/// <summary>
/// 行列の逆行列計算メソッド
/// </summary>
/// <param name="mat"></param>
/// <returns></returns>
public static Matrix Inverse(Matrix mat)
{
int n = mat.height;
Matrix ret = mat.Clone();
LUP lum = DecomposeLUP(mat);
if (lum == null)
{
throw new Exception("Unable to compute inverse");
}
double[] b = new double[n];
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; j++)
{
if (i == lum.perm[j])
{
b[j] = 1.0;
}
else
{
b[j] = 0.0;
}
}
double[] x = HelperSolve(lum.mat, b);
for (int j = 0; j < n; ++j)
{
ret[j][i] = x[j];
}
}
return(ret);
}
/// <summary>
/// 行列の行列式計算メソッド
/// </summary>
/// <param name="mat"></param>
/// <returns></returns>
public static double Det(Matrix mat)
{
LUP lum = DecomposeLUP(mat);
if (lum == null)
{
throw new Exception("Unable to compute MatrixDeterminant");
}
double ret = lum.toggle;
Parallel.For(0, lum.mat.height, i => { ret *= lum.mat[i][i]; });
return(ret);
}
/// <summary>
/// 行列のLUP分解メソッド
/// </summary>
/// <param name="mat"></param>
/// <returns></returns>
private static LUP DecomposeLUP(Matrix mat)
{
LUP ret = new LUP();
ret.toggle = 1;
ret.mat = mat.Clone();
ret.perm = new int[mat.height];
Parallel.For(0, mat.height, i => { ret.perm[i] = i; });
for (int j = 0; j < mat.height - 1; j++)
{
double colMax = Math.Abs(ret.mat[j][j]); // largest val in col j
int pRow = j;
for (int i = j + 1; i < mat.height; ++i)
{
if (ret.mat[i][j] > colMax)
{
colMax = ret.mat[i][j];
pRow = i;
}
}
if (pRow != j) // swap rows
{
double[] rowPtr = ret.mat[pRow];
ret.mat[pRow] = ret.mat[j];
ret.mat[j] = rowPtr;
int tmp = ret.perm[pRow]; // and swap perm info
ret.perm[pRow] = ret.perm[j];
ret.perm[j] = tmp;
ret.toggle = -ret.toggle; // row-swap toggle
}
if (Math.Abs(ret.mat[j][j]) < 1.0E-20)
{
return(null); // consider a throw
}
for (int i = j + 1; i < mat.height; ++i)
{
ret.mat[i][j] /= ret.mat[j][j];
for (int k = j + 1; k < mat.height; k++)
{
ret.mat[i][k] -= ret.mat[i][j] * ret.mat[j][k];
}
}
}
return(ret);
}
