public void SetCol(LUDecompositionCommons v, int k)
{
for (int i = 0; i < rows; i++)
{
mat[i, k] = v[i, 0];
}
}
public LUDecompositionCommons SolveWith(LUDecompositionCommons v) // Function solves Ax = v in confirmity with solution vector "v"
{
if (rows != cols)
{
throw new MException("The LUDecompositionCommons is not square!");
}
if (rows != v.rows)
{
throw new MException("Wrong number of results in solution vector!");
}
if (L == null)
{
MakeLU();
}
LUDecompositionCommons b = new LUDecompositionCommons(rows, 1);
for (int i = 0; i < rows; i++)
{
b[i, 0] = v[pi[i], 0]; // switch two items in "v" due to permutation LUDecompositionCommons
}
LUDecompositionCommons z = SubsForth(L, b);
LUDecompositionCommons x = SubsBack(U, z);
return(x);
}
private static void AminusBintoC(LUDecompositionCommons A, int xa, int ya, LUDecompositionCommons B, int xb, int yb, LUDecompositionCommons C, int size)
{
for (int i = 0; i < size; i++) // rows
{
for (int j = 0; j < size; j++)
{
C[i, j] = A[ya + i, xa + j] - B[yb + i, xb + j];
}
}
}
public static LUDecompositionCommons IdentityLUDecompositionCommons(int iRows, int iCols) // Function generates the identity LUDecompositionCommons
{
LUDecompositionCommons LUDecompositionCommons = ZeroLUDecompositionCommons(iRows, iCols);
for (int i = 0; i < Math.Min(iRows, iCols); i++)
{
LUDecompositionCommons[i, i] = 1;
}
return(LUDecompositionCommons);
}
private static void ACopytoC(LUDecompositionCommons A, int xa, int ya, LUDecompositionCommons C, int size)
{
for (int i = 0; i < size; i++) // rows
{
for (int j = 0; j < size; j++)
{
C[i, j] = A[ya + i, xa + j];
}
}
}
public LUDecompositionCommons GetCol(int k)
{
LUDecompositionCommons m = new LUDecompositionCommons(rows, 1);
for (int i = 0; i < rows; i++)
{
m[i, 0] = mat[i, k];
}
return(m);
}
public static LUDecompositionCommons Transpose(LUDecompositionCommons m) // LUDecompositionCommons transpose, for any rectangular LUDecompositionCommons
{
LUDecompositionCommons t = new LUDecompositionCommons(m.cols, m.rows);
for (int i = 0; i < m.rows; i++)
{
for (int j = 0; j < m.cols; j++)
{
t[j, i] = m[i, j];
}
}
return(t);
}
public static LUDecompositionCommons ZeroLUDecompositionCommons(int iRows, int iCols) // Function generates the zero LUDecompositionCommons
{
LUDecompositionCommons matrix = new LUDecompositionCommons(iRows, iCols);
for (int i = 0; i < iRows; i++)
{
for (int j = 0; j < iCols; j++)
{
matrix[i, j] = 0;
}
}
return(matrix);
}
public LUDecompositionCommons Duplicate() // Function returns the copy of this LUDecompositionCommons
{
LUDecompositionCommons LUDecompositionCommons = new LUDecompositionCommons(rows, cols);
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
LUDecompositionCommons[i, j] = mat[i, j];
}
}
return(LUDecompositionCommons);
}
private static LUDecompositionCommons Multiply(double n, LUDecompositionCommons m) // Multiplication by constant n
{
LUDecompositionCommons r = new LUDecompositionCommons(m.rows, m.cols);
for (int i = 0; i < m.rows; i++)
{
for (int j = 0; j < m.cols; j++)
{
r[i, j] = m[i, j] * n;
}
}
return(r);
}
public static LUDecompositionCommons RandomLUDecompositionCommons(int iRows, int iCols, int dispersion) // Function generates the random LUDecompositionCommons
