private int _AssignID; // 0 == assign, 1 == increment, 2 == decrement, 3 == auto increment, 4 == auto decrement
public TNodeMatrixUnitAssign(TNode Parent, CellMatrix Data, FNode Node, FNode RowID, FNode ColumnID, int AssignID)
: base(Parent)
{
this._matrix = Data;
this._Node = Node;
this._AssignID = AssignID;
this._row_id = RowID;
this._col_id = ColumnID;
}
/// <summary>
/// Create a cell matrix from another matrix, effectively cloning the matrix
/// </summary>
/// <param name="A"></param>
public CellMatrix(CellMatrix A)
{
// Build Matrix //
this._Rows = A._Rows;
this._Columns = A._Columns;
this._Data = new Cell[this._Rows, this._Columns];
for (int i = 0; i < this._Rows; i++)
for (int j = 0; j < this._Columns; j++)
this._Data[i, j] = A[i, j];
this._Affinity = A.Affinity;
}
public CellMatrix getU()
{
CellMatrix X = new CellMatrix(n, n, LU.Affinity);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i <= j)
{
X[i, j] = LU[i, j];
}
else
{
X[i, j] = Cell.ZeroValue(LU.Affinity);
}
}
}
return X;
}
public LUDecomposition(CellMatrix A)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
this._zero = Cell.ZeroValue(A.Affinity);
LU = new CellMatrix(A);
m = A.RowCount;
n = A.ColumnCount;
piv = new int[m];
for (int i = 0; i < m; i++)
{
piv[i] = i;
}
pivsign = 1;
Cell[] LUcolj = new Cell[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);
Cell s = this._zero;
for (int k = 0; k < kmax; k++)
{
s += LU[i, k] * LUcolj[k];
}
LU[i, j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++)
{
if (Cell.Abs(LUcolj[i]) > Cell.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < n; k++)
{
Cell t = LU[p, k];
LU[p, k] = LU[j, k];
LU[j, k] = t;
}
int l = piv[p];
piv[p] = piv[j];
piv[j] = l;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m & LU[j, j] != this._zero)
{
for (int i = j + 1; i < m; i++)
{
LU[i, j] /= LU[j, j];
}
}
}
}
public CellMatrix getL()
{
CellMatrix L = new CellMatrix(m, n, LU.Affinity);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (i > j)
{
L[i, j] = LU[i, j];
}
else if (i == j)
{
L[i, j] = Cell.OneValue(LU.Affinity);
}
else
{
L[i, j] = Cell.ZeroValue(LU.Affinity);
}
}
}
return L;
}
public static Cell SumSquare(CellMatrix A)
{
Cell d = Cell.ZeroValue(A.Affinity);
for (int i = 0; i < A.RowCount; i++)
for (int j = 0; j < A.ColumnCount; j++)
d += A[i, j] * A[i, j];
return d;
}
public static CellMatrix Trace(CellMatrix A)
{
if (!A.IsSquare)
throw new Exception(string.Format("Cannot trace a non-square matrix : {0} x {1}", A.RowCount, A.ColumnCount));
CellMatrix B = new CellMatrix(A.RowCount, A.RowCount, Cell.ZeroValue(A.Affinity));
for (int i = 0; i < A.RowCount; i++)
B[i, i] = A[i, i];
return B;
}
/// <summary>
/// Use for checking matrix multiplication
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns></returns>
private static bool CheckDimensions2(CellMatrix A, CellMatrix B)
{
return (A.ColumnCount == B.RowCount);
}
public static CellMatrix Invert(CellMatrix A)
{
// New decomposition //
LUDecomposition lu = new LUDecomposition(A);
// New identity //
CellMatrix I = CellMatrix.Identity(A.RowCount, A.Affinity);
return lu.solve(I);
}
public CellMatrix solve(CellMatrix B)
{
if (B.RowCount != m)
{
throw new Exception("Matrix row dimensions must agree.");
}
if (!this.isNonsingular())
{
throw new Exception("Matrix is singular.");
}
// Copy right hand side with pivoting
int nx = B.ColumnCount;
CellMatrix X = this.getMatrix(B, piv, 0, nx - 1);
// 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 X;
}
public MNodeLiteral(MNode Parent, CellMatrix Value)
: base(Parent)
{
this._value = Value;
}
public static CellMatrix CheckDivide(CellMatrix A, Cell B)
{
CellMatrix C = new CellMatrix(A.RowCount, A.ColumnCount, A.Affinity);
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < A.ColumnCount; j++)
{
C._Data[i, j] = Cell.CheckDivide(A._Data[i, j], B);
}
}
return C;
}
/// <summary>
/// Performs the true matrix multiplication between two matricies
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns></returns>
public static CellMatrix operator ^(CellMatrix A, CellMatrix B)
{
if (CellMatrix.CheckDimensions2(A, B) == false)
{
