/// <summary>
/// //gives R, the rotation matrix, U - the left eigenvectors, VT - right transposed eigenvectors, EV - the eigenvalues
/// </summary>
/// <param name="H"></param>
public static void Eigenvalues_Helper_Alglib(Matrix3d H)
{
double[,] Harray = H.ToDoubleArray();
double[,] Uarray = new double[3, 3];
double[,] VTarray = new double[3, 3];
double[] EVarray = new double[3];
alglib.svd.rmatrixsvd(Harray, 3, 3, 2, 2, 2, ref EVarray, ref Uarray, ref VTarray);
U = U.FromDoubleArray(Uarray);
VT = VT.FromDoubleArray(VTarray);
EV = EV.FromDoubleArray(EVarray);
R = Matrix3d.Mult(U, VT);
}
///<summary> Return triangular factor</summary>
///<returns>L</returns>
public Matrix3d getL()
{
Matrix3d mat = new Matrix3d();
mat = mat.FromDoubleArray(L);
return(mat);
}
/// <summary>
/// parses a string to produce a matrix
/// </summary>
/// <param name="str">The string to parse</param>
/// <param name="matrixFrontCap">placed at the beginning of the string</param>
/// <param name="rowFrontCap">placed at the beginning of each row</param>
/// <param name="rowDelimiter">delimiter for rows</param>
/// <param name="columnDelimiter">delimiter for Columns</param>
/// <param name="rowEndCap">placed at the end of each row</param>
/// <param name="matrixEndCap">placed at the beginning of the string</param>
/// <returns></returns>
public static Matrix3d Parse(this Matrix3d mat, string str, string matrixFrontCap, string rowFrontCap, string rowDelimiter, string columnDelimiter, string rowEndCap, string matrixEndCap)
{
if (!str.StartsWith(matrixFrontCap))
{
throw new Exception("string does not begin with proper value: " + matrixFrontCap + " was expected, but " + str.Substring(0, matrixFrontCap.Length) + " was found.");
}
if (!str.StartsWith(matrixFrontCap))
{
throw new Exception("string does not end with proper value: " + matrixEndCap + " was expected, but " + str.Substring(str.Length - matrixEndCap.Length, matrixEndCap.Length) + " was found.");
}
string working = str.Substring(matrixFrontCap.Length, str.Length - matrixFrontCap.Length - matrixEndCap.Length);
string[] rDelim = { rowEndCap + rowDelimiter + rowFrontCap };
string[] rows = working.Split(rDelim, StringSplitOptions.RemoveEmptyEntries);
if (rows.Length == 0)
{
throw new Exception("No rows present");
}
rows[0] = rows[0].Substring(rowFrontCap.Length);
rows[rows.Length - 1] = rows[rows.Length - 1].Substring(0, rows[rows.Length - 1].Length - rowEndCap.Length);
double[,] matrixArray = new double[rows.Length, rows.Length];
int columnCount = 0;
for (int iRow = 0; iRow < rows.Length; iRow++)
{
string[] cols = rows[iRow].Split(new string[] { columnDelimiter }, StringSplitOptions.RemoveEmptyEntries);
if (columnCount != 0)
{
if (columnCount != cols.Length)
{
throw new Exception("Rows are not of consistant lenght");
}
}
else
{
columnCount = cols.Length;
}
double[] row = new double[columnCount];
for (int iCol = 0; iCol < columnCount; iCol++)
{
row[iCol] = double.Parse(cols[iCol]);
}
for (int i = 0; i < cols.Length; i++)
{
matrixArray[iRow, i] = row[i];
}
}
mat = mat.FromDoubleArray(matrixArray);
return(mat);
}
///<Sumary>Least squares solution of A*X = B</Sumary>
///<param name="B">A Matrix with as many rows as A and any number of columns.</param>
///<returns> X that minimizes the two norm of Q*R*X-B.</returns>
public Matrix3d Solve(Matrix3d B)
{
if (B.RowLength() != m)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!IsFullRank())
{