{
Random random = new Random();
LUDecompositionCommons LUDecompositionCommons = new LUDecompositionCommons(iRows, iCols);
for (int i = 0; i < iRows; i++)
{
for (int j = 0; j < iCols; j++)
{
LUDecompositionCommons[i, j] = random.Next(-dispersion, dispersion);
}
}
return(LUDecompositionCommons);
}
private static void SafeACopytoC(LUDecompositionCommons A, int xa, int ya, LUDecompositionCommons C, int size)
{
for (int i = 0; i < size; i++) // rows
{
for (int j = 0; j < size; j++) // cols
{
C[i, j] = 0;
if (xa + j < A.cols && ya + i < A.rows)
{
C[i, j] += A[ya + i, xa + j];
}
}
}
}
public LUDecompositionCommons GetP() // Function returns permutation LUDecompositionCommons "P" due to permutation vector "pi"
{
if (L == null)
{
MakeLU();
}
LUDecompositionCommons LUDecompositionCommons = ZeroLUDecompositionCommons(rows, cols);
for (int i = 0; i < rows; i++)
{
LUDecompositionCommons[pi[i], i] = 1;
}
return(LUDecompositionCommons);
}
private static LUDecompositionCommons Add(LUDecompositionCommons m1, LUDecompositionCommons m2) // Sčítání matic
{
if (m1.rows != m2.rows || m1.cols != m2.cols)
{
throw new MException("Matrices must have the same dimensions!");
}
LUDecompositionCommons r = new LUDecompositionCommons(m1.rows, m1.cols);
for (int i = 0; i < r.rows; i++)
{
for (int j = 0; j < r.cols; j++)
{
r[i, j] = m1[i, j] + m2[i, j];
}
}
return(r);
}
public LUDecompositionCommons Invert() // Function returns the inverted LUDecompositionCommons
{
if (L == null)
{
MakeLU();
}
LUDecompositionCommons inv = new LUDecompositionCommons(rows, cols);
for (int i = 0; i < rows; i++)
{
LUDecompositionCommons Ei = LUDecompositionCommons.ZeroLUDecompositionCommons(rows, 1);
Ei[i, 0] = 1;
LUDecompositionCommons col = SolveWith(Ei);
inv.SetCol(col, i);
}
return(inv);
}
private static void SafeAminusBintoC(LUDecompositionCommons A, int xa, int ya, LUDecompositionCommons B, int xb, int yb, LUDecompositionCommons C, int size)
{
for (int i = 0; i < size; i++) // rows
{
for (int j = 0; j < size; j++) // cols
{
C[i, j] = 0;
if (xa + j < A.cols && ya + i < A.rows)
{
C[i, j] += A[ya + i, xa + j];
}
if (xb + j < B.cols && yb + i < B.rows)
{
C[i, j] -= B[yb + i, xb + j];
}
}
}
}
public static LUDecompositionCommons SubsForth(LUDecompositionCommons A, LUDecompositionCommons b) // Function solves Ax = b for A as a lower triangular LUDecompositionCommons
{
if (A.L == null)
{
A.MakeLU();
}
int n = A.rows;
LUDecompositionCommons x = new LUDecompositionCommons(n, 1);
for (int i = 0; i < n; i++)
{
x[i, 0] = b[i, 0];
for (int j = 0; j < i; j++)
{
x[i, 0] -= A[i, j] * x[j, 0];
}
x[i, 0] = x[i, 0] / A[i, i];
}
return(x);
}
public static LUDecompositionCommons SubsBack(LUDecompositionCommons A, LUDecompositionCommons b) // Function solves Ax = b for A as an upper triangular LUDecompositionCommons
{
if (A.L == null)
{
A.MakeLU();
}
int n = A.rows;
LUDecompositionCommons x = new LUDecompositionCommons(n, 1);
for (int i = n - 1; i > -1; i--)
{
x[i, 0] = b[i, 0];
for (int j = n - 1; j > i; j--)
{
x[i, 0] -= A[i, j] * x[j, 0];
}
x[i, 0] = x[i, 0] / A[i, i];
}
return(x);
}
