private Matrix Solve(Matrix Mat)
{
int nRows = Mat.RowCount;
int nCols = Mat.ColumnCount;
if (nRows != nCols)
{
throw new ArgumentOutOfRangeException("HessenBerg matrix must be derived from a square matrix");
}
Matrix H = Mat;
for (int k = 1; k < nCols - 1; k++)
{
double max = 0.0;
int i_max = 0;
for (int j = k; j < nCols; j++)
{
double t = H[j, k - 1];
if (Math.Abs(t) > Math.Abs(max))
{
max = t;
i_max = j;
}
}
if (max != 0.0)
{
if (i_max != k)
{
for (int j = k - 1; j < nCols; j++)
{
int u = i_max * nCols + j;
int v = k * nCols + j;
U.Swap(H.Values, u, v);
}
U.SwapColumn(H.Values, i_max, k, nRows, nCols);
}
for (i_max = k + 1; i_max < nCols; i_max++)
{
double t = H[i_max, k - 1] / max;
H[i_max, k - 1] = 0.0;
for (int j = k; j < nCols; j++)
{
H[i_max, j] -= t * H[k, j];
}
for (int j = 0; j < nCols; j++)
{
H[j, k] += t * H[j, i_max];
}
}
}
}
return(H);
}
private void Solve(Matrix mat)
{
int nRows = mat.RowCount;
int nCols = mat.ColumnCount;
if (nRows != nCols)
{
throw new ArgumentOutOfRangeException("LU Decomposition only support square matrix");
}
int n = nRows;
P = SpecialMatrices.Eye(n);
SwapTimes = 1;
for (int i = 0; i < n; i++) //pivot
{
double max = mat[i, i];
int max_row = i;
for (int j = i; j < n; j++)
{
if (mat[j, i] > max)
{
max = mat[j, i];
max_row = j;
}
}
if (i != max_row)
{
Utility.SwapRow(P.Values, i, max_row, nCols);
SwapTimes *= (-1);
}
}
L = new Matrix(n);
U = new Matrix(n);
Matrix A = P * mat;
for (int j = 0; j < n; j++)
{
L[j, j] = 1.0;
for (int i = 0; i <= j; i++)
{
double sum = 0.0;
for (int k = 0; k < i; k++)
{
sum += U[k, j] * L[i, k];
}
U[i, j] = A[i, j] - sum;
}
for (int i = j; i < n; i++)
{
double sum = 0.0;
for (int k = 0; k < j; k++)
{
sum += U[k, j] * L[i, k];
}
L[i, j] = (A[i, j] - sum) / U[j, j];
}
}
}
private void Solve(Matrix mat)
{
int nRows = mat.RowCount;
int nCols = mat.ColumnCount;
if (nRows < nCols)
{
throw new ArgumentOutOfRangeException("To make QR factorization,the rows count of matrix must greater than or equal columns count of it");
}
Q = SpecialMatrices.Eye(nRows, nRows);
R = mat;
int n = nCols;
if (nRows == nCols)
{
n--;
}
double d, w;
int p, u, v;
double alpha, t;
double[] q = Q.Values;
double[] r = R.Values;
for (int k = 0; k < n; k++)
{
d = 0.0;
u = k * nCols + k;
for (int i = k; i < nRows; i++)
{
v = i * nCols + k;
w = Math.Abs(r[v]);
if (w > d)
{
d = w;
}
}
alpha = 0.0;
for (int i = k; i < nRows; i++)
{
v = i * nCols + k;
t = r[v] / d;
alpha += t * t;
}
if (r[u] > 0.0)
{
d = -d;
}
alpha = d * Math.Sqrt(alpha);
if (Math.Abs(alpha) < eps)
{
throw new Exception("QR Factorization unsolved");
}
d = Math.Sqrt(2.0 * alpha * (alpha - r[u]));
if (d > eps)
{
r[u] = (r[u] - alpha) / d;
for (int i = k + 1; i < nRows; i++)
{
R[i, k] /= d;
}
for (int j = 0; j < nRows; j++)
{
t = 0.0;
for (int m = k; m < nRows; m++)
{
t += R[m, k] * q[m * nRows + j];
}
for (int i = k; i < nRows; i++)
{
p = i * nRows + j;
q[p] -= 2.0 * t * R[i, k];
}
}
for (int j = k + 1; j < nCols; j++)
{
t = 0.0;
for (int m = k; m < nRows; m++)
{
t += R[m, k] * R[m, j];
}
for (int i = k; i < nRows; i++)
{
R[i, j] -= 2.0 * t * R[i, k];
}
}
r[u] = alpha;
for (int i = k + 1; i < nRows; i++)
{
R[i, k] = 0.0;
}
}
}
for (int i = 0; i < nRows - 1; i++)
{
for (int j = i + 1; j < nRows; j++)
{
p = i * nRows + j;
u = j * nRows + i;
Utility.Swap(q, u, p);
}
}
}
