private static Tensor <float> _simplifyDot(Tensor <float> x, Tensor <float> y, Einstein[] einstein)
{
// "ij,jk->ik" is a dot
// "ji,jk->ik" is a dot
int outerX = -1, inner = -1, outerY = -1;
bool valid = true;
for (int i = 0; i < einstein.Length; ++i)
{
switch (einstein[i].mode)
{
case EinsteinMode.INNER:
if (inner < 0)
{
inner = i;
}
else
{
valid = false;
}
break;
case EinsteinMode.OUTERX:
if (outerX == -1)
{
outerX = i;
}
break;
case EinsteinMode.OUTERY:
outerY = i;
break;
}
}
if (valid && inner >= 0)
{
if (x.NDim <= 2 && y.NDim <= 2)
{
var transX = outerX >= 0 && einstein[outerX].axisX > einstein[inner].axisX;
var transY = outerY >= 0 && einstein[outerY].axisY < einstein[inner].axisY;
var transZ = outerX >= 0 && outerY >= 0 && einstein[outerX].axisZ > einstein[outerY].axisZ;
if (!transZ)
{
return(Op.Dot(x, y, transposeX: transX, transposeY: transY));
}
else
{
return(Op.Dot(y, x, transposeX: !transY, transposeY: !transX));
}
}
else
{
return(Op.TensorDot(
x, new int[] { (int)einstein[inner].axisX },
y, new int[] { (int)einstein[inner].axisY }
));
}
}
return(null);
}
public static Tensor <float> Create(Tensor <float> a, IEnumerable <int> axesA, Tensor <float> b, IEnumerable <int> axesB)
{
var removeA = axesA.Select(i => i < 0 ? i + a.NDim : i).ToArray();
var removeB = axesB.Select(i => i < 0 ? i + b.NDim : i).ToArray();
int n = removeA.Length;
if (removeB.Length != n)
{
throw new RankException(string.Format(
"The axes parameters of TensorDot should have the same size. Found [{0}] and [{1}].",
string.Join(", ", removeA.AsEnumerable()), string.Join(", ", removeB.AsEnumerable())));
}
for (int d = 0; d < n; ++d)
{
ShapeExtension.Bind(ref a.Shape[removeA[d]], ref b.Shape[removeB[d]]);
}
var keptX = Enumerable.Range(0, a.NDim).Where(d => !removeA.Contains(d)).ToArray();
var keptY = Enumerable.Range(0, b.NDim).Where(d => !removeB.Contains(d)).ToArray();
// Move the axes to sum over to the end of "a"
var keptA = Enumerable.Range(0, a.NDim).Where(d => !removeA.Contains(d));
var at = a.DimShuffle(keptA.Concat(removeA).ToArray());
// Move the axes to sum over to the front of "b"
var keptB = Enumerable.Range(0, b.NDim).Where(d => !removeB.Contains(d));
var bt = b.DimShuffle(removeB.Concat(keptB).ToArray());
var resultShape = keptA.Select(axis => a.Shape[axis]).Concat(keptB.Select(axis => b.Shape[axis])).ToArray();
var a2d = Reshape2D(at, a.NDim - n);
var b2d = Reshape2D(bt, n);
var res = Op.Dot(a2d, b2d).Reshape(resultShape);
res.Comment = "TensorDot";
return(res);
//return new TensorDot(a, ToAxes(_axesX), b, ToAxes(_axesY));
}
public void DontDuplicatesGradient()
{
var x = Op.Vector <float>("x");
var W = Op.Shared(NN.Random.Uniform(-1f, 1f, 10, 10), "W1");
var x1 = Op.Dot(W, x);
x1.Name = nameof(x1);
var y = Op.Sigmoid(Op.Tanh(x1));
y.Name = nameof(y);
var cost = Op.Norm2(y) + Op.Norm2(x1);
var dW = Op.Grad(cost, W);
var update = new OrderedDictionary {
[W] = W - 0.05f * dW
};
var f = Op.Function(input: x, output: cost, updates: update);
AssertSourceContains("Dot", exactly: 2);
}