public SquareDecimalMatrix ToThePower(long e)
{
if (e == 0)
{
return(Identity(NumberOfColumns));
}
SquareDecimalMatrix result = null;
SquareDecimalMatrix currentPower = this;
while (e > 0)
{
if (e % 2 == 1)
{
if (result == null)
{
result = currentPower;
}
else
{
result = (SquareDecimalMatrix)result.Times(currentPower);
}
}
currentPower = (SquareDecimalMatrix)currentPower.Times(currentPower);
e /= 2;
}
return(result);
}
public static SquareDecimalMatrix Identity(int size)
{
var result = new SquareDecimalMatrix(size);
for (int i = 0; i < size; i++)
{
result[i, i] = 1;
}
return(result);
}
public SquareDecimalMatrix Inverse()
{
IList <IList <decimal> > oldMatrix = new List <IList <decimal> >();
IList <IList <decimal> > newMatrix = new List <IList <decimal> >();
for (int r = 0; r < NumberOfColumns; r++)
{
IList <decimal> oldRow = new List <decimal>();
IList <decimal> newRow = new List <decimal>();
for (int c = 0; c < NumberOfColumns; c++)
{
newRow.Add(c == r ? 1 : 0);
oldRow.Add(this[r, c]);
}
oldMatrix.Add(oldRow);
newMatrix.Add(newRow);
}
for (int i = 0; i < NumberOfColumns; i++)
{
int j = i;
while (oldMatrix[i][i] == 0)
{
j++;
}
if (j != i)
{
MoveRow(j, i);
}
ScalarMultiplyRow(i, 1 / oldMatrix[i][i]);
for (int k = i + 1; k < NumberOfColumns; k++)
{
if (oldMatrix[k][i] != 0)
{
AddNthRowKTimesToMthRow(i, k, -oldMatrix[k][i]);
}
}
}
for (int i = NumberOfColumns - 1; i >= 0; i--)
{
for (int k = i - 1; k >= 0; k--)
{
if (oldMatrix[k][i] != 0)
{
AddNthRowKTimesToMthRow(i, k, -oldMatrix[k][i]);
}
}
}
var result = new SquareDecimalMatrix(NumberOfColumns);
for (int r = 0; r < NumberOfColumns; r++)
{
for (int c = 0; c < NumberOfColumns; c++)
{
result[r, c] = newMatrix[r][c];
}
}
return(result);
void MoveRow(int from, int to)
{
var oldRowToMove = oldMatrix[from];
oldMatrix.Insert(to, oldRowToMove);
oldMatrix.RemoveAt(from + (to <= from ? 1 : 0));
var newRoTowMove = newMatrix[from];
newMatrix.Insert(to, newRoTowMove);
newMatrix.RemoveAt(from + (to <= from ? 1 : 0));
}
void AddNthRowKTimesToMthRow(int n, int m, decimal k)
{
var oldNthRow = oldMatrix[n];
var oldMthRow = oldMatrix[m];
var newNthRow = newMatrix[n];
var newMthRow = newMatrix[m];
for (int i = 0; i < NumberOfColumns; i++)
{
oldMthRow[i] += k * oldNthRow[i];
newMthRow[i] += k * newNthRow[i];
}
}
void ScalarMultiplyRow(int n, decimal k)
{
var oldRow = oldMatrix[n];
var newRow = newMatrix[n];
for (int c = 0; c < NumberOfColumns; c++)
{
oldRow[c] *= k;
newRow[c] *= k;
}
}
}
