public static ContinuousDistribution[,] Inverse(ContinuousDistribution[,] xx)
{
if (xx.GetLength(0) == 2 && xx.GetLength(1) == 2) {
ContinuousDistribution det = RandomMatrix.Determinant(xx);
ContinuousDistribution[,] yy = new ContinuousDistribution[2, 2];
yy[0, 0] = xx[1, 1].DividedBy(det);
yy[0, 1] = xx[0, 1].Negate().DividedBy(det);
yy[1, 0] = xx[1, 0].Negate().DividedBy(det);
yy[1, 1] = xx[0, 0].DividedBy(det);
return yy;
}
if (xx.GetLength(0) == 3 && xx.GetLength(1) == 3) {
// from http://www.dr-lex.be/random/matrix_inv.html
ContinuousDistribution det = RandomMatrix.Determinant(xx);
ContinuousDistribution[,] yy = new ContinuousDistribution[3, 3];
yy[0, 0] = xx[2,2].Times(xx[1,1]).Minus(xx[2,1].Times(xx[1,2])).DividedBy(det);
yy[0, 1] = xx[2,2].Times(xx[0,1]).Minus(xx[2,1].Times(xx[0,2])).Negate().DividedBy(det);
yy[0, 2] = xx[1,2].Times(xx[0,1]).Minus(xx[1,1].Times(xx[0,2])).DividedBy(det);
yy[1, 0] = xx[2,2].Times(xx[1,0]).Minus(xx[2,0].Times(xx[1,2])).Negate().DividedBy(det);
yy[1, 1] = xx[2,2].Times(xx[0,0]).Minus(xx[2,0].Times(xx[0,2])).DividedBy(det);
yy[1, 2] = xx[1,2].Times(xx[0,0]).Minus(xx[1,0].Times(xx[0,2])).Negate().DividedBy(det);
yy[2, 0] = xx[2,1].Times(xx[1,0]).Minus(xx[2,0].Times(xx[1,1])).DividedBy(det);
yy[2, 1] = xx[2,1].Times(xx[0,0]).Minus(xx[2,0].Times(xx[0,1])).Negate().DividedBy(det);
yy[2, 2] = xx[1,1].Times(xx[0,0]).Minus(xx[1,0].Times(xx[0,1])).DividedBy(det);
return yy;
}
throw new ArgumentException("Unknown matrix dimensions");
}
public static ContinuousDistribution[,] Multiply(ContinuousDistribution[,] xx, ContinuousDistribution[,] yy)
{
if (xx.GetLength(1) != yy.GetLength(0))
throw new ArgumentException("Inside dimensions must match");
ContinuousDistribution[,] zz = new ContinuousDistribution[xx.GetLength(0), yy.GetLength(1)];
for (int rr = 0; rr < xx.GetLength(0); rr++)
for (int cc = 0; cc < yy.GetLength(1); cc++) {
ContinuousDistribution sum = new FlatDistribution();
for (int ii = 0; ii < xx.GetLength(1); ii++)
sum = sum.Plus(xx[rr, ii].Times(yy[ii, cc]));
zz[rr, cc] = sum;
}
return zz;
}
public static ContinuousDistribution Determinant(ContinuousDistribution[,] xx)
{
if (xx.GetLength(0) == 1 && xx.GetLength(1) == 1)
return xx[0, 0];
if (xx.GetLength(0) == 2 && xx.GetLength(1) == 2)
return xx[0, 0].Times(xx[1, 1]).Minus(xx[0, 1].Times(xx[1, 0]));
if (xx.GetLength(0) == 3 && xx.GetLength(1) == 3) {
ContinuousDistribution one = xx[0,0].Times(xx[2,2].Times(xx[1,1]).Minus(xx[2,1].Times(xx[1,2])));
ContinuousDistribution two = xx[1,0].Times(xx[2,2].Times(xx[0,1]).Minus(xx[2,1].Times(xx[0,2])));
ContinuousDistribution three = xx[2,0].Times(xx[1,2].Times(xx[0,1]).Minus(xx[1,1].Times(xx[0,2])));
return one.Minus(two).Plus(three);
}
throw new ArgumentException("Unknown matrix dimensions");
}
public static ContinuousDistribution[,] Transpose(ContinuousDistribution[,] xx)
{
ContinuousDistribution[,] yy = new ContinuousDistribution[xx.GetLength(1), xx.GetLength(0)];
for (int rr = 0; rr < xx.GetLength(0); rr++)
for (int cc = 0; cc < xx.GetLength(1); cc++)
yy[cc, rr] = xx[rr, cc];
return yy;
}