public static LUDecompositionCommons StupidMultiply(LUDecompositionCommons m1, LUDecompositionCommons m2) // Stupid LUDecompositionCommons multiplication
{
if (m1.cols != m2.rows)
{
throw new MException("Wrong dimensions of LUDecompositionCommons!");
}
LUDecompositionCommons result = ZeroLUDecompositionCommons(m1.rows, m2.cols);
for (int i = 0; i < result.rows; i++)
{
for (int j = 0; j < result.cols; j++)
{
for (int k = 0; k < m1.cols; k++)
{
result[i, j] += m1[i, k] * m2[k, j];
}
}
}
return(result);
}
public static LUDecompositionCommons Parse(string ps) // Function parses the LUDecompositionCommons from string
{
string s = NormalizeLUDecompositionCommonsString(ps);
string[] rows = Regex.Split(s, "\r\n");
string[] nums = rows[0].Split(' ');
LUDecompositionCommons LUDecompositionCommons = new LUDecompositionCommons(rows.Length, nums.Length);
try
{
for (int i = 0; i < rows.Length; i++)
{
nums = rows[i].Split(' ');
for (int j = 0; j < nums.Length; j++)
{
LUDecompositionCommons[i, j] = double.Parse(nums[j]);
}
}
}
catch (FormatException exc) { throw new MException("Wrong input format!"); }
return(LUDecompositionCommons);
}
public static LUDecompositionCommons Power(LUDecompositionCommons m, int pow) // Power LUDecompositionCommons to exponent
{
if (pow == 0)
{
return(IdentityLUDecompositionCommons(m.rows, m.cols));
}
if (pow == 1)
{
return(m.Duplicate());
}
if (pow == -1)
{
return(m.Invert());
}
LUDecompositionCommons x;
if (pow < 0)
{
x = m.Invert(); pow *= -1;
}
else
{
x = m.Duplicate();
}
LUDecompositionCommons ret = IdentityLUDecompositionCommons(m.rows, m.cols);
while (pow != 0)
{
if ((pow & 1) == 1)
{
ret *= x;
}
x *= x;
pow >>= 1;
}
return(ret);
}
public static LUDecompositionCommons operator *(double n, LUDecompositionCommons m)
{
return(LUDecompositionCommons.Multiply(n, m));
}
public static LUDecompositionCommons operator *(LUDecompositionCommons m1, LUDecompositionCommons m2)
{
return(LUDecompositionCommons.StrassenMultiply(m1, m2));
}
public static LUDecompositionCommons operator -(LUDecompositionCommons m1, LUDecompositionCommons m2)
{
return(LUDecompositionCommons.Add(m1, -m2));
}
// O P E R A T O R S
public static LUDecompositionCommons operator -(LUDecompositionCommons m)
{
return(LUDecompositionCommons.Multiply(-1, m));
}
// function for square LUDecompositionCommons 2^N x 2^N
private static void StrassenMultiplyRun(LUDecompositionCommons A, LUDecompositionCommons B, LUDecompositionCommons C, int l, LUDecompositionCommons[,] f) // A * B into C, level of recursion, LUDecompositionCommons field
{
int size = A.rows;
int h = size / 2;
if (size < 32)
{
for (int i = 0; i < C.rows; i++)
{
for (int j = 0; j < C.cols; j++)
{
C[i, j] = 0;
for (int k = 0; k < A.cols; k++)
{
C[i, j] += A[i, k] * B[k, j];
}
}
}
return;
}
AplusBintoC(A, 0, 0, A, h, h, f[l, 0], h);
AplusBintoC(B, 0, 0, B, h, h, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 1], l + 1, f); // (A11 + A22) * (B11 + B22);
AplusBintoC(A, 0, h, A, h, h, f[l, 0], h);
ACopytoC(B, 0, 0, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 2], l + 1, f); // (A21 + A22) * B11;
ACopytoC(A, 0, 0, f[l, 0], h);
AminusBintoC(B, h, 0, B, h, h, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 3], l + 1, f); //A11 * (B12 - B22);
