public static MatrixR Minor(MatrixR m, int row, int col)
{
MatrixR mm = new MatrixR(m.GetRows() - 1, m.GetCols() - 1);
int ii = 0, jj = 0;
for (int i = 0; i < m.GetRows(); i++)
{
if (i == row)
{
continue;
}
jj = 0;
for (int j = 0; j < m.GetCols(); j++)
{
if (j == col)
{
continue;
}
mm[ii, jj] = m[i, j];
jj++;
}
ii++;
}
return(mm);
}
public static VectorR Transform(VectorR v, MatrixR m)
{
VectorR result = new VectorR(v.GetSize());
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
if (m.GetRows() != v.GetSize())
{
throw new ArgumentOutOfRangeException(
"Size", v.GetSize(), "The size of the vector must be equal"
+ "to the number of rows of the matrix!");
}
for (int i = 0; i < m.GetRows(); i++)
{
result[i] = 0.0;
for (int j = 0; j < m.GetCols(); j++)
{
result[i] += v[j] * m[j, i];
}
}
return(result);
}
private void LUDecompose(MatrixR m)
{
int n = m.GetRows();
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
double d = m[i, j];
for (int k = 0; k < Math.Min(i, j); k++)
{
d -= m[i, k] * m[k, j];
}
if (j > i)
{
double dd = m[i, i];
if (Math.Abs(d) < epsilon)
{
throw new ArgumentException("Diagonal element is too small!");
}
d /= dd;
}
m[i, j] = d;
}
}
}
public static MatrixR Adjoint(MatrixR m)
{
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
MatrixR ma = new MatrixR(m.GetRows(), m.GetCols());
for (int i = 0; i < m.GetRows(); i++)
{
for (int j = 0; j < m.GetCols(); j++)
{
ma[i, j] = Math.Pow(-1, i + j) * (Determinant(Minor(m, i, j)));
}
}
return(ma.GetTranspose());
}
public static bool CompareDimension(MatrixR m1, MatrixR m2)
{
if (m1.GetRows() == m2.GetRows() && m1.GetCols() == m2.GetCols())
{
return(true);
}
else
{
return(false);
}
}
public static double Determinant(MatrixR m)
{
double result = 0.0;
if (!m.IsSquared())
{
throw new ArgumentOutOfRangeException(
"Dimension", m.GetRows(), "The matrix must be squared!");
}
if (m.GetRows() == 1)
{
result = m[0, 0];
}
else
{
for (int i = 0; i < m.GetRows(); i++)
{
result += Math.Pow(-1, i) * m[0, i] * Determinant(MatrixR.Minor(m, 0, i));
}
}
return(result);
}
public MatrixR LUInverse(MatrixR m)
{
int n = m.GetRows();
MatrixR u = m.Identity();
LUDecompose(m);
VectorR uv = new VectorR(n);
for (int i = 0; i < n; i++)
{
uv = u.GetRowVector(i);
LUSubstitute(m, uv);
u.ReplaceRow(uv, i);
}
MatrixR inv = u.GetTranspose();
return(inv);
}
private void Triangulate(MatrixR A, VectorR b)
{
int n = A.GetRows();
VectorR v = new VectorR(n);
for (int i = 0; i < n - 1; i++)
{
//double d = A[i, i];
double d = pivot(A, b, i);
if (Math.Abs(d) < epsilon)
{
throw new ArgumentException("Diagonal element is too small!");
}
for (int j = i + 1; j < n; j++)
{
double dd = A[j, i] / d;
for (int k = i + 1; k < n; k++)
{
A[j, k] -= dd * A[i, k];
}
b[j] -= dd * b[i];
}
}
}
public MatrixR(MatrixR m)
{
Rows = m.GetRows();
Cols = m.GetCols();
matrix = m.matrix;
}