throw new Exception(string.Format("Dimension mismatch A {0}x{1} B {2}x{3}", A.RowCount, A.ColumnCount, B.RowCount, B.ColumnCount));
}
CellMatrix C = new CellMatrix(A.RowCount, B.ColumnCount, Cell.ZeroValue(A.Affinity));
// Main Loop //
for (int i = 0; i < A.RowCount; i++)
{
// Sub Loop One //
for (int j = 0; j < B.ColumnCount; j++)
{
// Sub Loop Two //
for (int k = 0; k < A.ColumnCount; k++)
{
C[i, j] = C[i, j] + A[i, k] * B[k, j];
}
}
}
// Return C //
return C;
}
public static CellMatrix CheckDivide(Cell A, CellMatrix B)
{
CellMatrix C = new CellMatrix(B.RowCount, B.ColumnCount, A.AFFINITY);
for (int i = 0; i < B.RowCount; i++)
{
for (int j = 0; j < B.ColumnCount; j++)
{
C._Data[i, j] = Cell.CheckDivide(A, B._Data[i, j]);
}
}
return C;
}
/// <summary>
/// Divides a matrix by another matrix, but checks for N / 0 erros
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns></returns>
public static CellMatrix CheckDivide(CellMatrix A, CellMatrix B)
{
// Check bounds are the same //
if (CellMatrix.CheckDimensions(A, B) == false)
{
throw new Exception(string.Format("Dimension mismatch A {0}x{1} B {2}x{3}", A.RowCount, A.ColumnCount, B.RowCount, B.ColumnCount));
}
// Build a matrix //
CellMatrix C = new CellMatrix(A.RowCount, A.ColumnCount, A.Affinity);
// Main loop //
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < A.ColumnCount; j++)
{
C[i, j] = B[i, j].IsZero ? Cell.ZeroValue(A[i, j].Affinity) : A[i, j] / B[i, j];
}
}
// Return //
return C;
}
public static CellMatrix operator /(CellMatrix A, Cell B)
{
CellMatrix C = new CellMatrix(A.RowCount, A.ColumnCount, A.Affinity);
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < A.ColumnCount; j++)
{
C._Data[i, j] = A._Data[i, j] / B;
}
}
return C;
}
public static CellMatrix operator /(Cell A, CellMatrix B)
{
CellMatrix C = new CellMatrix(B.RowCount, B.ColumnCount, A.AFFINITY);
for (int i = 0; i < B.RowCount; i++)
{
for (int j = 0; j < B.ColumnCount; j++)
{
C._Data[i, j] = A / B._Data[i, j];
}
}
return C;
}
/// <summary>
/// Negates a matrix
/// </summary>
/// <param name="A">Matrix to negate</param>
/// <returns>0 - A</returns>
public static CellMatrix operator -(CellMatrix A)
{
// Build a matrix //
CellMatrix C = new CellMatrix(A.RowCount, A.ColumnCount, A.Affinity);
// Main loop //
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < A.ColumnCount; j++)
{
C[i, j] = -A[i, j];
}
}
// Return //
return C;
}
/// <summary>
/// Transposes a matrix
/// </summary>
/// <param name="A"></param>
/// <returns></returns>
public static CellMatrix operator ~(CellMatrix A)
{
// Create Another Matrix //
CellMatrix B = new CellMatrix(A.ColumnCount, A.RowCount, A.Affinity);
// Loop through A and copy element to B //
for (int i = 0; i < A.RowCount; i++)
for (int j = 0; j < A.ColumnCount; j++)
B[j, i] = A[i, j];
// Return //
return B;
}
/// <summary>
/// Returns the identity matrix given a dimension
/// </summary>
/// <param name="Dimension"></param>
/// <returns></returns>
public static CellMatrix Identity(int Dimension, CellAffinity Affinity)
{
// Check that a positive number was passed //
if (Dimension < 1)
throw new Exception("Dimension must be greater than or equal to 1");
// Create a matrix //
CellMatrix A = new CellMatrix(Dimension, Dimension, Affinity);
for (int i = 0; i < Dimension; i++)
{
for (int j = 0; j < Dimension; j++)
{
if (i != j)
A[i, j] = Cell.ZeroValue(A.Affinity);
else
A[i, j] = Cell.OneValue(A.Affinity);
}
}
return A;
}
public static void AllocateMemory(Workspace Home, MemoryStruct Heap, ExpressionVisitor Evaluator, HScriptParser.DeclareMatrix2DContext context)
{
string name = context.IDENTIFIER().GetText();
CellAffinity type = GetAffinity(context.type());
int rows = (int)Evaluator.ToNode(context.expression()[0]).Evaluate().valueINT;
int cols = (int)Evaluator.ToNode(context.expression()[1]).Evaluate().valueINT;
CellMatrix mat = new CellMatrix(rows, cols, type);
Heap.Arrays.Reallocate(name, mat);
}
public CellMatrix getMatrix(CellMatrix A, int[] r, int j0, int j1)
{
CellMatrix X = new CellMatrix(r.Length, j1 - j0 + 1, A.Affinity);
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
X[i, j - j0] = A[r[i], j];
}
}
return X;
}