ACopytoC(A, h, h, f[l, 0], h);
AminusBintoC(B, 0, h, B, 0, 0, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 4], l + 1, f); //A22 * (B21 - B11);
AplusBintoC(A, 0, 0, A, h, 0, f[l, 0], h);
ACopytoC(B, h, h, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 5], l + 1, f); //(A11 + A12) * B22;
AminusBintoC(A, 0, h, A, 0, 0, f[l, 0], h);
AplusBintoC(B, 0, 0, B, h, 0, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 6], l + 1, f); //(A21 - A11) * (B11 + B12);
AminusBintoC(A, h, 0, A, h, h, f[l, 0], h);
AplusBintoC(B, 0, h, B, h, h, f[l, 1], h);
StrassenMultiplyRun(f[l, 0], f[l, 1], f[l, 1 + 7], l + 1, f); // (A12 - A22) * (B21 + B22);
/// C11
for (int i = 0; i < h; i++) // rows
{
for (int j = 0; j < h; j++) // cols
{
C[i, j] = f[l, 1 + 1][i, j] + f[l, 1 + 4][i, j] - f[l, 1 + 5][i, j] + f[l, 1 + 7][i, j];
}
}
/// C12
for (int i = 0; i < h; i++) // rows
{
for (int j = h; j < size; j++) // cols
{
C[i, j] = f[l, 1 + 3][i, j - h] + f[l, 1 + 5][i, j - h];
}
}
/// C21
for (int i = h; i < size; i++) // rows
{
for (int j = 0; j < h; j++) // cols
{
C[i, j] = f[l, 1 + 2][i - h, j] + f[l, 1 + 4][i - h, j];
}
}
/// C22
for (int i = h; i < size; i++) // rows
{
for (int j = h; j < size; j++) // cols
{
C[i, j] = f[l, 1 + 1][i - h, j - h] - f[l, 1 + 2][i - h, j - h] + f[l, 1 + 3][i - h, j - h] + f[l, 1 + 6][i - h, j - h];
}
}
}
public void MakeLU() // Function for LU decomposition
{
if (!IsSquare())
{
throw new MException("The LUDecompositionCommons is not square!");
}
L = IdentityLUDecompositionCommons(rows, cols);
U = Duplicate();
pi = new int[rows];
for (int i = 0; i < rows; i++)
{
pi[i] = i;
}
double p = 0;
double pom2;
int k0 = 0;
int pom1 = 0;
for (int k = 0; k < cols - 1; k++)
{
p = 0;
for (int i = k; i < rows; i++) // find the row with the biggest pivot
{
if (Math.Abs(U[i, k]) > p)
{
p = Math.Abs(U[i, k]);
k0 = i;
}
}
if (p == 0) // samé nuly ve sloupci
{
throw new MException("The LUDecompositionCommons is singular!");
}
pom1 = pi[k]; pi[k] = pi[k0]; pi[k0] = pom1; // switch two rows in permutation LUDecompositionCommons
for (int i = 0; i < k; i++)
{
pom2 = L[k, i]; L[k, i] = L[k0, i]; L[k0, i] = pom2;
}
if (k != k0)
{
detOfP *= -1;
}
for (int i = 0; i < cols; i++) // Switch rows in U
{
pom2 = U[k, i]; U[k, i] = U[k0, i]; U[k0, i] = pom2;
}
for (int i = k + 1; i < rows; i++)
{
L[i, k] = U[i, k] / U[k, k];
for (int j = k; j < cols; j++)
{
U[i, j] = U[i, j] - L[i, k] * U[k, j];
}
}
}
}
private static LUDecompositionCommons StrassenMultiply(LUDecompositionCommons A, LUDecompositionCommons B) // Smart LUDecompositionCommons multiplication
{
if (A.cols != B.rows)
{
throw new MException("Wrong dimension of LUDecompositionCommons!");
}
LUDecompositionCommons R;
int msize = Math.Max(Math.Max(A.rows, A.cols), Math.Max(B.rows, B.cols));
if (msize < 32)
{
R = ZeroLUDecompositionCommons(A.rows, B.cols);
for (int i = 0; i < R.rows; i++)
{
for (int j = 0; j < R.cols; j++)
{
for (int k = 0; k < A.cols; k++)
{
R[i, j] += A[i, k] * B[k, j];
}
}
}
return(R);
}
int size = 1; int n = 0;
while (msize > size)
{
size *= 2; n++;
}
;
int h = size / 2;
LUDecompositionCommons[,] mField = new LUDecompositionCommons[n, 9];
/*
* 8x8, 8x8, 8x8, ...
