public static MatrixX CombineColumns(List <MatrixX> spaces)
{
int width = 0;
foreach (var space in spaces)
{
width += space.Width;
}
MatrixX matrix = new MatrixX(width, spaces[0].Height);
for (int i = 0; i < width; i++)
{
foreach (var space in spaces)
{
for (int j = 0; j < space.Width; j++)
{
for (int k = 0; k < space.Height; k++)
{
matrix[i, k] = space[j, k];
}
i++;
}
}
}
return(matrix);
}
MatrixX GetMinorsMatrixX()
{
DateTime t0 = DateTime.Now;
MatrixX minorsMatrixX = new MatrixX(Width, Height);
MatrixX minorMatrixX = new MatrixX(Width - 1, Height - 1);
int numerator = Width * Height;
byte size = (byte)numerator.ToString().Length;
for (int i = 0; i < Width; i++)
{
for (int j = 0; j < Height; j++)
{
if (j + i != 0)
{
DateTime t = DateTime.Now;
TimeSpan dt = t - t0;
double ratio = numerator / (i * Width + j + 0d);
Console.WriteLine("Get Minors Matrix: {0}/{1} = {2}% Complete. ETA: {3}", (i * Width + j).ToString().PadLeft(size), numerator, Math.Round(100 / ratio, 4).ToString().PadRight(8)
, t0.Add(TimeSpan.FromMilliseconds(dt.TotalMilliseconds * ratio)));
}
GetMinor(i, j, ref minorMatrixX);
minorsMatrixX[i, j] = minorMatrixX.Determinant();
}
}
Console.WriteLine("Ending time: {0}", DateTime.Now);
return(minorsMatrixX);
}
void GetMinor(int i, int j, ref MatrixX destination)
{
int k = 0;
for (; k < i; k++)
{
int h = 0;
for (; h < j; h++)
{
destination[k, h] = Elements[k, h];
}
h++;
for (; h < Height; h++)
{
destination[k, h - 1] = Elements[k, h];
}
}
k++;
for (; k < Width; k++)
{
int h = 0;
for (; h < j; h++)
{
destination[k - 1, h] = Elements[k, h];
}
h++;
for (; h < Height; h++)
{
destination[k - 1, h - 1] = Elements[k, h];
}
}
}
//private methods
MatrixX GetMinor(int i, int j)
{
MatrixX m = new MatrixX(Width - 1, Height - 1);
GetMinor(i, j, ref m);
return(m);
}
public static MatrixX operator *(IntX a, MatrixX b)
{
MatrixX product = new MatrixX(b.Width, b.Height);
for (int i = 0; i < product.Width; i++)
{
for (int j = 0; j < product.Height; j++)
{
product[i, j] = a * b[i, j];
}
}
return(product);
}
//MatrixX RowReducedEchelonForm()
//{
// var copy = Copy();
// int row = 0;
// for (int column = 0; column < Width; column++)
// {
// //finding canidate row
// var r = row;
// for (; r < Height; r++)
// if (copy[r, column] != 0)
// break;
// //moving canidate row to proper row location
// //and dividing out magnitude
// if (r == Height)
// continue;
// var mlt = 1 / copy[r, column];
// for (int j = column; j < Width; j++)
// {
// var swap = copy[r, j];
// copy[r, j] = copy[row, j];
// copy[row, j] = swap * mlt;
// }
// //Normalizing Column
// for (int i = 0; i < Height; i++)
// {
// var m = copy[i, column];
// for (int j = column; j < Width; j++)
// {
// copy[j, i] -= m * copy[row, j];
// }
// }
// row++;
// if (row == Height)
// break;
// }
// return copy;
//}
//FractionX[] FindEigenValues()
//{
// var poly = FindCharacteristicPolynomial();
// return poly.FindAllRoots();
//}
//MatrixX GetEigenSpace(FractionX eigenValue, int dimensions)
//{
// MatrixX m = (this - eigenValue * DiagonalMatrixX.IdentityMatrixX(Width));
// m = m.RowReducedEchelonForm();
// MatrixX eigenSpace = new MatrixX(dimensions, Height);
// int basis = 0;
// for (int i = 0; i + basis < Width; i++)
// {
// if (m[i + basis, i] != 1)
// {
// int j = 0;
// for (; j < i + basis; j++)
// eigenSpace[i, j] = -m[i, j];
// eigenSpace[i, j++] = (FractionX)1;
// for (; j < Height; j++)
// eigenSpace[i, j] = -m[i, j];
// basis++;
// }
// }
// return eigenSpace;
//}
//Vector[] GetColumns()
//{
// Vector[] columns = new Vector[Width];
// for (int i = 0; i < Width; i++)
// {
// FractionX[] elements = new FractionX[Height];
