/// <summary>QR Decomposition, computed by Householder reflections.</summary>
/// <param name="A"> Rectangular matrix
/// </param>
/// <returns> Structure to access R and the Householder vectors and compute Q.
/// </returns>
public QRDecomposition(GeneralMatrix A)
{
// Initialize.
QR = A.ArrayCopy;
m = A.RowDimension;
n = A.ColumnDimension;
Rdiag = new double[n];
// Main loop.
for (int k = 0; k < n; k++)
{
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
for (int i = k; i < m; i++)
{
nrm = Maths.Hypot(nrm, QR[i][k]);
}
if (nrm != 0.0)
{
// Form k-th Householder vector.
if (QR[k][k] < 0)
{
nrm = - nrm;
}
for (int i = k; i < m; i++)
{
QR[i][k] /= nrm;
}
QR[k][k] += 1.0;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++)
{
double s = 0.0;
for (int i = k; i < m; i++)
{
s += QR[i][k] * QR[i][j];
}
s = (- s) / QR[k][k];
for (int i = k; i < m; i++)
{
QR[i][j] += s * QR[i][k];
}
}
}
Rdiag[k] = - nrm;
}
}
/// <summary>A = A - B</summary>
/// <param name="B"> another matrix
/// </param>
/// <returns> A - B
/// </returns>
public virtual GeneralMatrix SubtractEquals(GeneralMatrix B)
{
CheckMatrixDimensions(B);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
A[i][j] = A[i][j] - B.A[i][j];
}
}
return this;
}
/// <summary>Linear algebraic matrix multiplication, A * B</summary>
/// <param name="B"> another matrix
/// </param>
/// <returns> Matrix product, A * B
/// </returns>
/// <exception cref="System.ArgumentException"> Matrix inner dimensions must agree.
/// </exception>
public virtual GeneralMatrix Multiply(GeneralMatrix B)
{
if (B.m != n)
{
throw new System.ArgumentException("GeneralMatrix inner dimensions must agree.");
}
GeneralMatrix X = new GeneralMatrix(m, B.n);
double[][] C = X.Array;
double[] Bcolj = new double[n];
for (int j = 0; j < B.n; j++)
{
for (int k = 0; k < n; k++)
{
Bcolj[k] = B.A[k][j];
}
for (int i = 0; i < m; i++)
{
double[] Arowi = A[i];
double s = 0;
for (int k = 0; k < n; k++)
{
s += Arowi[k] * Bcolj[k];
}
C[i][j] = s;
}
}
return X;
}
/// <summary>Least squares solution of A*X = B</summary>
/// <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>
/// <exception cref="System.ArgumentException"> Matrix row dimensions must agree.
/// </exception>
/// <exception cref="System.SystemException"> Matrix is rank deficient.
/// </exception>
public virtual GeneralMatrix Solve(GeneralMatrix B)
{
if (B.RowDimension != m)
{
throw new System.ArgumentException("GeneralMatrix row dimensions must agree.");
}
if (!this.FullRank)
{
throw new System.SystemException("Matrix is rank deficient.");
}
// Copy right hand side
int nx = B.ColumnDimension;
double[][] X = B.ArrayCopy;
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < nx; j++)
{
double s = 0.0;
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];
}
}
}
return (new GeneralMatrix(X, n, nx).GetMatrix(0, n - 1, 0, nx - 1));
}
/// <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>Check for symmetry, then construct the eigenvalue decomposition</summary>
/// <param name="Arg"> Square matrix
/// </param>
/// <returns> Structure to access D and V.
/// </returns>
public void 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));
}
/// <summary>Element-by-element left division in place, A = A.\B</summary>
/// <param name="B"> another matrix
/// </param>
/// <returns> A.\B
/// </returns>
public virtual GeneralMatrix ArrayLeftDivideEquals(GeneralMatrix B)
{
CheckMatrixDimensions(B);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
A[i][j] = B.A[i][j] / A[i][j];
}
}
return this;
}
/// <summary>Construct a matrix from a copy of a 2-D array.</summary>
/// <param name="A"> Two-dimensional array of doubles.
/// </param>
/// <exception cref="System.ArgumentException"> All rows must have the same length
/// </exception>
public static GeneralMatrix Create(double[][] A)
{
int m = A.Length;
int n = A[0].Length;
GeneralMatrix X = new GeneralMatrix(m, n);
double[][] C = X.Array;
for (int i = 0; i < m; i++)
{
if (A[i].Length != n)
{
throw new System.ArgumentException("All rows must have the same length.");
}
for (int j = 0; j < n; j++)
{
C[i][j] = A[i][j];
}
}
return X;
}
/// <summary>Check if size(A) == size(B) *</summary>
private void CheckMatrixDimensions(GeneralMatrix B)
{
if (B.m != m || B.n != n)
{
throw new System.ArgumentException("GeneralMatrix dimensions must agree.");
}
}
/// <summary>Generate identity matrix</summary>
/// <param name="m"> Number of rows.
