public static Trivector MulVGrad(Trivector v, Quaternion.Quaternion q)
{
double x = v.X, y = v.Y, z = v.Z, r = q.R, i = q.I, j = q.J, k = q.K;
return(new Trivector(
x * (r * r + i * i - j * j - k * k) + 2 * y * (i * j + r * k) + 2 * z * (k * i - r * j),
y * (r * r - i * i + j * j - k * k) + 2 * z * (j * k + r * i) + 2 * x * (i * j - r * k),
z * (r * r - i * i - j * j + k * k) + 2 * x * (k * i + r * j) + 2 * y * (j * k - r * i)
));
}
public static Quaternion.Quaternion MulQGrad(Trivector v, Trivector u, Quaternion.Quaternion q)
{
double vx = v.X, vy = v.Y, vz = v.Z, ux = u.X, uy = u.Y, uz = u.Z, r = q.R, i = q.I, j = q.J, k = q.K;
return(new Quaternion.Quaternion(
ux * (2 * j * vz - 2 * k * vy + 2 * r * vx) + uy * (2 * k * vx - 2 * i * vz + 2 * r * vy) + uz * (2 * i * vy - 2 * j * vx + 2 * r * vz),
ux * (2 * k * vz + 2 * j * vy + 2 * i * vx) + uy * (2 * j * vx - 2 * r * vz - 2 * i * vy) + uz * (2 * r * vy + 2 * k * vx - 2 * i * vz),
ux * (2 * r * vz + 2 * i * vy - 2 * j * vx) + uy * (2 * i * vx + 2 * k * vz + 2 * j * vy) + uz * (2 * k * vy - 2 * r * vx - 2 * j * vz),
ux * (2 * i * vz - 2 * r * vy - 2 * k * vx) + uy * (2 * r * vx + 2 * j * vz - 2 * k * vy) + uz * (2 * j * vy + 2 * i * vx + 2 * k * vz)
));
}
public void MulTest()
{
Trivector v = new Trivector(4, 3, 2);
Quaternion.Quaternion q = new Quaternion.Quaternion(5, -6, 7, -8);
Trivector u = v * q;
Assert.AreEqual(112, u.X);
Assert.AreEqual(-838, u.Y);
Assert.AreEqual(-404, u.Z);
}
public void MulVGradTest()
{
Trivector v = new Trivector(4, 3, 2);
Quaternion.Quaternion q = new Quaternion.Quaternion(5, -6, 7, -8);
Trivector u = Trivector.MulVGrad(v, q);
Assert.AreEqual(-648, u.X);
Assert.AreEqual(-438, u.Y);
Assert.AreEqual(516, u.Z);
}
public void MulQGradTest()
{
Trivector v = new Trivector(4, -3, 2);
Trivector u = new Trivector(-2, 5, -7);
Quaternion.Quaternion q = new Quaternion.Quaternion(5, -6, 7, -8);
Quaternion.Quaternion p = Trivector.MulQGrad(v, u, q);
Assert.AreEqual(-390, p.R);
Assert.AreEqual(734, p.I);
Assert.AreEqual(-470, p.J);
Assert.AreEqual(814, p.K);
}
public static Quaternion.QuaternionFilter2D Reference(TrivectorMap2D x, TrivectorMap2D gy, Quaternion.QuaternionFilter2D w, int kwidth, int kheight, int stride)
{
int inchannels = x.Channels, outchannels = gy.Channels, batch = x.Batch;
int inw = x.Width, inh = x.Height, outw = gy.Width, outh = gy.Height;
if (outw != (inw - kwidth) / stride + 1 || outh != (inh - kheight) / stride + 1)
{
throw new ArgumentException("mismatch shape");
}
Quaternion.QuaternionFilter2D gw = new Quaternion.QuaternionFilter2D(inchannels, outchannels, kwidth, kheight);
for (int kx, ky = 0; ky < kheight; ky++)
{
for (kx = 0; kx < kwidth; kx++)
{
for (int th = 0; th < batch; th++)
{
for (int inch, outch = 0; outch < outchannels; outch++)
{
for (inch = 0; inch < inchannels; inch++)
{
Quaternion.Quaternion sum = 0;
Quaternion.Quaternion q = w[inch, outch, kx, ky];
for (int ix, iy = ky, ox, oy = 0; oy < outh; iy += stride, oy++)
{
for (ix = kx, ox = 0; ox < outw; ix += stride, ox++)
{
sum += Trivector.MulQGrad(x[inch, ix, iy, th], gy[outch, ox, oy, th], q);
}
}
gw[inch, outch, kx, ky] += sum;
}
}
}
}
}
return(gw);
}
public static Quaternion.QuaternionFilter0D Reference(TrivectorMap0D x, TrivectorMap0D gy, Quaternion.QuaternionFilter0D w)
{
int inchannels = x.Channels, outchannels = gy.Channels, batch = x.Batch;
Quaternion.QuaternionFilter0D gw = new Quaternion.QuaternionFilter0D(inchannels, outchannels);
for (int inch, outch = 0; outch < outchannels; outch++)
{
for (inch = 0; inch < inchannels; inch++)
{
Quaternion.Quaternion sum = 0;
Quaternion.Quaternion q = w[inch, outch];
for (int th = 0; th < batch; th++)
{
sum += Trivector.MulQGrad(x[inch, th], gy[outch, th], q);
}
gw[inch, outch] += sum;
}
}
return(gw);
}
public static Quaternion.QuaternionFilter1D Reference(TrivectorMap1D x, TrivectorMap1D gy, Quaternion.QuaternionFilter1D w, int kwidth, int stride)
{
int inchannels = x.Channels, outchannels = gy.Channels, batch = x.Batch;
int inw = x.Width, outw = gy.Width;
if (outw != (inw - kwidth) / stride + 1)
{
throw new ArgumentException("mismatch shape");
}
Quaternion.QuaternionFilter1D gw = new Quaternion.QuaternionFilter1D(inchannels, outchannels, kwidth);
for (int kx = 0; kx < kwidth; kx++)
{
for (int th = 0; th < batch; th++)
{
for (int inch, outch = 0; outch < outchannels; outch++)
{
for (inch = 0; inch < inchannels; inch++)
{
Quaternion.Quaternion sum = 0;
Quaternion.Quaternion q = w[inch, outch, kx];
for (int ix = kx, ox = 0; ox < outw; ix += stride, ox++)
{
sum += Trivector.MulQGrad(x[inch, ix, th], gy[outch, ox, th], q);
}
gw[inch, outch, kx] += sum;
}
}
}
}
return(gw);
}