* 4x4, 4x4, 4x4, ...
* 2x2, 2x2, 2x2, ...
* . . .
*/
int z;
for (int i = 0; i < n - 4; i++) // rows
{
z = (int)Math.Pow(2, n - i - 1);
for (int j = 0; j < 9; j++)
{
mField[i, j] = new LUDecompositionCommons(z, z);
}
}
SafeAplusBintoC(A, 0, 0, A, h, h, mField[0, 0], h);
SafeAplusBintoC(B, 0, 0, B, h, h, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 1], 1, mField); // (A11 + A22) * (B11 + B22);
SafeAplusBintoC(A, 0, h, A, h, h, mField[0, 0], h);
SafeACopytoC(B, 0, 0, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 2], 1, mField); // (A21 + A22) * B11;
SafeACopytoC(A, 0, 0, mField[0, 0], h);
SafeAminusBintoC(B, h, 0, B, h, h, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 3], 1, mField); //A11 * (B12 - B22);
SafeACopytoC(A, h, h, mField[0, 0], h);
SafeAminusBintoC(B, 0, h, B, 0, 0, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 4], 1, mField); //A22 * (B21 - B11);
SafeAplusBintoC(A, 0, 0, A, h, 0, mField[0, 0], h);
SafeACopytoC(B, h, h, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 5], 1, mField); //(A11 + A12) * B22;
SafeAminusBintoC(A, 0, h, A, 0, 0, mField[0, 0], h);
SafeAplusBintoC(B, 0, 0, B, h, 0, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 6], 1, mField); //(A21 - A11) * (B11 + B12);
SafeAminusBintoC(A, h, 0, A, h, h, mField[0, 0], h);
SafeAplusBintoC(B, 0, h, B, h, h, mField[0, 1], h);
StrassenMultiplyRun(mField[0, 0], mField[0, 1], mField[0, 1 + 7], 1, mField); // (A12 - A22) * (B21 + B22);
R = new LUDecompositionCommons(A.rows, B.cols); // result
/// C11
for (int i = 0; i < Math.Min(h, R.rows); i++) // rows
{
for (int j = 0; j < Math.Min(h, R.cols); j++) // cols
{
R[i, j] = mField[0, 1 + 1][i, j] + mField[0, 1 + 4][i, j] - mField[0, 1 + 5][i, j] + mField[0, 1 + 7][i, j];
}
}
/// C12
for (int i = 0; i < Math.Min(h, R.rows); i++) // rows
{
for (int j = h; j < Math.Min(2 * h, R.cols); j++) // cols
{
R[i, j] = mField[0, 1 + 3][i, j - h] + mField[0, 1 + 5][i, j - h];
}
}
/// C21
for (int i = h; i < Math.Min(2 * h, R.rows); i++) // rows
{
for (int j = 0; j < Math.Min(h, R.cols); j++) // cols
{
R[i, j] = mField[0, 1 + 2][i - h, j] + mField[0, 1 + 4][i - h, j];
}
}
/// C22
for (int i = h; i < Math.Min(2 * h, R.rows); i++) // rows
{
for (int j = h; j < Math.Min(2 * h, R.cols); j++) // cols
{
R[i, j] = mField[0, 1 + 1][i - h, j - h] - mField[0, 1 + 2][i - h, j - h] + mField[0, 1 + 3][i - h, j - h] + mField[0, 1 + 6][i - h, j - h];
}
}
return(R);
}
