, i]);
}
}
private void PerformCpuFft(float time)
{
// Compute _h.
int n = CpuSize;
for (int x = -n / 2; x < n / 2; x++)
{
for (int y = -n / 2; y < n / 2; y++)
{
var indexX = GetIndex(x, n);
var indexY = GetIndex(y, n);
// The frequency domain images have a different order:
var fftIndexX = x & (n - 1);
var fftIndexY = y & (n - 1);
var k = new Vector2F(GetKx(x), GetKy(y));
//float omega = GetOmega(water, k.Length);
float omega = _omega[indexX, indexY];
// h = h0(x, y) * e^(i * omega * t) + conj(h0(-x, -y)) * e^(-i * omega * t).
float cos = (float)Math.Cos(omega * time);
float sin = (float)Math.Sin(omega * time);
// conj(Z) = Z.Re - i * Z.Im.
// e^(ix) = cos(x) + i * sin(x)
// e^(-ix) = cos(x) - i * sin(x)
// Multiplication of two complex: (a + ib) * (c + id) = (ac - bd) + i(ad + bc)
// --> h.Re = h0(x, y).Re * cos - h0(x, y).Im *sin + h0(-x, -y).Re * cos - h0(-x, -y).Im * sin
// h.Im = h0(x, y).Re * sin + h0(x, y).Im * cos - h0(-x, -y).Re * sin - h0(-x, -y).Im * cos
var h0XY = _h0[indexX, indexY] * HeightScale;
var h0NegXNegY = _h0[GetIndex(-x, n), GetIndex(-y, n)] * HeightScale;
var h = new Vector2F((h0XY.X + h0NegXNegY.X) * cos - (h0XY.Y + h0NegXNegY.Y) * sin,
(h0XY.X - h0NegXNegY.X) * sin + (h0XY.Y - h0NegXNegY.Y) * cos);
_h[fftIndexX, fftIndexY] = h;
// For normals, we have to perform inverse FFT for normal.X and normal.Y.
// normal.x = InverseFFT(-i * k.x / kLength * h).Re
// normal.y = InverseFFT(-i * k.y / kLength * h).Re
// However, since FFT is linear and normal.X/Y are real (imaginary values are 0),
// we can combine them into a single FFT:
// FFT(Nx) = SpectrumNx, FFT(Ny) = SpectrumNy
// Add and multiply by any constant, e.g. i!
// FFT(Nx + i * Ny) = SpectrumNx + i * SpectrumNy
// Nx + i * Ny = InverseFFT(SpectrumNx + i * SpectrumNy)
// SpectrumNx = i * k.X * h = i * (k.X * h.Re + i * k.X * h.Im) = -k.X * h.Im + i * k.X * h.Re
// i * SpectrumNy = i * i * k.Y * h = -1 * (k.Y * h.Re + i * k.Y * h.Im)
_N[fftIndexX, fftIndexY] = new Vector2F(-k.X * h.Y - k.Y * h.X,
k.X * h.X - k.Y * h.Y);
// Horizontal displacements for choppy waves:
// Again we combine the x and y displacement into one FFT.
// D.x = InverseFFT(-i * k.x / kLength * h).Re
// D.y = InverseFFT(-i * k.y / kLength * h).Re
k *= _oneOverKLength[indexX, indexY];
_D[fftIndexX, fftIndexY] = new Vector2F(k.X * h.Y + k.Y * h.X,
-k.X * h.X + k.Y * h.Y);
}
}
// Transform data from frequency domain to spatial domain.
if (_fft == null)
_fft = new FastFourierTransformF(n);
else if (_fft.Capacity < n)
_fft.Capacity = n;
_fft.Transform2D(_h, false);
_fft.Transform2D(_D, false);
_fft.Transform2D(_N, false);
}
public void Transform2DArguments()
{
var fft = new FastFourierTransformF(16);
Assert.Throws<ArgumentNullException>(() => fft.Transform2D(null, true));
// Senseless.
Assert.Throws<ArgumentException>(() => fft.Transform2D(new Vector2F[0, 0], true));
// Not POT.
Assert.Throws<ArgumentException>(() => fft.Transform2D(new Vector2F[13, 2], true));
Assert.Throws<ArgumentException>(() => fft.Transform2D(new Vector2F[2, 6], true));
// Too large for capacity.
Assert.Throws<ArgumentException>(() => fft.Transform2D(new Vector2F[32, 6], true));
fft.Transform2D(new Vector2F[1, 1], true);
// This is ok.
fft.Transform2D(new Vector2F[2, 4], true);
fft.Transform2D(new Vector2F[16, 1], false);
}
public void Transform2D()
{
// Transform forward and inverse and compare with initial values.
var random = new Random(1234567);
var s = new Vector2F[16, 8];
var t = new Vector2F[16, 8];
for (int i = 0; i < s.GetLength(0); i++)
{
for (int j = 0; j < s.GetLength(1); j++)
{
s[i, j] = random.NextVector2F(-10, 10);
t[i, j] = s[i, j];
}
}
var fft = new FastFourierTransformF(16);
fft.Transform2D(t, true);
Assert.IsFalse(Vector2F.AreNumericallyEqual(s[0, 0], t[0, 0]));
fft.Transform2D(t, false);
for (int i = 0; i < s.GetLength(0); i++)
for (int j = 0; j < s.GetLength(1); j++)
Assert.IsTrue(Vector2F.AreNumericallyEqual(s[i, j], t[i, j]));
}
