/// <summary>
/// Extracts main diagonal vector of the Matriz as a column vector.
/// </summary>
/// <returns>Vector diagonal</returns>
public Matriz DiagVector()
{
if (!this.IsSquare())
{
throw new InvalidOperationException("Cannot get diagonal of non-square Matriz.");
}
Matriz v = new Matriz(this.columnCount, 1);
for (int i = 1; i <= this.columnCount; i++)
{
v[i] = this[i, i];
}
return v;
}
/// <summary>
/// Retrieves column with one-based index j.
/// </summary>
/// <param name="j">Index j of the matrix</param>
/// <returns>j-th column of the matrix</returns>
public Matriz Column(int j)
{
Matriz buf = new Matriz(this.rowCount, 1);
for (int i = 1; i <= this.rowCount; i++)
{
buf[i] = this[i, j];
}
return buf;
}
/// <summary>
/// Replaces each Matriz entry z = x + iy with x - iy.
/// </summary>
/// <returns>Conjugated Matriz.</returns>
public Matriz Conjugate()
{
Matriz m = new Matriz(this.rowCount, this.columnCount);
for (int i = 1; i <= this.rowCount; i++)
{
for (int j = 1; j <= this.columnCount; j++)
{
m[i, j] = Complex.Conj(this[i, j]);
}
}
return m;
}
/// <summary>
/// Define operator multiplication with a complex number
/// </summary>
/// <param name="x">First complex number in the operation</param>
/// <param name="a">Second matrix in the operation</param>
/// <returns>Matrix result</returns>
public static Matriz operator *(Complex x, Matriz a)
{
Matriz b = new Matriz(a.RowCount, a.ColumnCount);
for (int i = 1; i <= a.RowCount; i++)
{
for (int j = 1; j <= a.ColumnCount; j++)
{
b[i, j] = a[i, j] * x;
}
}
return b;
}
/// <summary>
/// Provides a shallow copy of this Matriz in O(m).
/// </summary>
/// <returns>Matrix clonned</returns>
public Matriz Clone()
{
Matriz a = new Matriz();
a.rowCount = this.rowCount;
a.columnCount = this.columnCount;
for (int i = 0; i < this.rowCount; i++)
{
a.values.Add(((ArrayList)this.values[i]).Clone());
}
return a;
}
/// <summary>
/// Creates n by n Matriz filled with ones.
/// </summary>
/// <param name="n">Number of columns.</param>
/// <returns>n by n Matriz filled with ones.</returns>
public static Matriz Ones(int n)
{
Matriz m = new Matriz(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
((ArrayList)m.values[i])[j] = Complex.One;
}
}
return m;
}
/// <summary>
/// Define operator multiplication
/// </summary>
/// <param name="a">First matrix in the operation</param>
/// <param name="b">Second matrix in the operation</param>
/// <returns>Matrix result</returns>
public static Matriz operator *(Matriz a, Matriz b)
{
if (a.ColumnCount != b.RowCount)
{
throw new ArgumentException("Inner Matriz dimensions must agree.");
}
Matriz c = new Matriz(a.RowCount, b.ColumnCount);
for (int i = 1; i <= a.RowCount; i++)
{
for (int j = 1; j <= b.ColumnCount; j++)
{
c[i, j] = Dot(a.Row(i), b.Column(j));
}
}
return c;
}
/// <summary>
/// Implements the dot product of two vectors.
/// </summary>
/// <param name="v">Row or column vector.</param>
/// <param name="w">Row or column of other vector.</param>
/// <returns>Dot product.</returns>
public static Complex Dot(Matriz v, Matriz w)
{
int m = v.VectorLength();
int n = w.VectorLength();
if (m == 0 || n == 0)
{
throw new ArgumentException("Arguments need to be vectors.");
}
else if (m != n)
{
throw new ArgumentException("Vectors must be of the same length.");
}
Complex buf = Complex.Zero;
for (int i = 1; i <= m; i++)
{
buf += v[i] * w[i];
}
return buf;
}
/// <summary>
/// Creates m by n Matriz filled with ones.
/// </summary>
/// <param name="m">Number of rows.</param>
/// <param name="n">Number of columns.</param>
/// <returns>m by n Matriz filled with ones.</returns>
public static Matriz Ones(int m, int n)
{
Matriz mat = new Matriz(m, n);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
((ArrayList)mat.values[i])[j] = Complex.One;
}
}
return mat;
}
/// <summary>
/// Generates diagonal Matriz
/// </summary>
/// <param name="diag_vector">column vector containing the diag elements</param>
/// <returns>Diagonal matrix</returns>
public static Matriz Diag(Matriz diag_vector)
{
int dim = diag_vector.VectorLength();
if (dim == 0)
{
throw new ArgumentException("diag_vector must be 1xN or Nx1");
}
Matriz m = new Matriz(dim, dim);
for (int i = 1; i <= dim; i++)
{
m[i, i] = diag_vector[i];
}
return m;
}
/// <summary>
/// Generates diagonal Matriz
/// </summary>
/// <param name="diag_vector">column vector containing the diag elements</param>
/// <param name="offset">Offset of matrix</param>
/// <returns>Diagonal matrix</returns>
public static Matriz Diag(Matriz diag_vector, int offset)
{
int dim = diag_vector.VectorLength();
if (dim == 0)
{
throw new ArgumentException("diag_vector must be 1xN or Nx1.");
}
////if (Math.Abs(offset) >= dim)
//// throw new ArgumentException("Absolute value of offset must be less than length of diag_vector.");
Matriz m = new Matriz(dim + Math.Abs(offset), dim + Math.Abs(offset));
dim = m.RowCount;
if (offset >= 0)
{
for (int i = 1; i <= dim - offset; i++)
{
m[i, i + offset] = diag_vector[i];
}
}
else
{
for (int i = 1; i <= dim + offset; i++)
{
m[i - offset, i] = diag_vector[i];
}
}
return m;
}
/// <summary>
/// Swaps each Matriz entry A[i, j] with A[j, i].