// for (int j = 0; j < Height; j++)
// elements[j] = this[i, j];
// columns[i] = new Vector(elements);
// }
// return columns;
//}
//MatrixX GramSchmit()
//{
// Vector[] vectors = GetColumns();
// Vector[] normalized = new Vector[vectors.Length - 1];
// for (int i = 0; i < vectors.Length; i++)
// {
// for (int j = 0; j < i; j++)
// vectors[i] -= normalized[j] * vectors[i] * normalized[j];
// if (i < normalized.Length)
// normalized[i] = vectors[i].Normalize();
// }
// return CombineColumns(vectors);
//}
//public void Diagonalize(out MatrixX basis, out DiagonalMatrixX diagonal)
//{
// var eigenValues = FindEigenValues();
// var l = eigenValues.ToList();
// l.Sort((FractionX a, FractionX b) => { return a.Real < b.Real ? 1 : 0; });
// eigenValues = l.ToArray();
// int m = 0;
// List<MatrixX> spaces = new List<MatrixX>();
// for (int i = 0; i < eigenValues.Length; i += m)
// {
// m = 1;//multiplicity
// while (i + m < eigenValues.Length && eigenValues[i] == eigenValues[i + m])
// m++;
// //finding eigen space
// var space = GetEigenSpace(eigenValues[i], m);
// //using Gram Schmit to orthogonalize stuff.
// space.GramSchmit();
// spaces.Add(space);
// }
// basis = CombineColumns(spaces);
// diagonal = new DiagonalMatrixX(eigenValues);
//}
MatrixX Copy()
{
MatrixX matrix = new MatrixX(Width, Height);
for (int i = 0; i < matrix.Width; i++)
{
for (int j = 0; j < matrix.Height; j++)
{
matrix[i, j] = this[i, j];
}
}
return(matrix);
}
public MatrixX Transpose()
{
MatrixX m = new MatrixX(Width, Height);
for (int i = 0; i < Width; i++)
{
for (int j = 0; j < Height; j++)
{
m[i, j] = this[j, i];
}
}
return(m);
}
//public static MatrixX CombineColumns(Vector[] columns)
//{
// MatrixX matrix = new MatrixX(columns.Length, columns[0].Dimensions);
// for (int i = 0; i < matrix.Width; i++)
// for (int j = 0; j < matrix.Height; j++)
// matrix[i, j] = columns[i][j];
// return matrix;
//}
//public methods
/// <summary>
///
/// </summary>
/// <returns>Inverse matrix if invertable, else returns NULL</returns>
public MatrixX GetAdjointMatrix()
{
MatrixX adjointMatrix = GetMinorsMatrixX();
for (int i = 0; i < adjointMatrix.Width; i++)
{
for (int j = 0; j < adjointMatrix.Height; j++)
{
if ((i + j) % 2 == 1)
{
adjointMatrix[i, j] = -adjointMatrix[i, j];
}
}
}
adjointMatrix = adjointMatrix.Transpose();
return(adjointMatrix);
}
//public MatrixX Pow(FractionX exp) => Pow(this, exp);
//public static MatrixX Pow(MatrixX a, FractionX exp)
//{
// a.Diagonalize(out MatrixX s, out DiagonalMatrixX b);
// var s1 = s.Invert();
// return s * DiagonalMatrixX.Pow(b, exp) * s1;
//}
//Operators
public static MatrixX operator *(MatrixX a, MatrixX b)
{
if (a.Width != b.Height)
{
return(null);
}
MatrixX product = new MatrixX(a.Height, b.Width);
for (int i = 0; i < product.Width; i++)
{
for (int j = 0; j < product.Height; j++)
{
product[i, j] = 0;
for (int h = 0; h < a.Width; h++)
{
product[i, j] += a[h, i] * b[j, h];
}
}
}
return(product);
}
public static PolynomialX Generate(IntX[] input, IntX[] output)
{
if (input.Length != output.Length)
{
return(null);
}
MatrixX A = new MatrixX(input.Length, input.Length);
MatrixX column = new MatrixX(1, input.Length);
for (int i = 0; i < input.Length; i++)
{
IntX prod = 1;
for (int j = 0; j < input.Length; j++)
{
A[j, i] = prod;
prod *= input[i];
}
column[0, i] = output[i];
}
var det = A.Determinant();
if (det == 0)
{
return(null);
}
var adjoint = A.GetAdjointMatrix();
PolynomialX poly = new PolynomialX(input.Length);
var result = adjoint * column;
for (int i = 0; i < input.Length; i++)
{
poly.Coefficients[i] = (FractionX)result[i, 0] / det;
}
return(poly);
}