/// <summary>
/// Actual implmentation of an operation that performs combination of two NdArray values and aggregates the results.
/// If the aggregation operation is addition, and the combination operation is multiplication, the operation is essentially the dot product,
/// but the operation aggregation occurs accross all dimensions.
/// </summary>
/// <typeparam name="T">The type of data to operate on</typeparam>
/// <typeparam name="CAGGREGATE">The typed add operator</typeparam>
/// <typeparam name="CCOMBINE">The typed multiply operator</typeparam>
/// <param name="aggregate">The add operator</param>
/// <param name="combine">The multiply operator</param>
/// <param name="in1">The left-hand-side argument</param>
/// <param name="in2">The right-hand-side argument</param>
private static T UFunc_CombineAndAggregate_Inner_Flush <T, CAGGREGATE, CCOMBINE>(CAGGREGATE aggregate, CCOMBINE combine, NdArray <T> in1, NdArray <T> in2)
where CAGGREGATE : struct, IBinaryOp <T>
where CCOMBINE : struct, IBinaryOp <T>
{
T result;
T[] d1 = in1.AsArray();
T[] d2 = in2.AsArray();
if (in1.Shape.Dimensions.Length == 1)
{
long totalOps = in1.Shape.Dimensions[0].Length;
long ix1 = in1.Shape.Offset;
long ix2 = in2.Shape.Offset;
long stride1 = in1.Shape.Dimensions[0].Stride;
long stride2 = in2.Shape.Dimensions[0].Stride;
result = combine.Op(d1[ix1], d2[ix2]);
ix1 += stride1;
ix2 += stride2;
for (long i = 1; i < totalOps; i++)
{
result = aggregate.Op(result, combine.Op(d1[ix1], d2[ix2]));
ix1 += stride1;
ix2 += stride2;
}
}
else if (in1.Shape.Dimensions.Length == 2)
{
long opsOuter = in1.Shape.Dimensions[0].Length;
long opsInner = in1.Shape.Dimensions[1].Length;
long ix1 = in1.Shape.Offset;
long ix2 = in2.Shape.Offset;
long outerStride1 = in1.Shape.Dimensions[0].Stride;
long outerStride2 = in2.Shape.Dimensions[0].Stride;
long innerStride1 = in1.Shape.Dimensions[1].Stride;
long innerStride2 = in2.Shape.Dimensions[1].Stride;
outerStride1 -= innerStride1 * in1.Shape.Dimensions[1].Length;
outerStride2 -= innerStride2 * in2.Shape.Dimensions[1].Length;
result = combine.Op(d1[ix1], d2[ix2]);
ix1 += innerStride1;
ix2 += innerStride2;
for (long i = 0; i < opsOuter; i++)
{
for (long j = (i == 0 ? 1 : 0); j < opsInner; j++)
{
result = aggregate.Op(result, combine.Op(d1[ix1], d2[ix2]));
ix1 += innerStride1;
ix2 += innerStride2;
}
ix1 += outerStride1;
ix2 += outerStride2;
}
}
else
{
long n = in1.Shape.Dimensions.LongLength - 3;
long[] limits = in1.Shape.Dimensions.Where(x => n-- > 0).Select(x => x.Length).ToArray();
long[] counters = new long[limits.LongLength];
long totalOps = limits.LongLength == 0 ? 1 : limits.Aggregate <long>((a, b) => a * b);
//This chunck of variables are used to prevent repeated calculations of offsets
long dimIndex0 = 0 + limits.LongLength;
long dimIndex1 = 1 + limits.LongLength;
long dimIndex2 = 2 + limits.LongLength;
long opsOuter = in1.Shape.Dimensions[dimIndex0].Length;
long opsInner = in1.Shape.Dimensions[dimIndex1].Length;
long opsInnerInner = in1.Shape.Dimensions[dimIndex2].Length;
long outerStride1 = in1.Shape.Dimensions[dimIndex0].Stride;
long innerStride1 = in1.Shape.Dimensions[dimIndex1].Stride;
long innerInnerStride1 = in1.Shape.Dimensions[dimIndex2].Stride;
long outerStride2 = in2.Shape.Dimensions[dimIndex0].Stride;
long innerStride2 = in2.Shape.Dimensions[dimIndex1].Stride;
long innerInnerStride2 = in2.Shape.Dimensions[dimIndex2].Stride;
outerStride1 -= innerStride1 * in1.Shape.Dimensions[dimIndex1].Length;
innerStride1 -= innerInnerStride1 * in1.Shape.Dimensions[dimIndex2].Length;
outerStride2 -= innerStride2 * in2.Shape.Dimensions[dimIndex1].Length;
innerStride2 -= innerInnerStride2 * in2.Shape.Dimensions[dimIndex2].Length;
result = combine.Op(d1[in1.Shape[counters]], d2[in2.Shape[counters]]);
bool first = true;
for (long outer = 0; outer < totalOps; outer++)
{
//Get the array offset for the first element in the outer dimension
long ix1 = in1.Shape[counters];
long ix2 = in2.Shape[counters];
if (first)
{
ix1 += innerInnerStride1;
ix2 += innerInnerStride2;
}
for (long i = 0; i < opsOuter; i++)
{
for (long j = 0; j < opsInner; j++)
{
for (long k = (first ? 1 : 0); k < opsInnerInner; k++)
{
result = aggregate.Op(result, combine.Op(d1[ix1], d2[ix2]));
ix1 += innerInnerStride1;
ix2 += innerInnerStride2;
}
first = false;
ix1 += innerStride1;
ix2 += innerStride2;
}
ix1 += outerStride1;
ix2 += outerStride2;
}
if (counters.LongLength > 0)
{
//Basically a ripple carry adder
long p = counters.LongLength - 1;
while (++counters[p] == limits[p] && p > 0)
{
counters[p] = 0;
p--;
}
}
}
}
return(result);
}
/// <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;
}
}