/// </param>
/// <param name="n"> Number of colums.
/// </param>
/// <returns> An m-by-n matrix with ones on the diagonal and zeros elsewhere.
/// </returns>
public static GeneralMatrix Identity(int m, int n)
{
GeneralMatrix A = new GeneralMatrix(m, n);
double[][] X = A.Array;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
X[i][j] = (i == j ? 1.0 : 0.0);
}
}
return A;
}
/// <summary>Generate matrix with random elements</summary>
/// <param name="m"> Number of rows.
/// </param>
/// <param name="n"> Number of colums.
/// </param>
/// <returns> An m-by-n matrix with uniformly distributed random elements.
/// </returns>
public static GeneralMatrix Random(int m, int n)
{
System.Random random = new System.Random();
GeneralMatrix A = new GeneralMatrix(m, n);
double[][] X = A.Array;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
X[i][j] = random.NextDouble();
}
}
return A;
}
/// <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>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));
}
/// <summary>Element-by-element multiplication in place, A = A.*B</summary>
/// <param name="B"> another matrix
/// </param>
/// <returns> A.*B
/// </returns>
public virtual GeneralMatrix ArrayMultiplyEquals(GeneralMatrix B)
{
CheckMatrixDimensions(B);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
A[i][j] = A[i][j] * B.A[i][j];
}
}
return this;
}
/// <summary>Element-by-element left division, C = A.\B</summary>
/// <param name="B"> another matrix
/// </param>
/// <returns> A.\B
/// </returns>
public virtual GeneralMatrix ArrayLeftDivide(GeneralMatrix B)
{
CheckMatrixDimensions(B);
GeneralMatrix X = new GeneralMatrix(m, n);
double[][] C = X.Array;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i][j] = B.A[i][j] / A[i][j];
}
}
return X;
}
/// <summary>Get a submatrix.</summary>
/// <param name="i0"> Initial row index
/// </param>
/// <param name="i1"> Final row index
/// </param>
/// <param name="c"> Array of column indices.
/// </param>
/// <returns> A(i0:i1,c(:))
/// </returns>
/// <exception cref="System.IndexOutOfRangeException"> Submatrix indices
/// </exception>
public virtual GeneralMatrix GetMatrix(int i0, int i1, int[] c)
{
GeneralMatrix X = new GeneralMatrix(i1 - i0 + 1, c.Length);
double[][] B = X.Array;
try
{
for (int i = i0; i <= i1; i++)
{
for (int j = 0; j < c.Length; j++)
{
B[i - i0][j] = A[i][c[j]];
}
}
}
catch (System.IndexOutOfRangeException e)
{
throw new System.IndexOutOfRangeException("Submatrix indices", e);
}
return X;
}
/// <summary>Multiply a matrix by a scalar, C = s*A</summary>
/// <param name="s"> scalar
/// </param>
/// <returns> s*A
/// </returns>
public virtual GeneralMatrix Multiply(double s)
{
GeneralMatrix X = new GeneralMatrix(m, n);
double[][] C = X.Array;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i][j] = s * A[i][j];
}
}
return X;
}
/// <summary>Get a submatrix.</summary>
/// <param name="r"> Array of row indices.
/// </param>
/// <param name="j0"> Initial column index
/// </param>
/// <param name="j1"> Final column index
/// </param>
/// <returns> A(r(:),j0:j1)
/// </returns>
/// <exception cref="System.IndexOutOfRangeException"> Submatrix indices
/// </exception>
public virtual GeneralMatrix GetMatrix(int[] r, int j0, int j1)
{
GeneralMatrix X = new GeneralMatrix(r.Length, j1 - j0 + 1);
double[][] B = X.Array;
try
{
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
B[i][j - j0] = A[r[i]][j];
}
}
}
catch (System.IndexOutOfRangeException e)
{
throw new System.IndexOutOfRangeException("Submatrix indices", e);
}
return X;
}
/// <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>Set a submatrix.</summary>
/// <param name="r"> Array of row indices.
/// </param>
/// <param name="j0"> Initial column index
/// </param>
/// <param name="j1"> Final column index
/// </param>
/// <param name="X"> A(r(:),j0:j1)
/// </param>
/// <exception cref="System.IndexOutOfRangeException"> Submatrix indices
/// </exception>
public virtual void SetMatrix(int[] r, int j0, int j1, GeneralMatrix X)
{
try
{
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
A[r[i]][j] = X.GetElement(i, j - j0);
}
}
}
catch (System.IndexOutOfRangeException e)
{
throw new System.IndexOutOfRangeException("Submatrix indices", e);
}
}
/// <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*U*X = B(piv,:)
/// </returns>
/// <exception cref="System.ArgumentException"> Matrix row dimensions must agree.
