// Sčítání matic
private static SuperMatrix Add(SuperMatrix m1, SuperMatrix m2)
{
if (m1.rows != m2.rows || m1.cols != m2.cols) throw new MException("Matrices must have the same dimensions!");
SuperMatrix r = new SuperMatrix(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;
}
// Function solves Ax = v in confirmity with solution vector "v"
public SuperMatrix SolveWith(SuperMatrix v)
{
if (rows != cols) throw new MException("The matrix is not square!");
if (rows != v.rows) throw new MException("Wrong number of results in solution vector!");
if (L == null) MakeLU();
SuperMatrix b = new SuperMatrix(rows, 1);
for (int i = 0; i < rows; i++) b[i, 0] = v[pi[i], 0]; // switch two items in "v" due to permutation matrix
SuperMatrix z = SubsForth(L, b);
SuperMatrix x = SubsBack(U, z);
return x;
}
private static void ACopytoC(SuperMatrix A, int xa, int ya, SuperMatrix 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];
}
// Power matrix to exponent
public static SuperMatrix Power(SuperMatrix m, int pow)
{
if (pow == 0) return IdentityMatrix(m.rows, m.cols);
if (pow == 1) return m.Duplicate();
if (pow == -1) return m.Invert();
SuperMatrix x;
if (pow < 0) { x = m.Invert(); pow *= -1; }
else x = m.Duplicate();
SuperMatrix ret = IdentityMatrix(m.rows, m.cols);
while (pow != 0)
{
if ((pow & 1) == 1) ret *= x;
x *= x;
pow >>= 1;
}
return ret;
}
public void SetCol(SuperMatrix v, int k)
{
for (int i = 0; i < rows; i++) mat[i, k] = v[i, 0];
}
private static void SafeACopytoC(SuperMatrix A, int xa, int ya, SuperMatrix 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];
}
}
// Smart matrix multiplication
private static SuperMatrix StrassenMultiply(SuperMatrix A, SuperMatrix B)
{
if (A.cols != B.rows) throw new MException("Wrong dimension of matrix!");
SuperMatrix R;
int msize = Math.Max(Math.Max(A.rows, A.cols), Math.Max(B.rows, B.cols));
if (msize < 32)
{
R = ZeroMatrix(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;
SuperMatrix[,] mField = new SuperMatrix[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 SuperMatrix(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 SuperMatrix(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;
}
// Function generates the zero matrix
public static SuperMatrix ZeroMatrix(int iRows, int iCols)
{
SuperMatrix matrix = new SuperMatrix(iRows, iCols);
for (int i = 0; i < iRows; i++)
for (int j = 0; j < iCols; j++)
matrix[i, j] = 0;
return matrix;
}
// Function returns the copy of this matrix
public SuperMatrix Duplicate()
{
SuperMatrix matrix = new SuperMatrix(rows, cols);
for (int i = 0; i < rows; i++)
for (int j = 0; j < cols; j++)
matrix[i, j] = mat[i, j];
return matrix;
}
// Function solves Ax = b for A as a lower triangular matrix
public static SuperMatrix SubsForth(SuperMatrix A, SuperMatrix b)
{
if (A.L == null) A.MakeLU();
int n = A.rows;
SuperMatrix x = new SuperMatrix(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;
}
// Matrix transpose, for any rectangular matrix
public static SuperMatrix Transpose(SuperMatrix m)
{
SuperMatrix t = new SuperMatrix(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;
}
// Function solves Ax = b for A as an upper triangular matrix
public static SuperMatrix SubsBack(SuperMatrix A, SuperMatrix b)
{
if (A.L == null) A.MakeLU();
int n = A.rows;
SuperMatrix x = new SuperMatrix(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;
}
// Stupid matrix multiplication
public static SuperMatrix StupidMultiply(SuperMatrix m1, SuperMatrix m2)
{
if (m1.cols != m2.rows) throw new MException("Wrong dimensions of matrix!");
SuperMatrix result = ZeroMatrix(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;
}
// Function generates the random matrix
public static SuperMatrix RandomMatrix(int iRows, int iCols, int dispersion)
{
Random random = new Random();
SuperMatrix matrix = new SuperMatrix(iRows, iCols);
for (int i = 0; i < iRows; i++)
for (int j = 0; j < iCols; j++)
matrix[i, j] = random.Next(-dispersion, dispersion);
return matrix;
}
private static void AplusBintoC(SuperMatrix A, int xa, int ya, SuperMatrix B, int xb, int yb, SuperMatrix 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 SuperMatrix GetCol(int k)
{
SuperMatrix m = new SuperMatrix(rows, 1);
for (int i = 0; i < rows; i++) m[i, 0] = mat[i, k];
return m;
}
// Multiplication by constant n
private static SuperMatrix Multiply(double n, SuperMatrix m)
{
SuperMatrix r = new SuperMatrix(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;
}
// Function returns the inverted matrix
public SuperMatrix Invert()
{
if (L == null) MakeLU();
SuperMatrix inv = new SuperMatrix(rows, cols);
for (int i = 0; i < rows; i++)
{
SuperMatrix Ei = SuperMatrix.ZeroMatrix(rows, 1);
Ei[i, 0] = 1;
SuperMatrix col = SolveWith(Ei);
inv.SetCol(col, i);
}
return inv;
}
private static void SafeAplusBintoC(SuperMatrix A, int xa, int ya, SuperMatrix B, int xb, int yb, SuperMatrix 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];
}
}
// Function for LU decomposition
public void MakeLU()
{
addToLog("Starting LU Decomposition");
addToLog("Create L & U Matrices..");
if (!IsSquare()) throw new MException("The matrix is not square!");
L = IdentityMatrix(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 matrix is singular!");
pom1 = pi[k]; pi[k] = pi[k0]; pi[k0] = pom1; // switch two rows in permutation matrix
addToLog("Switching rows in A: "+k+" & "+k0);
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;
addToLog("Switching rows in U: " + k + " & " + k0);
}
for (int i = k + 1; i < rows; i++)
{
L[i, k] = U[i, k] / U[k, k];
addToLog("R:" + i + " C:" + 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];
addToLog("R:"+i+" C:"+j+" = "+U[i, j]+" - "+L[i, k]+" * "+U[k, j]);
}
}
}
}
// A * B into C, level of recursion, matrix field
// function for square matrix 2^N x 2^N
private static void StrassenMultiplyRun(SuperMatrix A, SuperMatrix B, SuperMatrix C, int l, SuperMatrix[,] f)
{
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];
}
// Function parses the matrix from string
public static SuperMatrix Parse(string ps)
{
string s = NormalizeMatrixString(ps);
string[] rows = Regex.Split(s, "\r\n");
string[] nums = rows[0].Split(' ');
SuperMatrix matrix = new SuperMatrix(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++) matrix[i, j] = double.Parse(nums[j]);
}
}
catch (FormatException exc) { throw new MException("Wrong input format!"); }
return matrix;
}
