public static CellArray Multiply(CellArray A, CellArray B)
{
if (!CellArray.IsMatrix(A) || !CellArray.IsMatrix(B))
{
throw new Exception("Both A and B must be matrixes");
}
int A_Rows = A.Count, B_Rows = B.Count;
int A_Cols = CellArray.ColumnCount(A), B_Cols = CellArray.ColumnCount(B);
if (A_Cols != B_Rows)
{
throw new Exception(string.Format("Dimension mismatch A {0}:{1} B {2}:{3}", A_Rows, A_Cols, B_Rows, B_Cols));
}
CellArray C = CellArray.Matrix(A_Rows, B_Cols);
// Main Loop //
for (int i = 0; i < A_Rows; i++)
{
// Sub Loop One //
for (int j = 0; j < B_Cols; j++)
{
// Sub Loop Two //
for (int k = 0; k < A_Cols; k++)
{
C[i].valueARRAY[j] = (C[i].valueARRAY[j].IsNull ? A[i].valueARRAY[k] * B[k].valueARRAY[j] : A[i].valueARRAY[k] * B[k].valueARRAY[j] + C[i].valueARRAY[j]);
}
}
}
// Return C //
return(C);
}
public CellArray solve(CellArray B)
{
if (B.Count != 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 = CellArray.ColumnCount(B);
CellArray 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].ARRAY[j] -= X[k].ARRAY[j] * LU[i].ARRAY[k];
}
}
}
// Solve U*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < nx; j++)
{
X[k].ARRAY[j] /= LU[k].ARRAY[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i].ARRAY[j] -= X[k].ARRAY[j] * LU[i].ARRAY[k];
}
}
}
return(X);
}
public static Cell Determinant(CellArray A)
{
if (!CellArray.IsMatrix(A))
{
throw new Exception("A must be a matrix");
}
int A_Rows = A.Count;
int A_Cols = CellArray.ColumnCount(A);
if (A_Rows != A_Cols)
{
throw new Exception(string.Format("Matrix must be square {0}:{1}", A_Rows, A_Cols));
}
LUDecomposition engine = new LUDecomposition(A);
return(engine.det());
}
public static CellArray Inverse(CellArray A)
{
if (!CellArray.IsMatrix(A))
{
throw new Exception("A must be a matrix");
}
int A_Rows = A.Count;
int A_Cols = CellArray.ColumnCount(A);
if (A_Rows != A_Cols)
{
throw new Exception(string.Format("Matrix must be square {0}:{1}", A_Rows, A_Cols));
}
LUDecomposition engine = new LUDecomposition(A);
CellArray B = CellArray.Identity(A_Rows);
return(engine.solve(B));
}
