/// <summary>
/// Evaluates dot operation of vector/matrix lazily.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="x"> [<c>x.Rank == 1 || x.Rank == 2</c>] </param>
/// <param name="y"> [<c>y.Rank == 1 || y.Rank == 2</c>] </param>
/// <returns>
/// <para> The result of dot operation of <paramref name="x"/> and <paramref name="y"/>. </para>
/// <para> - If <c>x.Shape == {p} && y.Rank == {p}</c>, then <c>$ReturnValue.Shape == {1}</c>. </para>
/// <para> - If <c>x.Shape == {p} && y.Shape == {p, n}</c>, then <c>$ReturnValue.Shape == {n}</c>. </para>
/// <para> - If <c>x.Shape == {m, p} && y.Shape == {p}</c>, then <c>$ReturnValue.Shape == {m}</c>. </para>
/// <para> - If <c>x.Shape == {m, p} && y.Shape == {p, n}</c>, then <c>$ReturnValue.Shape == {m, n}</c>. </para>
/// <para> - If the shape patterns does not match with above patterns, throw <see cref="ShapeMismatchException"/>. </para>
/// </returns>
/// <exception cref="ShapeMismatchException"></exception>
public static NdArray <T> Dot <T>(this NdArray <T> x, NdArray <T> y)
{
var xEntity = x.GetOrCopyBuffer();
switch (y.Rank)
{
case 1:
var yEntity = y.GetOrCopyBuffer();
switch (x.Rank)
{
case 1:
return(Dot1x1(xEntity, yEntity));
case 2:
return(Dot2x1(xEntity, yEntity));
default:
break;
}
break;
case 2:
var yTEntity = y.Transpose().ToMutable().GetOrCopyBuffer();
switch (x.Rank)
{
case 1:
return(Dot1x2(xEntity, yTEntity));
case 2:
return(Dot2x2(xEntity, yTEntity));
default:
break;
}
break;
default:
break;
}
Guard.ThrowShapeMismatch($"The ranks of x and y must be 1 or 2. (x.Rank={x.Rank}, y.Rank={y.Rank})");
throw new NotSupportedException();
}
/// <summary>
/// Actual implmentation of the matrix multiplication operation.
/// </summary>
/// <typeparam name="T">The type of data to operate on</typeparam>
/// <typeparam name="CADD">The typed add operator</typeparam>
/// <typeparam name="CMUL">The typed multiply operator</typeparam>
/// <param name="addop">The add operator</param>
/// <param name="mulop">The multiply operator</param>
/// <param name="in1">The left-hand-side argument</param>
/// <param name="in2">The right-hand-side argument</param>
/// <param name="out">An optional output argument, use for in-place operations</param>
private static void UFunc_Matmul_Inner_Flush <T, CADD, CMUL>(CADD addop, CMUL mulop, NdArray <T> in1, NdArray <T> in2, NdArray <T> @out)
where CADD : struct, IBinaryOp <T>
where CMUL : struct, IBinaryOp <T>
{
//Matrix multiplication of two vectors is the dot product
if (@out.Shape.Elements == 1)
{
@out.Value[0] = UFunc_CombineAndAggregate_Inner_Flush <T, CADD, CMUL>(addop, mulop, in1, in2);
return;
}
if (@out.Shape.Dimensions.LongLength != 2)
{
throw new Exception("Matrix multiplication is only supported for 1 and 2 dimensional arrays");
}
long opsOuter = @out.Shape.Dimensions[0].Length;
long opsInner = @out.Shape.Dimensions[1].Length;
long opsInnerInner = in1.Shape.Dimensions[1].Length;
T[] d1 = in1.AsArray();
T[] d2 = in2.AsArray();
T[] d3 = @out.AsArray();
long ix1Base = in1.Shape.Offset;
long outerStride1 = in1.Shape.Dimensions[0].Stride;
long innerStride1 = in1.Shape.Dimensions[1].Stride;
//outerStride1 -= innerStride1 * in1.Shape.Dimensions[1].Length;
NdArray <T> rhs = in2.Transpose();
long ix2Base = rhs.Shape.Offset;
long outerStride2 = rhs.Shape.Dimensions[0].Stride;
long innerStride2 = rhs.Shape.Dimensions[1].Stride;
outerStride2 -= innerStride2 * rhs.Shape.Dimensions[1].Length;
long ix3 = @out.Shape.Offset;
long outerStride3 = @out.Shape.Dimensions[0].Stride;
long innerStride3 = @out.Shape.Dimensions[1].Stride;
outerStride3 -= innerStride3 * @out.Shape.Dimensions[1].Length;
for (long i = 0; i < opsOuter; i++)
{
long ix2 = ix2Base;
for (long j = 0; j < opsInner; j++)
{
long ix1 = ix1Base;
T result = mulop.Op(d1[ix1], d2[ix2]);
ix1 += innerStride1;
ix2 += innerStride2;
for (long k = 1; k < opsInnerInner; k++)
{
result = addop.Op(result, mulop.Op(d1[ix1], d2[ix2]));
ix1 += innerStride1;
ix2 += innerStride2;
}
d3[ix3] = result;
ix3 += innerStride3;
ix2 += outerStride2;
}
ix3 += outerStride3;
ix1Base += outerStride1;
}
}
public void TransposeForXDim(int[] axesMap, NdArray <int> from, NdArray <int> to)
{
Assert.Equal(to, from.Transpose(axesMap), NdArrayComparer <int> .Default);
Assert.Equal(to.ToMutable(), from.ToMutable().Transpose(axesMap), NdArrayComparer <int> .Default);
}