/// <summary>
/// 指定された行列の逆行列を作成する．
/// </summary>
/// <param name="X">逆行列を求める行列（書き換えられることはない）</param>
/// <returns>Xの逆行列</returns>
public static Matrix Inverse(Matrix X)
{
MatrixChecker.IsSquare(X);
Solver solver = new Solver(X, (new Matrix(X.RowSize, X.ColumnSize)).Identity());
return(solver.X);
}
/// <summary>
/// 逆行列を返す．
/// </summary>
/// <param name="m">逆行列を求める行列（書き換えられることはない）</param>
/// <returns></returns>
public static Matrix Inverse(Matrix m)
{
MatrixChecker.IsSquare(m);
Solved result = Func.Solve(m, (new Matrix(m.RowSize, m.ColumnSize)).Identity());
return(result.X);
}
/// <summary>
/// 固有値分解
/// </summary>
/// <param name="x">正方行列</param>
/// <returns></returns>
public static Eigen Eigen(Matrix x)
{
MatrixChecker.IsSquare(x);
if (x.RowSize < 2)
{
throw new ArgumentException("Matrix size is less than 2.");
}
Matrix tmp = new Matrix(x);
Vector _reValues = new Vector();
Vector _imValues = new Vector();
double[][] r_vecs = null;
double[][] i_vecs = null;
krdlab.law.func.dgeev(tmp._body, tmp._rsize, tmp._csize,
ref _reValues._body, ref _imValues._body, ref r_vecs, ref i_vecs);
List <Vector> _reVectors = new List <Vector>();
List <Vector> _imVectors = new List <Vector>();
foreach (double[] vec in r_vecs)
{
_reVectors.Add(new Vector(vec));
}
foreach (double[] vec in i_vecs)
{
_imVectors.Add(new Vector(vec));
}
return(new Eigen(_reValues, _imValues, _reVectors, _imVectors));
}
/// <summary>
/// この行列を単位行列（I = diag(1,1,...,1)）にする．
/// </summary>
/// <returns></returns>
public Matrix Identity()
{
MatrixChecker.IsSquare(this);
this.Zero();
for (int i = 0; i < this.RowSize; ++i)
{
this[i, i] = 1;
}
return(this);
}
/// <summary>
/// AX = B を解く．
/// </summary>
/// <param name="a">[n, n] 行列</param>
/// <param name="b">[n, *] 行列</param>
/// <returns></returns>
public static Solved Solve(Matrix a, Matrix b)
{
MatrixChecker.IsSquare(a);
Matrix _a = new Matrix(a);
Matrix _b = new Matrix(b);
Matrix x = new Matrix();
krdlab.law.func.dgesv(ref x._body, ref x._rsize, ref x._csize,
_a._body, _a._rsize, _a._csize, _b._body, _b._rsize, _b._csize);
return(new Solved(x));
}
/// <summary>
/// 逆行列化する．
/// </summary>
/// <returns>逆行列化後の自身への参照</returns>
/// <exception cref="Exception.NotSquareMatrixException">
/// 正方行列でないときに throw される．
/// </exception>
public Matrix Inverse()
{
MatrixChecker.IsSquare(this);
Matrix A = new Matrix(this);
this.Identity();
clapack.Function.dgesv(ref this._body, ref this._rsize, ref this._csize,
A._body, A._rsize, A._csize, this._body, this._rsize, this._csize);
return(this);
}
/// <summary>
/// 逆行列化する．
/// </summary>
/// <returns>逆行列化後の自身への参照</returns>
/// <exception cref="System.ArgumentException">
/// 正方行列でないときに throw される．
/// </exception>
public Matrix Inverse()
{
MatrixChecker.IsSquare(this);
Matrix A = new Matrix(this);
this.Identity();
krdlab.law.func.dgesv(ref this._body, ref this._rsize, ref this._csize,
A._body, A._rsize, A._csize, this._body, this._rsize, this._csize);
return(this);
}