//operator *
public static SqrMatrix operator *(SqrMatrix left, SqrMatrix right)
{
if (left.N != right.N)
return null;
SqrMatrix c = new SqrMatrix(left.N);
for (int i = 0; i < left.N; i++)
{
for (int j = 0; j < left.N; j++)
{
c[i, j] = 0;
for (int k = 0; k < left.N; k++)
c[i, j] = c[i, j] + left[i, k] * right[k, j];
}
}
return c;
}
// operator -
public static SqrMatrix operator -(SqrMatrix left, SqrMatrix right)
{
if (left.N != right.N)
return null;
SqrMatrix c = new SqrMatrix(left.N);
for (int i = 0; i < left.N; i++)
for (int j = 0; j < left.N; j++)
c[i, j] = left[i, j] - right[i, j];
return c;
}
// removing complete to exp of 2
private static SqrMatrix deleteComplete(SqrMatrix mat,int origN)
{
SqrMatrix temp = new SqrMatrix(origN);
for (int j = 0; j < origN; j++)
for (int k = 0; k < origN; k++)
{
temp[j, k] = mat[j, k];
}
return temp;
}
// complete values to exp of 2
private static SqrMatrix completeMatrix(SqrMatrix mat)
{
int i=mat.N;
while (!IsPowerOfTwo((ulong)(i)))
{
i++;
}
SqrMatrix temp = new SqrMatrix(i);
for(int j=0;j<i;j++)
temp[j,j]=1;
for(int j=0;j<mat.N;j++)
for(int k=0;k<mat.N;k++)
{
temp[j, k] = mat[j, k];
}
return temp;
}
// make the invertion
public static SqrMatrix inv(SqrMatrix source)
{
if (!IsPowerOfTwo((ulong)source.N)) // if the dimension is not a pow of 2
{
SqrMatrix result1;
result1= inv( completeMatrix(source));
return deleteComplete(result1,source.N);
}
// source.print();
SqrMatrix result;
if (source.N == 1) // break condition when reaching 1
{
result = new SqrMatrix(1);
result[0,0]=1/source[0,0];
return result;
}
SqrMatrix A = new SqrMatrix(source.N / 2);
SqrMatrix B = new SqrMatrix(source.N / 2);
SqrMatrix C = new SqrMatrix(source.N / 2);
SqrMatrix D = new SqrMatrix(source.N / 2);
SqrMatrix iA,iB,iC,iD,invDCAB,invA;
for (int i = 0; i < A.N; i++) // putting values back to matrixes A,B,C,D
for (int j = 0; j < A.N; j++)
{
A[i, j] = source[i, j];
B[i, j] = source[i, j + B.N];
C[i, j] = source[i + C.N, j];
D[i, j] = source[i + D.N, j + D.N];
}
// according to the formula
invA = inv(A);
invDCAB = inv(D-C*invA*B);
iA = invA + invA*B*invDCAB*C*invA;
iB = -invA*B*invDCAB;
iC = -invDCAB*C*invA;
iD = invDCAB;
result = new SqrMatrix(source.N);
for(int i=0;i<iA.N;i++) // putting values to a bigger matrix
for(int j =0;j<iA.N;j++)
{
result[i,j]=iA[i,j];
result[i, j + iB.N] = iB[i, j];
result[i + iC.N, j] = iC[i, j];
result[i + iD.N, j + iD.N] = iD[i, j];
}
return result;
}
//unary operator -
public static SqrMatrix operator -(SqrMatrix left)
{
SqrMatrix c = new SqrMatrix(left.N);
for (int i = 0; i < left.N; i++)
for (int j = 0; j < left.N; j++)
c[i, j] = -left[i, j] ;
return c;
}