/// <summary>
/// [i, j, k...]th element of the resulting tensor is
/// operation(a[i, j, k...], b[i, j, k...])
/// </summary>
public static GenTensor <T> Zip(GenTensor <T> a,
GenTensor <T> b, Func <T, T, T> operation)
{
#if ALLOW_EXCEPTIONS
if (a.Shape != b.Shape)
{
throw new InvalidShapeException("Arguments should be of the same shape");
}
#endif
var res = new GenTensor <T>(a.Shape);
if (res.Shape.shape.Length == 1)
{
for (int x = 0; x < res.Shape.shape[0]; x++)
{
res.Data[x] = ConstantsAndFunctions <T> .Forward(
operation(a.GetValueNoCheck(x), b.GetValueNoCheck(x)));
}
}
else if (res.Shape.shape.Length == 2)
{
for (int x = 0; x < res.Shape.shape[0]; x++)
{
for (int y = 0; y < res.Shape.shape[1]; y++)
{
res.Data[x * res.Blocks[0] + y] = ConstantsAndFunctions <T> .Forward(
operation(a.GetValueNoCheck(x, y), b.GetValueNoCheck(x, y)));
}
}
}
else if (res.Shape.shape.Length == 3)
{
for (int x = 0; x < res.Shape.shape[0]; x++)
{
for (int y = 0; y < res.Shape.shape[1]; y++)
{
for (int z = 0; z < res.Shape.shape[2]; z++)
{
res.Data[x * res.Blocks[0] + y * res.Blocks[1] + z] = ConstantsAndFunctions <T> .Forward(
operation(a.GetValueNoCheck(x, y, z), b.GetValueNoCheck(x, y, z)));
}
}
}
}
else
{
foreach (var index in res.IterateOverElements())
{
res.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(
operation(a.GetValueNoCheck(index), b.GetValueNoCheck(index))), index);
}
}
return(res);
}
/// <summary>
/// Finds matrix multiplication result
/// a and b are matrices
/// a.Shape[1] should be equal to b.Shape[0]
/// the resulting matrix is [a.Shape[0] x b.Shape[1]] shape
///
/// O(N^3)
/// </summary>
public static GenTensor <T> MatrixMultiply(GenTensor <T> a,
GenTensor <T> b)
{
#if ALLOW_EXCEPTIONS
if (!a.IsMatrix || !b.IsMatrix)
{
throw new InvalidShapeException($"Both {nameof(a)} and {nameof(b)} should be matrices");
}
if (a.Shape[1] != b.Shape[0])
{
throw new InvalidShapeException($"{nameof(a)}'s height must be equal to {nameof(b)}'s width");
}
#endif
var width = a.Shape[0];
var height = b.Shape[1];
var row = a.Shape[1];
var res = CreateMatrix(width, height);
for (int x = 0; x < width; x++)
{
for (int y = 0; y < height; y++)
{
var s = ConstantsAndFunctions <T> .CreateZero();
for (int i = 0; i < row; i++)
{
var v1 = a.GetValueNoCheck(x, i);
var v2 = b.GetValueNoCheck(i, y);
s = ConstantsAndFunctions <T> .Add(s, ConstantsAndFunctions <T> .Multiply(v1, v2));
}
res.SetValueNoCheck(s, x, y);
}
}
return(res);
}
private static void GetCofactor(GenTensor <T> a, GenTensor <T> temp, int rowId,
int colId, int diagLength)
{
int i = 0, j = 0;
for (int row = 0; row < diagLength; row++)
{
for (int col = 0; col < diagLength; col++)
{
if (row != rowId && col != colId)
{
temp.SetValueNoCheck(a.GetValueNoCheck(row, col), i, j++);
if (j == diagLength - 1)
{
j = 0;
i++;
}
}
}
}
}
public static GenTensor <T> Concat(GenTensor <T> a, GenTensor <T> b)
{
#if ALLOW_EXCEPTIONS
if (a.Shape.SubShape(1, 0) != b.Shape.SubShape(1, 0))
{
throw new InvalidShapeException("Excluding the first dimension, all others should match");
}
#endif
if (a.IsVector)
{
var resultingVector = GenTensor <T> .CreateVector(a.Shape.shape[0] + b.Shape.shape[0]);
for (int i = 0; i < a.Shape.shape[0]; i++)
{
resultingVector.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(a.GetValueNoCheck(i)), i);
}
for (int i = 0; i < b.Shape.shape[0]; i++)
{
resultingVector.SetValueNoCheck(ConstantsAndFunctions <T> .Forward(b.GetValueNoCheck(i)), i + a.Shape.shape[0]);
}
return(resultingVector);
}
else
{
var newShape = a.Shape.Copy();
newShape.shape[0] = a.Shape.shape[0] + b.Shape.shape[0];
var res = new GenTensor <T>(newShape);
for (int i = 0; i < a.Shape.shape[0]; i++)
{
res.SetSubtensor(a.GetSubtensor(i), i);
}
for (int i = 0; i < b.Shape.shape[0]; i++)
{
res.SetSubtensor(b.GetSubtensor(i), i + a.Shape.shape[0]);
}
return(res);
}
}
/// <summary>
/// Finds the scalar product of two vectors
///
/// O(N)
/// </summary>
public static T VectorDotProduct(GenTensor <T> a,
GenTensor <T> b)
{
#if ALLOW_EXCEPTIONS
if (!a.IsVector || !b.IsVector)
{
throw new InvalidShapeException($"{nameof(a)} and {nameof(b)} should be vectors");
}
if (a.Shape[0] != b.Shape[0])
{
throw new InvalidShapeException($"{nameof(a)}'s length should be the same as {nameof(b)}'s");
}
#endif
var res = ConstantsAndFunctions <T> .CreateZero();
for (int i = 0; i < a.Shape[0]; i++)
{
res = ConstantsAndFunctions <T> .Add(res,
ConstantsAndFunctions <T> .Multiply(a.GetValueNoCheck(i), b.GetValueNoCheck(i)));
}
return(res);
}
public bool Equals(GenTensor <T> obj)
{
if (obj.Shape != Shape)
{
return(false);
}
foreach (var(index, _) in obj.Iterate())
{
if (!ConstantsAndFunctions <T> .AreEqual(this.GetValueNoCheck(index), obj.GetValueNoCheck(index)))
{
return(false);
}
}
return(true);
}
