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); }