/// </exception>
/// <exception cref="System.SystemException"> Matrix is singular.
/// </exception>
public virtual GeneralMatrix Solve(GeneralMatrix B)
{
if (B.RowDimension != m)
{
throw new System.ArgumentException("Matrix row dimensions must agree.");
}
if (!this.IsNonSingular)
{
throw new System.SystemException("Matrix is singular.");
}
// Copy right hand side with pivoting
int nx = B.ColumnDimension;
GeneralMatrix Xmat = B.GetMatrix(piv, 0, nx - 1);
double[][] X = Xmat.Array;
// Solve L*Y = B(piv,:)
for (int k = 0; k < n; k++)
{
for (int i = k + 1; i < n; i++)
{
for (int j = 0; j < nx; j++)
{
X[i][j] -= X[k][j] * LU[i][k];
}
}
}
// Solve U*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < nx; j++)
{
X[k][j] /= LU[k][k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i][j] -= X[k][j] * LU[i][k];
}
}
}
return Xmat;
}
/// <summary>Set a submatrix.</summary>
/// <param name="i0"> Initial row index
/// </param>
/// <param name="i1"> Final row index
/// </param>
/// <param name="c"> Array of column indices.
/// </param>
/// <param name="X"> A(i0:i1,c(:))
/// </param>
/// <exception cref="System.IndexOutOfRangeException"> Submatrix indices
/// </exception>
public virtual void SetMatrix(int i0, int i1, int[] c, GeneralMatrix X)
{
try
{
for (int i = i0; i <= i1; i++)
{
for (int j = 0; j < c.Length; j++)
{
A[i][c[j]] = X.GetElement(i - i0, j);
}
}
}
catch (System.IndexOutOfRangeException e)
{
throw new System.IndexOutOfRangeException("Submatrix indices", e);
}
}
public void covariance()
{
covMatrix = new double[2][];
for (int i = 0; i < 2; i++)
covMatrix[i] = new double[2];
V = new double[2][];
for (int i = 0; i < 2; i++)
V[i] = new double[2];
d = new double[2];
// //covMatrix[0][0] = 0;
// //covMatrix[0][1] = 0;
// //covMatrix[1][0] = 0;
// //covMatrix[1][1] = 0;
for (int i = 0; i < totalCount; i++)
{
covMatrix[0][0] += (intermediatePoints[i].X - meanX) * (intermediatePoints[i].X - meanX);
covMatrix[0][1] += (intermediatePoints[i].X - meanX) * (intermediatePoints[i].Y - meanY);
covMatrix[1][0] = covMatrix[0][1];
covMatrix[1][1] += (intermediatePoints[i].Y - meanY) * (intermediatePoints[i].Y - meanY);
}
covMatrix[0][0] = covMatrix[0][0] / (totalCount - 1);
covMatrix[0][1] = covMatrix[0][1] / (totalCount - 1);
covMatrix[1][0] = covMatrix[1][0] / (totalCount - 1);
covMatrix[1][1] = covMatrix[1][1] / (totalCount - 1);
// Console.WriteLine(" testing covariance matrix: {0} {1} {2} {3}", covMatrix[0][0], covMatrix[0][1], covMatrix[1][0], covMatrix[1][1]);
// Console.WriteLine(" matrix testing : {0}", covMatrix);
//yeta baata eigenvalue ra eigenvector niskincha
GeneralMatrix generalMatrix = new GeneralMatrix(covMatrix);
EigenvalueDecomposition eigenvalueDecomposition = new EigenvalueDecomposition(generalMatrix);
d = eigenvalueDecomposition.getD(); // get eigen values
V = eigenvalueDecomposition.getV(); // get eigen vectors
//for (int i = 0; i < 2; i++)
//Console.WriteLine("eigenvalue: " + d[i]);
//for (int i = 0; i < 2; i++)
//{
// for (int j = 0; j < 2; j++)
// Console.WriteLine("eigenvector " + V[i][j]);
//}
}
/// <summary>Matrix transpose.</summary>
/// <returns> A'
/// </returns>
public virtual GeneralMatrix Transpose()
{
GeneralMatrix X = new GeneralMatrix(n, m);
double[][] C = X.Array;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[j][i] = A[i][j];
}
}
return X;
}
/// <summary>Unary minus</summary>
/// <returns> -A
/// </returns>
public virtual GeneralMatrix UnaryMinus()
{
GeneralMatrix X = new GeneralMatrix(m, n);
double[][] C = X.Array;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i][j] = -A[i][j];
}
}
return X;
}
/// <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];
}
}
}
}
