public static GenTensor <T, TWrapper> MatrixPower(GenTensor <T, TWrapper> m, int power, Threading threading)
{
#if ALLOW_EXCEPTIONS
if (!m.IsSquareMatrix)
{
throw new InvalidShapeException("Square matrix required");
}
#endif
if (power == 0)
{
return(Constructors <T, TWrapper> .CreateIdentityMatrix(m.Shape.shape[0]));
}
if (power < 0)
{
m = m.Forward();
m.InvertMatrix();
power *= -1;
}
if (power == 1)
{
return(m);
}
if (power == 2)
{
return(MatrixMultiplication <T, TWrapper> .Multiply(m, m, threading));
}
var half = power / 2;
var m1 = MatrixPower(m, half, threading);
var dotted = MatrixMultiplication <T, TWrapper> .Multiply(m1, m1, threading);
if (power % 2 == 0)
{
return(dotted);
}
else
{
return(MatrixMultiplication <T, TWrapper> .Multiply(dotted, m, threading));
}
}
public static GenTensor <T, TWrapper> PiecewiseSubtract(GenTensor <T, TWrapper> a,
T b, Threading threading)
=> Constructors <T, TWrapper> .CreateTensor(a.Shape, ind =>
default(TWrapper).Subtract(a[ind], b), threading);
public static GenTensor <T, TWrapper> PiecewiseSubtract(
T a, GenTensor <T, TWrapper> b, Threading threading)
=> Constructors <T, TWrapper> .CreateTensor(b.Shape, ind =>
default(TWrapper).Subtract(a, b[ind]), threading);
internal static GenTensor <T, TWrapper> Multiply(GenTensor <T, TWrapper> a,
GenTensor <T, TWrapper> b, Threading threading = Threading.Single)
{
#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 = Constructors <T, TWrapper> .CreateMatrix(width, height);
var parallel = threading == Threading.Multi || (threading == Threading.Auto && a.Volume > 125);
var aBlocks0 = a.blocks[0];
var aBlocks1 = a.blocks[1];
var bBlocks0 = b.blocks[0];
var bBlocks1 = b.blocks[1];
var aLinoffset = a.LinOffset;
var bLinoffset = b.LinOffset;
if (!parallel)
{
for (int x = 0; x < width; x++)
{
for (int y = 0; y < height; y++)
{
var s = default(TWrapper).CreateZero();
for (int i = 0; i < row; i++)
{
var v1 = a.data[x * aBlocks0 + i * aBlocks1 + aLinoffset];
var v2 = b.data[i * bBlocks0 + y * bBlocks1 + bLinoffset];
s = default(TWrapper).Add(s, default(TWrapper).Multiply(v1, v2));
}
res.data[x * height + y] = s;
}
}
}
else
{
Parallel.For(0, width, x =>
{
for (int y = 0; y < height; y++)
{
var s = default(TWrapper).CreateZero();
for (int i = 0; i < row; i++)
{
var v1 = a.data[x * aBlocks0 + i * aBlocks1 + aLinoffset];
var v2 = b.data[i * bBlocks0 + y * bBlocks1 + bLinoffset];
s = default(TWrapper).Add(s, default(TWrapper).Multiply(v1, v2));
}
res.data[x * height + y] = s;
}
});
}
return(res);
}