/// <summary>LU Decomposition</summary>
/// <param name="A"> Rectangular matrix
/// </param>
/// <returns> Structure to access L, U and piv.
/// </returns>
public LUDecomposition(GeneralMatrix A)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = A.ArrayCopy;
m = A.RowDimension;
n = A.ColumnDimension;
piv = new int[m];
for (int i = 0; i < m; i++)
{
piv[i] = i;
}
pivsign = 1;
double[] LUrowi;
double[] LUcolj = new double[m];
// Outer loop.
for (int j = 0; j < n; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++)
{
LUcolj[i] = LU[i][j];
}
// Apply previous transformations.
for (int i = 0; i < m; i++)
{
LUrowi = LU[i];
// Most of the time is spent in the following dot product.
int kmax = System.Math.Min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++)
{
s += LUrowi[k] * LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++)
{
if (System.Math.Abs(LUcolj[i]) > System.Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < n; k++)
{
double t = LU[p][k]; LU[p][k] = LU[j][k]; LU[j][k] = t;
}
int k2 = piv[p]; piv[p] = piv[j]; piv[j] = k2;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m & LU[j][j] != 0.0)
{
for (int i = j + 1; i < m; i++)
{
LU[i][j] /= LU[j][j];
}
}
}
}
/// <summary>Solve X*A = B, which is also A'*X' = B'</summary>
/// <param name="B"> right hand side
/// </param>
/// <returns> solution if A is square, least squares solution otherwise.
/// </returns>
public virtual GeneralMatrix SolveTranspose(GeneralMatrix B)
{
return(Transpose().Solve(B.Transpose()));
}
/// <summary>Check for symmetry, then construct the eigenvalue decomposition</summary>
/// <param name="Arg"> Square matrix
/// </param>
/// <returns> Structure to access D and V.
/// </returns>
public EigenvalueDecomposition(GeneralMatrix Arg)
{
double[][] A = Arg.Array;
n = Arg.ColumnDimension;
V = new double[n][];
for (int i = 0; i < n; i++)
{
V[i] = new double[n];
}
d = new double[n];
e = new double[n];
issymmetric = true;
for (int j = 0; (j < n) & issymmetric; j++)
{
for (int i = 0; (i < n) & issymmetric; i++)
{
issymmetric = (A[i][j] == A[j][i]);
}
}
if (issymmetric)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
V[i][j] = A[i][j];
}
}
// Tridiagonalize.
tred2();
// Diagonalize.
tql2();
}
else
{
H = new double[n][];
for (int i2 = 0; i2 < n; i2++)
{
H[i2] = new double[n];
}
ort = new double[n];
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
H[i][j] = A[i][j];
}
}
// Reduce to Hessenberg form.
orthes();
// Reduce Hessenberg to real Schur form.
hqr2();
}
}
/// <summary>Solve A*X = B</summary>
/// <param name="B"> right hand side
/// </param>
/// <returns> solution if A is square, least squares solution otherwise
/// </returns>
public virtual GeneralMatrix Solve(GeneralMatrix B)
{
return(m == n ? (new LUDecomposition(this)).Solve(B):(new QRDecomposition(this)).Solve(B));
}