/// </summary>
/// <returns>A transposed Matriz.</returns>
public Matriz Transpose()
{
Matriz m = new Matriz(this.columnCount, this.rowCount);
for (int i = 1; i <= this.columnCount; i++)
{
for (int j = 1; j <= this.rowCount; j++)
{
m[i, j] = this[j, i];
}
}
return m;
}
/// <summary>
/// Retrieves row with one-based index i.
/// </summary>
/// <param name="i">Define position searching</param>
/// <returns>i-th row in the matrix</returns>
public Matriz Row(int i)
{
if (i <= 0 || i > this.rowCount)
{
throw new ArgumentException("Index exceed matrix dimension.");
}
////return (new Matrix((Complex[])((ArrayList)Values[i - 1]).ToArray(typeof(Complex)))).Transpose();
Matriz buf = new Matriz(this.columnCount, 1);
for (int j = 1; j <= this.columnCount; j++)
{
buf[j] = this[i, j];
}
return buf;
}
public override double[] CrossValidation()
{
double[] output = new double[2];
List<Kpoint> cpointsCross = new List<Kpoint>();
double SSerror = 0;
double sumAllValues = 0;
double quad = 0; ;
for (int drop = 0; drop < this.NumPoints; drop++)
{
cpointsCross = new List<Kpoint>();
for (int i = 0; i < this.NumPoints; i++)
if (i != drop)
cpointsCross.Add(this.Kpoints[i]);
this.result = GenerateMatrixCross(this.order, this.npoints - 1, cpointsCross);
Kpoint value = this.Kpoints[drop];
double[] inter = this.Interpolate(value.X, value.Y,value.Z, false);
value.Zinte = inter[0];
value.SdtError = value.W - value.Zinte;
sumAllValues += value.SdtError;
quad += (value.Zinte * value.Zinte);
SSerror += (value.SdtError * value.SdtError);
}
output[0] = Math.Sqrt(SSerror / this.npoints); //RMS
output[1] = sumAllValues / this.npoints; //Mean Prediction errors
this.GenerateMatrix(this.order, this.npoints, this.Kpoints);
return output;
}
public Matriz GenerateMatrixCross(int order, int num, List<Kpoint> data)
{
int matrixSize = SerieCoef(order).Length;
Matriz matrix = new Matriz(matrixSize);
Matriz ZMatrix = new Matriz(matrixSize, 1);
double width = extent[2] - extent[0];
double height = extent[3] - extent[1];
double difZ = extentZ[1] - extentZ[0];
for (int v = 0; v < num; v++)
{
double x = (data[v].X - extent[0]) / width;
double y = (data[v].Y - extent[1]) / height;
double z = data[v].W;
for (int row = 0; row < matrixSize; row++)
{
for (int col = 0; col < matrixSize; col++)
{
matrix[row + 1, col + 1] = matrix[row + 1, col + 1] + Seq(num, order, col, row, x, y);
}
ZMatrix[row + 1, 1] = ZMatrix[row + 1, 1] + Seq(num, order, row, 0, x, y, z);
}
}
Matriz inver = matrix.Inverse();
Matriz ind = matrix * inver;
Matriz result = inver * ZMatrix;
return result;
}
public void GenerateMatrix(int order, int num, double[,] data)
{
int matrixSize = SerieCoef(order).Length;
Matriz matrix = new Matriz(matrixSize);
Matriz ZMatrix = new Matriz(matrixSize, 1);
double width = this.extent[2] - this.extent[0];
double height = this.extent[3] - this.extent[1];
double difZ = this.extentZ[1] - this.extentZ[0];
for (int v = 0; v < num; v++)
{
double x = (data[v, 0] - extent[0])/width;
double y = (data[v, 1] - extent[1])/height;
double z = data[v, 2];
for (int row = 0; row < matrixSize; row++)
{
for (int col = 0; col < matrixSize; col++)
{
matrix[row + 1, col + 1] = matrix[row + 1, col + 1] + Seq(num, order, col, row, x, y);
}
ZMatrix[row + 1, 1] = ZMatrix[row + 1, 1] + Seq(num, order, row, 0, x, y, z);
}
}
Matriz inver = matrix.Inverse();
Matriz ind = matrix * inver;
result = inver * ZMatrix;
}