public RMatrix Clone()
{
RMatrix m = new RMatrix(matrix);
m.matrix = (double[, ])matrix.Clone();
return(m);
}
public RMatrix GetTranspose()
{
RMatrix m = this;
m.Transpose();
return(m);
}
public static RMatrix Minor(RMatrix mat, int row, int col)
{
RMatrix mm = new RMatrix(mat.GetnRows - 1, mat.GetnCols - 1);
int ii = 0, jj = 0;
for (int i = 0; i < mat.GetnRows; i++)
{
if (i == row)
{
continue;
}
jj = 0;
for (int j = 0; j < mat.GetnCols; j++)
{
if (j == col)
{
continue;
}
mm[ii, jj] = mat[i, j];
jj++;
}
ii++;
}
return(mm);
}
public static RMatrix operator *(RMatrix m1, RMatrix m2)
{
if (m1.GetnCols != m2.GetnRows)
{
throw new Exception("The numbers of columns of the" +
" first matrix must be equal to the number of " +
" rows of the second matrix!");
}
double tmp;
RMatrix result = new RMatrix(m1.GetnRows, m2.GetnCols);
for (int i = 0; i < m1.GetnRows; i++)
{
for (int j = 0; j < m2.GetnCols; j++)
{
tmp = result[i, j];
for (int k = 0; k < result.GetnRows; k++)
{
tmp += m1[i, k] * m2[k, j];
}
result[i, j] = tmp;
}
}
return(result);
}
public static RMatrix Inverse(RMatrix mat)
{
if (Determinant(mat) == 0)
{
throw new Exception("Cannot inverse a matrix with a zero determinant!");
}
return(Adjoint(mat) / Determinant(mat));
}
public static bool CompareDimension(RMatrix m1, RMatrix m2)
{
if (m1.GetnRows == m2.GetnRows && m1.GetnCols == m2.GetnCols)
{
return(true);
}
else
{
return(false);
}
}
public void Transpose()
{
RMatrix m = new RMatrix(nCols, nRows);
for (int i = 0; i < nRows; i++)
{
for (int j = 0; j < nCols; j++)
{
m[j, i] = matrix[i, j];
}
}
this = m;
}
public static RMatrix operator /(double d, RMatrix m)
{
RMatrix result = new RMatrix(m.GetnRows, m.GetnCols);
for (int i = 0; i < m.GetnRows; i++)
{
for (int j = 0; j < m.GetnCols; j++)
{
result[i, j] = m[i, j] / d;
}
}
return(result);
}
public RMatrix IdentityMatrix()
{
RMatrix m = new RMatrix(nRows, nCols);
for (int i = 0; i < nRows; i++)
{
for (int j = 0; j < nCols; j++)
{
if (i == j)
{
m[i, j] = 1;
}
}
}
return(m);
}
public static RMatrix Adjoint(RMatrix mat)
{
if (!mat.IsSquared())
{
throw new Exception("The matrix must be squared!");
}
RMatrix ma = new RMatrix(mat.GetnRows, mat.GetnCols);
for (int i = 0; i < mat.GetnRows; i++)
{
for (int j = 0; j < mat.GetnCols; j++)
{
ma[i, j] = Math.Pow(-1, i + j) * (Determinant(Minor(mat, i, j)));
}
}
return(ma.GetTranspose());
}
public static RMatrix Transform(RVector v1, RVector v2)
{
if (v1.GetVectorSize != v2.GetVectorSize)
{
throw new Exception("The vectors must have the same ndim!");
}
RMatrix result = new RMatrix(v1.GetVectorSize, v1.GetVectorSize);
for (int i = 0; i < v1.GetVectorSize; i++)
{
for (int j = 0; j < v1.GetVectorSize; j++)
{
result[j, i] = v1[i] * v2[j];
}
}
return(result);
}
public static RMatrix operator -(RMatrix m1, RMatrix m2)
{
if (!RMatrix.CompareDimension(m1, m2))
{
throw new Exception("The dimensions of two matrices must be the same!");
}
RMatrix result = new RMatrix(m1.GetnRows, m1.GetnCols);
for (int i = 0; i < m1.GetnRows; i++)
{
for (int j = 0; j < m1.GetnCols; j++)
{
result[i, j] = m1[i, j] - m2[i, j];
}
}
return(result);
}
public static double Determinant(RMatrix mat)
{
double result = 0.0;
if (!mat.IsSquared())
{
throw new Exception("The matrix must be squared!");
}
if (mat.GetnRows == 1)
{
result = mat[0, 0];
}
else
{
for (int i = 0; i < mat.GetnRows; i++)
{
result += Math.Pow(-1, i) * mat[0, i] *
Determinant(RMatrix.Minor(mat, 0, i));
}
}
return(result);
}
public static RVector Transform(RVector vec, RMatrix mat)
{
RVector result = new RVector(vec.GetVectorSize);
if (!mat.IsSquared())
{
throw new Exception("The matrix must be squared!");
}
if (mat.GetnRows != vec.GetVectorSize)
{
throw new Exception("The ndim of the vector must be equal"
+ " to the number of rows of the matrix!");
}
for (int i = 0; i < mat.GetnRows; i++)
{
result[i] = 0.0;
for (int j = 0; j < mat.GetnCols; j++)
{
result[i] += vec[j] * mat[j, i];
}
}
return(result);
}
public RMatrix(RMatrix m)
{
nRows = m.GetnRows;
nCols = m.GetnCols;
matrix = m.matrix;
}
public bool Equals(RMatrix m)
{
return(matrix == m.matrix);
}