throw new Exception("Matrix is rank deficient.");
}
// Copy right hand side
int nx = B.ColumnLength();
double[,] X = B.ToArray();
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < nx; j++)
{
double s = 0.0f;
for (int i = k; i < m; i++)
{
s += QR[i, k] * X[i, j];
}
s = -s / QR[k, k];
for (int i = k; i < m; i++)
{
X[i, j] += s * QR[i, k];
}
}
}
// Solve R*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < nx; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i, j] -= X[k, j] * QR[i, k];
}
}
}
Matrix3d mat = new Matrix3d();
mat = mat.FromDoubleArray(X);
return(mat.GetMatrix(0, n - 1, 0, nx - 1));
}
public static Matrix3d FromDataTable(this Matrix3d mat, DataTable dt)
{
double[,] X = new double[dt.Rows.Count, dt.Columns.Count];
for (int iRow = 0; iRow < dt.Rows.Count; iRow++)
{
double[] row = new double[dt.Columns.Count];
for (int iCol = 0; iCol < dt.Columns.Count; iCol++)
{
X[iRow, iCol] = (double)dt.Rows[iRow][iCol];
}
}
mat = mat.FromDoubleArray(X);
return(mat);
}
///<summary>Solve A*X = B</summary>
///<param name="B">A Matrix with as many rows as A and any number of columns.</param>
///<returns>X so that L*L'*X = B</returns>
///<exception cref="ArgumentException">System.ArgumentException Matrix row dimensions must agree.</exception>
///<exception cref="Exception">System.Exception Matrix is not symmetric positive definite.</exception>
public Matrix3d Solve(Matrix3d B)
{
if (B.RowLength() != n)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!isspd)
{
throw new Exception("Matrix is not symmetric positive definite.");
}
// Copy right hand side.
double[,] X = B.ToArray();
int nx = B.ColumnLength();
// Solve L*Y = B;
for (int k = 0; k < n; k++)
{
for (int j = 0; j < nx; j++)
{
for (int i = 0; i < k; i++)
{
X[k, j] -= X[i, j] * L[k, i];
}
X[k, j] /= L[k, k];
}
}
// Solve L'*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < nx; j++)
{
for (int i = k + 1; i < n; i++)
{
X[k, j] -= X[i, j] * L[i, k];
}
X[k, j] /= L[k, k];
}
}
Matrix3d mat = new Matrix3d();
mat = mat.FromDoubleArray(X);
return(mat);
}
/// <summary>
/// //gives R, the rotation matrix, U - the left eigenvectors, VT - right transposed eigenvectors, EV - the eigenvalues
/// </summary>
/// <param name="H"></param>
public static void Eigenvalues_Helper_VTK(Matrix3d H)
{
double[,] Harray = H.ToDoubleArray();
double[,] Uarray = new double[3, 3];
double[,] VTarray = new double[3, 3];
double[] EVarray = new double[3];
//alglib.svd.rmatrixsvd(Harray, 3, 3, 2, 2, 2, ref EVarray, ref Uarray, ref VTarray);
csharpMath.SingularValueDecomposition3x3(Harray, Uarray, EVarray, VTarray);
//U = new Matrix3d();
U = U.FromDoubleArray(Uarray);
U = U.FromDoubleArray(Uarray);
VT = VT.FromDoubleArray(VTarray);
EV = EV.FromDoubleArray(EVarray);
R = Matrix3d.Mult(U, VT);
}
public Matrix3d LUDecompose(Matrix3d A)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = A.ToArray();
m = A.RowLength();
n = A.ColumnLength();
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++)
{
// Most of the time is spent in the following dot product.
int kmax = Math.Min(i, j);
double s = 0.0f;
for (int k = 0; k < kmax; k++)
{
s += LU[i, k] * LU[k, i];
}
LU[j, i] = LU[i, j] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++)
{
if (Math.Abs(LU[i, j]) > Math.Abs(LU[p, j]))
{
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)
{
for (int i = j + 1; i < m; i++)
{
LU[i, j] /= LU[j, j];
}
}
}
Matrix3d mat = new Matrix3d();
mat = mat.FromDoubleArray(LU);
return(mat);
}