public void ComputeLU(Matrix A)
{
_N = A.RowCount;
_LU = (double[])A.Data.Clone();
_IPIV = new int[_N];
_Info = 0;
DGETRF _dgetrf = new DGETRF();
_dgetrf.Run(_N, _N, ref _LU, 0, _N, ref _IPIV, 0, ref _Info);
}
/// <summary>
/// Computes the LU and caches the results locally.
/// Either the native .NET library or Intel MKL is used.
/// </summary>
/// <param name="A"></param>
public void ComputeLU(Matrix A)
{
_N = A.RowCount;
_LU = (double[])A.Data.Clone();
_IPIV = new int[_N];
_Info = 0;
if (UseIntelMathKernel)
{
IntelMathKernel.dgetrf(ref _N, ref _N, _LU, ref _N, _IPIV, ref _Info);
}
else
{
DGETRF _dgetrf = new DGETRF();
_dgetrf.Run(_N, _N, ref _LU, 0, _N, ref _IPIV, 0, ref _Info);
}
}
/// <summary>
/// Calculates the determinant of the matrix.
/// </summary>
/// <returns>The determinant of the matrix.</returns>
public double Determinant()
{
double det = 1.0;
if (this.IsSquare != true)
{
throw new System.ArgumentException("This is not a square matrix.");
}
if (BaseMatrix._dgetrf == null)
{
BaseMatrix._dgetrf = new DGETRF();
}
Matrix clonMatrix = new Matrix(this.RowCount, this.ColumnCount, this.Data);
double[] clonData = clonMatrix.Data;
int[] ipiv = new int[this.RowCount];
int Info = 0;
BaseMatrix._dgetrf.Run(this.RowCount, this.ColumnCount, ref clonData, 0, this.RowCount, ref ipiv, 0, ref Info);
#region Error
// <param name="INFO">
// (output) INTEGER
//= 0: successful exit
// .LT. 0: if INFO = -i, the i-th argument had an illegal value
// .GT. 0: if INFO = i, U(i,i) is exactly zero. The factorization
// has been completed, but the factor U is exactly
// singular, and division by zero will occur if it is used
// to solve a system of equations.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
//else if (Info > 0)
//{
// string infoSTg = Math.Abs(Info).ToString();
// throw new Exception("The matrix is numerically singular..");
//}
#endregion
//The LU factorization yields three matrices, the product of which is the original
//complex matrix. Therefore the determinat is the product of the three determinants
//of P, L and U. The determinant of the triangular matrices L and U is the product
//of the elements on the diagonal - as for any triangular matrix (for L this is 1
//as all elements of the diagonal are one.) The determinant of P is either +1 or -1
//depending of whether the number of row permutations is even or odd.
//Thank you very much for your answer. It seems to be that your message got tructated somehow, but I think I got the point.
//I also did some searching on the web and found the following two pieces of code which both claim to calculate the determinant of a square matrix.
//============================================
//call dgetrf(n,n,a,n,piv,info)
//det = 0d0
//if (info.ne.0) then
//return
//endif
//det = 1d0
//do 10,i=1,n
//if (piv(i).ne.i) then
//det = -det * a(i,i)
//else
//det = det * a(i,i)
//endif
//10 continue
//end
for (int i = 0; i < this._RowCount; i++)
{
if (ipiv[i] != (i + 1)) // i+1 debido a que aqui la base es 0 y en fortran es 1
{
det *= -clonMatrix[i, i];
}
else
{
det *= clonMatrix[i, i];
}
}
return(det);
}
/// <summary>
/// Calculates the inverse of the matrix.
/// </summary>
/// <returns>The inverse of the matrix.</returns>
public Matrix Inverse()
{
if (this.IsSquare != true)
{
throw new System.ArgumentException("This is not a square matrix.");
}
if (BaseMatrix._dgetrf == null)
{
BaseMatrix._dgetrf = new DGETRF();
}
if (BaseMatrix._dgetri == null)
{
BaseMatrix._dgetri = new DGETRI();
}
Matrix inverseMatrix = new Matrix(this.RowCount, this.ColumnCount, this.Data);
double[] inverseData = inverseMatrix.Data;
int[] ipiv = new int[this.RowCount];
int Info = 0;
double[] Work = new double[1];
int LWork = -1;
//Calculamos LWORK
BaseMatrix._dgetri.Run(this.RowCount, ref inverseData, 0, this.RowCount, ipiv, 0, ref Work, 0, LWork, ref Info);
LWork = Convert.ToInt32(Work[0]);
if (LWork > 0)
{
Work = new double[LWork];
BaseMatrix._dgetrf.Run(this.RowCount, this.ColumnCount, ref inverseData, 0, this.RowCount, ref ipiv, 0, ref Info);
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, U(i,i) is exactly zero. The factorization
/// has been completed, but the factor U is exactly
/// singular, and division by zero will occur if it is used
/// to solve a system of equations.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The matrix is numerically singular..");
}
#endregion
BaseMatrix._dgetri.Run(this.RowCount, ref inverseData, 0, this.RowCount, ipiv, 0, ref Work, 0, LWork, ref Info);
}
else
{
//Error
}
#region Error
/// (output) INTEGER
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, U(i,i) is exactly zero; the matrix is
/// singular and its inverse could not be computed.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The matrix is numerically singular..");
}
#endregion
return(inverseMatrix);
}
public static bool Start()
{
Console.WriteLine("Testing LU decomposition");
int n = 3;
int info = 0;
int[] ipiv = new int[3];
Matrix Mtx = new Matrix(3);
Mtx[0, 0] = 1;
Mtx[0, 1] = 9;
Mtx[0, 2] = 5;
Mtx[1, 0] = 1;
Mtx[1, 1] = 3;
Mtx[1, 2] = 4;
Mtx[2, 0] = 5;
Mtx[2, 1] = 6;
Mtx[2, 2] = 7;
try
{
// Case 1
Console.WriteLine("Computing LU with MKL dgetrf...");
double[] A = (double[])Mtx.Data.Clone();
IntelMathKernel.dgetrf(ref n, ref n, A, ref n, ipiv, ref info);
// Case 2
Console.WriteLine("Computing LU with with .NET dgetrf...");
double[] B = (double[])Mtx.Data.Clone();
DGETRF _dgetrf = new DGETRF();
_dgetrf.Run(n, n, ref B, 0, n, ref ipiv, 0, ref info);
Console.WriteLine("Comparing results...");
for (int i = 0; i < 5; i++)
{
if (A[i] != B[i] || (B[i] > 0.0 & (A[i] - B[i]) / B[i] > 1E-5))
{
Console.WriteLine("TEST NOT PASSED");
return(false);
}
}
// Case 3
Console.WriteLine("Solving linear equations with MKL dgetrs...");
info = 0;
int nrhs = 1;
double[] R = new double[3];
R[0] = 1;
R[1] = 2;
R[2] = 5;
char[] trans = "No transponse".ToCharArray();
IntelMathKernel.dgetrs(trans, ref n, ref nrhs, A, ref n, ipiv, R, ref n, ref info);
Console.WriteLine("TEST PASSED");
return(true);
}
catch
{
Console.WriteLine("TEST NOT PASSED");
return(false);
}
}